A study of the thermal and physical properties and heat transfer coefficients of sulphate paper mill black liquor.

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A study of the thermal and physical properties and heat transfer coefficients of sulphate paper mill black liquor.
Harvin, R. L ( Richard L. ), 1922-
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141 leaves. : ; 28 cm.


Subjects / Keywords:
Free convection ( jstor )
Heat transfer ( jstor )
Liquids ( jstor )
Specific heat ( jstor )
Steam ( jstor )
Surface temperature ( jstor )
Temperature gradients ( jstor )
Thermal conductivity ( jstor )
Thermocouples ( jstor )
Viscosity ( jstor )
Heat -- Transmission ( lcsh )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Thesis (Ph. D.)--University of Florida, 1955.
Bibliography: leaves 138-140.
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Manuscript copy.
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Statement of Responsibility:
by Richard L. Harvin.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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000549599 ( ALEPH )
ACX3894 ( NOTIS )
13231799 ( OCLC )


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A STUDY OF THE THERMAL AND PHYSICAL PROPERTIES AND HEAT TRANSFER COEFFICIENTS OF SULPHATE PAPER MILL BLACK LIQUOR RICHARD L. HARVIN A Dissertation Presented to the Graduate Council of The University of Florida In Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy UNIVERSITY OF FLORIDA JANUARY, 1955


ACKNCWLEDGEMENT I wish to acknowledge the helpful assistance of my supervisory committee chairman. Dr. W. F. Brovm, and the other members of the committee. Dr. M. Tyner, Dr. H. E. Schweyer, Dr. H. A. Meyer and Dr. A. C. Klelnschmidt for their help and patient use of their time. The writer is grateful to Dr. W. H. Beisler, Head of the Chemical Engineering Departinent, for his part in making this study possible. Thanks are also due Dr. W. J. Nolan for helpful suggestions and comments throughout the course of this work. ii


TABLE OF CONTENTS Page ACK>;aiJLEDGEKEMT ii LIST OF ILLUSTRATICNS V LIST OF TABLES vii LIST OF SYMBOLS viii Chapter I. ITJTRODUCTION 1 II. HEAT TR.WSFER INVESTIGATIONS AND RESULTS 5 A. Theoretical E. Apparatus C. Experireents.l Procedure D. Data E. Sample Calculations F. Calculated Results G. Analysis of Results III. SPECIP'IC HEAT 66 A. Background 3. Apparatus C. Derivation of Equations D. Experimental Procedure E. Data F. Sample Calculations G. Calculated Results and Discussion IV. THE31MAL CONDUCTIVITY INVESTIGATIONS AND RP^SULTS .8'+ A. Background B 5 Apparatus C. Derivation of Eqxiations D. Experimental Procedure E. Data F. Sample Calculations G. Calculated Results and Discussion iii


Chapter Page V. VISCOSITY 105 A. Background B. Apparatus and Procedxxre C. Calculated Results and Discussion VI. SPECIFIC GRAVITY II3 A. Apparatus and Procedure E. Data and Calculated Results VII. INTERRELATION OF THERMAL j»JTD PHYSICAL PROPERTIES AND THE HEAT TRANSFER COEFFICIENTS 11? VIII. CONCLUSIONS I35 BIBLIOGRAPHY I38 APPENDIX lZ+1 BIOGRAPHICAL ITEMS ik^ iv


LIST OF ILLUSTRATIONS Figure Page 1. Heat Transfer Apparatus 11 2. Heat Transfer Apparatus 12 3. Diagramatlc Layout of Heat Transfer Apparatus ... 13 4. Thermocouple Installation in Heat Transfer Tube . . 15 5. Heat Transfer Tube— Inlet End l6 6. Heat Transfer Tube— Outlet End 17 7. Cross Section of Heat Transfer Tube ^3 8. Temperature Variation in Heat Transfer Tube .... ^5 9. Assembled Specific Heat Apparatus 68 10. Cross Section of Specific Heat i^paratus 69 11. Heating and Cooling Curves for Specific Heat Determination 73 12. Specific Heat versus Per Cent Solids 79 13. Ncxtiograph for Specific Heat 83 lU. Assembled Thermal Conductivity Apparatus 88 15. Thermal Conductivity Apparatus out of Insulated Container 89 16. Diagramatic View of the Thermal Conductivity Apparatus 90 17. Details of Thermal Conductivity Apparatus 92 18. Thermal Conductivity versus Per Cent Solids .... 101 V


Figure Page 19. Thermal Conductivity versus Per Cent Solids . . . I03 20. Nomograph for Thennal Conductivity 104 21. Viscosity versus Temperature 110 22. Ncsnograph for Viscosity 112 23. Specific Gravity versus Per Cent Solids 116 2^^. J Factor versus Reynolds Number 123 25 • j /(^ versus Reynolds Number (Sieder and Tate Natural Convection Factor) 12? 26. i /<^ versus Reynolds Number (Kern and Othmer Natural Convection Factor) 128 27. j /(p versus Rej7iolds Number (Eubank and Proctor Natural Convection Factor). 129 23. j /(|) versus Reynolds Number (Natural Convection Factor of Equation 50) I33 29. Thennal Conductivity of Water 142 30. Viscosity of Water 143 31. Sample Data and Work Sheet 144 yi


LIST OF TABLES Table Page 1. General Information on Fluid Systems 28 2. Experimental Heat Transfer Data 29 3. Calculated Heat Transfer Data 53 4. Experimental Specific Keat Data 75 5. Calculated Specific Heat Data 78 6. ExjJerimental and Calculated Thermal Conductivity Data 99 7. Experimental and Calculated Viscosity Data. . 109 8. Specific Gravity Data llij. 9. Heat Transfer j Factors— Reynolds Number Above 3000 118 10. Heat Transfer j Factors — Reynolds Number Below 3000 120 il


LIST OF SYMBOLS A Area Sq. ft. C Weight Fraction i Cp Specific Heat BTU/(Lb.)(°F.) D Diameter Ft. d Pipe Wall Thickness Ft. G Mass Velocity Lbs./(Hr.)(Sq. ] rt.) g Acceleration of GravityFt./(Hr2) . Hl Heat Loss BTU/Kin. h Film Heat Transfer Coefficient BTU/(Hr.)(Sa.ft .)(°F.) k Thermal ConductivityETU/(Hr.)(Sa.ft .)(^./ft.) L Length Ft. Q. q Quantity of Heat BTU r Radius Ft. S Cross Sectional Area Sq. ft. s Specific Gravity T, t Temperature ^. U Overall Heat Transfer Coefficient BTU/(Hr.)(Sq.ft .)(°F.) W Mass Rate of Flow Lbs./Hr. X Thickness of Liquid Layer Ft. Subscripts b Bulk f Film 1 Lower m Mean • o Outside s Surface u Upper w Wall ureeK /3 (Beta) Coefficient of Cubic Expansion % Sxpansion/^F. A (Delta) Finite Difference >t (Mu) Viscosity Lbs./(Hr.)(Ft.) /? (Rho) Density Lbs,/Ft3 (t> (Phi) Natural Convection Term e (Theta) TL-ne Hr.


CHAPTER I INTRGDDCTIOI^ This dissertation is concerned with the transfer of heat from a tube wall to a stream of moving sulphate black liquor, the determination of the physical properties pertaining thereto, the calculation of the film heat transfer coefficients prevailing at various conditions, and the interrelation of said physical properties and film coefficients. The general subject of heat transmission is one that has received considerable treatment in the literature. It vjas in 1798 that Count Rumford (26) first gave an account of his experiments on "An Inquiry Concerning the Source of Heat v/hicVi is Excited by Friction" and this paper may be regarded as marking the commencement of the study of heat as molecular kinetic energy. Yet today the problems remain so countless and the complexities so great that heat transmission continues to capture the thought and imagination of research workers. The study undertaken involves principally the process of heat transfer to a fluid moving inside a tubular heat exchanger and the mechanism is, therefore, primarily one of convection. Throughout the long history of this subject the knowledge and vmderstanding of the convection heat transfer mechanism has advanced steadily but has never shown any period of phenominal growth comparable with, say, the recent 1


2 expansion of the nuclear energy field. Jakob (13) pointed out that the study of heat transfer phenomena has never been brilliantly fashionable due to the slow cumbersome flow of heat and the difficulty of restraining the flow along well defined channels as compared with, for example, electricity. Consequently experimentalists in search of academic distinction have tended to avoid this subject as unwieldy and vmprofitable. On the other hand the steady advance of industry and the need by engineers of sound design methods has demanded a continued effort toward improvement in our methods of handling heat transmission. Early contributors such as Reynolds (25) and later Prandtl (24) and Nusselt (21) did much toward developing the basic concepts of heat flov/ and established powerful methods of correlation. However, it has been due to efforts of engineers of rather recent years that through semiempirical methods the basic correlations have been developed into reliable relations suitable for use with a wide variety of materials. All such relations involve the use of dimensionless moduli making possible correlation of data from various investigators without regard to the units employed in the work. The variables which by reasoning may be expected to have influence on the transfer of heat by convection may be classified as follows : A. Fixed variables (characteristics of the apparatus). Length of heat exchange tube, L; and inside diameter of The word "correlation" is used to mean an interrelation between variables, and does not have the usual statistical connotations.


3 tube, D. B. Independent variables (operating conditions). Mass rate of flow, W; inlet fluid tenperatiu'e , T, ; and the temperature of the heating medium, t .. The choice of the st fluid to be heated is another independent variable of primary importance. However, at a particular temperature it is characterized by its thermal and physical properties and enters into the relationships only in this way. C. Dependent variables. Temperature increase of fluid (duty), AT; driving force temperatur-e difference. At; constant pressure specific heat, Cp; viscosity, yW ; thermal conductivity, k; coefficient of cubic expansion, yS ; density, /O; and film heat transfer coefficient, h. Other variables and constants enter into the calculation of the above variables but do not have a direct bearing on the convection process. In the design of heat exchange equipment it is neces'jary to have knowledge of all variables in order to have confidence in the result. This presupposes that adequate thermal and physical data are available on the system under study. Such was not found to be the case in regard to sulphate black liquor and this was a primary reason for its selection for study in this work. A thorough study of the literature revealed only a limited amount of data on sulphate black liquor and some of this was in conflict. The general problem was divided into two parts; (l) the heat


transfer study consisting of operating suitable heat transfer apparatus usin^ liquors of various concentrations to measure the film heat transfer coefficients, and (2) a thorough study of the physical properties of black liquor. The final correlation of all properties and measxirements according to the most proven methods serves a twofold purpose. It demonstrates the reliability of the methods as well as the consistency of the data.


CHAPTBR II HEAT TRANSFER INVESTIGATIONS AND RESULTS A. Theoretical This dissertation will not attempt to review the history of the development of the basic dimensionless groups. Neither will it treat the early correlations which now have been superseded by improvements made possible by an ever mounting voliime of data collected using refined experLmental techniques. Exhaustive discussions on this subject are to be found in all of the standard texts (5, 13, 1^^, 19). Through the application of dimensional analysis it has been shown that the variables are logically grouped into four dimensionless numbers or moduli. Thus, the Reynolds number. Re = — , the Prandtl /^ number, Pr = y . the Stanton number, St = — — , and the Grashof number, Gr = 2^£^£A!L, The Interrelation of all the variables concerned would result in mathematical relations of considerable complexity were It not for the use of the dimensionless groups presented above. Thus, a perfectly general equation between the variables in convection can be written in the form: St » F (Pr Re Gr) (l) where F is an undetermined function. By the methods of dimensions the general relation between all the variables has been reduced to one with 5


6 only four variables. There is a distinct difference between the mechanism of heat transfer for fluids flowing in turbiilent motion on one hand and streamline motion on the other. Consequently, certain factors, notably average velocity of the fluid past the heattransfer surface, in general have a more marked effect upon the rate of heat transmission for fluids flowing in turbulent motion than in streamline motion. Other factors, such as tube length, often have greater importance for streamline motion than for turbulent flow. Hence, these two cases are treated separately, first consideration being given the more common turbulent flow. The general equation for convection heat transfer (l) may be simplified for the case of turbulent flow by eliminating the Grashof number, Gr, since this factor accounts only for that contribution due to heat flow by natural convection. In most instances of forced convection the "forced" current is many times more intense than the natural circulation. Thus, the equation for heat flow becomes, St = f (Pr Re) (2) where the functions must be determined experimentally, Colburn (6) determined these functions wherein all physical properties, except Cp in the Stanton number, are evaluated at the film temperature, which is taken as the average of the bulk mean temperature of the fluid and the mean temperatiire of the heat transfer surface. Thus, J » (St) (Pr)°*^^'^ . 0.023 (Re);°-^ (3) t^ + tg where t^ = — and j is a dimensionless group related to the


7 Stanton and Reynolds numbers. The properties in this equation were evaluated at the film temperature in order to effectively take into account the conditions in the viscous layer which offers the major resistance to heat flow. In fluids with large temperature coefficients of viscosity a somewhat more convenient method of including the radial variation in viscosity due to temperature gradients was also suggested by Colbum (6) but was later modified by Sieder and Tate (30)« This method added another dimensionless group which was the ratio of viscosity at the bulk stream temperature to the viscosity at the pipe wall or surface temperature. Thus Sieder and Tate were able to correlate a wide variety of data at Reynolds nvirabers greater than 10000, using their equation which is presented here in a form similar to equation (3)» i' . (St) CPr)"-^*'' {ji) "•'* = C.027 (R«)-°-' M All properties of the fluid are detennined at the convenient bulk stream temperature, except the viscosity at the wall surface temperature. This equation was used as a basis for interrelation of the heat transfer data in this work for Reynolds numbers in excess of 10000 where turbulent flow is well developed. Viscous or laminar flow is usually found at Reynolds numbers less than 21C0 but may also exist up to values of 3OOO in cases of undisturbed flow. In such systems Graetz (lo) showed that the ratio of the temperatiire rise produced in the liquid to the temperatttre difference between the fluid at the entrance and the wall was partially


dependent on the ratio of tube diameter to heated length. Longer tubes, other things being equal, are less effective at transferring heat to laminar liquids than short ones because longer tubes permit more time for the building up of temperature gradients vhich oppose heat transfer. In turbulent flow, the rapid mixing prevents this build-up. Thus, the ratio — is significant in viscous flow and must be included. Colburn (6) derived the expression, i ' (St) (Pr)5-*«7 , 1., (,,,-0.667 ^Sj°-333 ^^)^-333 ^^j wherein most of the properties are determined at the film temperature, Sieder and Tate (30) put this equation into a more convenient form by using the bulk temperature for evaluation of the properties and their viscosity correction term. Their equation as recomiriended by McAdams (19) was. y (St) (p.)^-^^ {^f-'' . i.a6

9 investigators have corabined a function of the Qrashof number with the equations for forced convection in the viscous region. Sieder and Tate (30) proposed that for values of Grashof ntsabers exceeding 25OOO a correction for free convection may be obtained by multiplying the values of "h" from equation (6) by the term (p = 0.8 (1 + C.OI5 Or^'^^^) where the terras are evaluated, using, the b\ilk stream temperature. Equation (6) becomes. Where (p = 0.8 (1 + O.OI5 Gr*^'^^^) (7) Kern and Othmer (I5) found that closer agreement of data from a wide range of pipe diameters could be obtained by defining a free convection factor which was a function of the Reynolds number as well as the Grashof number. By empirical means they arrived at a correction factor 6 . = £ '23 (1 •»• 0.010 Gr )^ Applying this factor to equation log Re (6) tere results, J-= ^ = 1.86(Rer^'^7^£f-^^^ (8) where <*' = 2.25 (1 ^ 0.010 Gr''^^-'^) ~ log Re Eubank and Proctor (9) critically surveyed the available data for viscous flow in horizontal tubes and arrived at a "tentative" empirical equation of a form considerably different from those presented previously. This was,


10 (Nu) o hD The term Nu is the Nusselt number and is equal to ~. The Nusselt k number is also equal to the product of the Stanton, Reynolds and Prandtl numbers. The term Gz is the Graetz number, which is equal to --^. This number is also equal to the product of the Reynolds and Prandtl ntanbers, and the ratio of £ and a constant. H. L k This dissertation vrill utilize the equations (6), (?), (5), and (9) as bases for correlation of the heat transfer data in the viscous region. B, Apparatus The design of the heat transfer apparatus was formulated by consideration of the designs of other investigators (5, 15, 30). The over-all ap;->aratus is sho\m in Figures 1 and 2 by photographs and in Figure 3 by a schematic diagram. It consisted essentially of (l) a heat transfer section, (2) a flow-straightening section, (3) a mixing chamber, (4) a fluid cooler, (5) a discharge measirring tank and scale, (6) a return pump, (7) a storage and preheating tank, (8) a circulating pump, (9) a preheating section, (lO) a steam pressure reducing and regulating system (ll) a vacuum system, (12) a potentiometer with its auxiliary equipment and (I3) the necessary piping, valves, fittings and gauges. The construction and function of each of these principal components will be discussed in detail below. The heat transfer section was mounted horizontally and consisted


I u u e n c n)


5 U U




Ik of two parts. The inner tube waia section of Type 30i^ stainless seamless tubing having an inside diameter of O.5I inches and an outside diameter of O.75 inches. This was surrounded by a steam jacket consisting of nominal 3 inch galvanized iron pipe. Eight copperconstantan thermocouples of No. 30 gauge wire in a fiberglass duplex cable were buried in the stainless steel wall and their leads were brought out through four equally spaced packing glands in the steam Jacket wall. The thermocouples were located in grooves milled longitudinally along the top of the tube. The grooves were -i_ of an inch 1 ^^ deep and __ of an inch wide and 2 1 inches in length. The thermocouple 16 2 junction was placed at the bottom of the groove at the end nearest the fluid inlet and the insulated leads extended through the groove emerging from the other end. The entire groove was filled by peening in a strip of soft solder and the surface was made smooth by filing away the excess solder followed by a fine emory cloth. The thermocouple leads were, thus, located in the pipe wall for at least 2 inches dowm stream from the point of measurement and another 5 or 6 inches of the leads remained in the steam space until they finally emerged from the packing glands in the wall of the steam jacket. Figure 4 shows an enlarged view of one ' themccouple groove with the thermocouple mounted as described above and emerging from one of four thermocouple packing glands. Two additional thermocoiiples passed through the packing glands into the annulus section and were used to measure the steam temperature at the two ends* The details of the construction of the ends of the heat exchanger are shown in Figures 5 and 6, The heated length of the tube was 6 feet


15 Leads to Potentiometer Rubber Stopper Figure 4 Thermocouple Installation in Heat Exchanger Tube






18 and the design of the end flanges was intended to prevent additional heat transfer surface beyond the prescribed heated section. This was acccMiiplished at the inlet end (Figure 5) by minimizing the metal to metal contact between the tube and the flanpie. At the outlet end the cross section of the tube was reduced by turning down the outside diameter to O.56 inches in an effort to minimize conduction of heat along the tube. The thermocouples were mounted at distances fron the inlet of U.5, 13.5, 22.5, 3I.5, ^0.5, ^^9*5, 58.5. and 67.5 inches or k,5 inches from each end and every 9.0 inches in between. The stainless steel heat exchange tube extended beyond the heated section at the inlet end for a distance of 18 inches and served as a straightening section for the flowing liquid. A standard jinch "tee" was attached to the end of the stainless steel tube as shown in Figure 5. A packing gland was provided at this point for the thermocouple tube for measuring the fluid inlet temperature. The thermocouple tube was made of a section of — inch brass tubing fitted with small 32 spacing struts to insure a central position. This entire' assembly was given a nickle coating to prevent corrosion by the black liquor. At the outlet end the fluid stream passed through a mixing chamber and thence past a short thermocouple tube which measured the fluid outlet temperature (Figure 6). The fluid then reversed its flow in the concentric annulus and finally left the heat exchanger via standard piping. The flow arrangement thus prevented heat loss from the mixing chamber prior to the temperature measurement. The entire apparatus, straightening section, heat exchange section and mixing


19 chamber were insulated with standard thickness, 85 per cent ma;^nesia pipe insulation. The fluid passed from the mixing chamber at the end of the heat exchanger into a seven-tube, single pass cooler containing: 1 — inch tubes, 1^ feet long. The cooler was used to remove sufficient heat from the fluid to allow for continuous recycling and to prevent flashing of the hot fluid in the weigh tank. Fresh city water was used as the coolant and was regulated by a one-inch globe valve to give the desired fluid temperature in the storage tank. The fluid discharged from the cooler into a 55 gallon steel tank resting on an indicating dial type Toledo Scale with i pound subdivision and a capacity of 800 pounds. Flow rates were measured using a stop timer in conjunction with the weigh tank and scales. Usually sufficient time was allowed for the accTomulation of 50 I50 pounds of fluid. The 1 — inch suction line from an open impeller centrifugal pump manufactured by the Gould Pump Company also dipped down into the weigh tank nearly to the bottom. The pump vjas used to return the fluid to the top of the storage vessel either continuously or intermittently and a convenient control was provided. A lever type quick opening valve on the 1 77 inch discharge line was used to prevent drain back through the pump into the weigh tank during flow measuring periods when the pump was not operating. The storage vessel was an 80 gallon stainless steel jacketed reactor manufactured by the BlowKnox Company. The temperature in the


20 storage tank was measured by a thermocouple inserted in a deep well extending down from the top of the vessel. The discharge line from the tank was in the center of the hemispherical bottom and lead to a positive displacement pump used for circulating the fluid through the heat exchange apparatus. The pump was a one inch rotary gear pump manufactured by the Worthington Pximp Company and was driven by a five horsepower electric motor. The pump was provided with a by-pass and valve and this was used as partial regulation of the flow rate. Upon leaving the pump the fluid first passed through a seventube single pass preheating unit. The tubes were 1 — inches in diameter and 1^ feet long and provided a hold up period in the flow sufficient to insure uniformity in the fluid temperature. Low pressure steam was used in the steam jacket in order to obtain rapid preheating of the entire system when starting up and in operation the steam was usually turned off and the large heat capacity of the unit was used simply to prevent rapid fluctuation of the fluid temperature. After passing through the preheater the fluid went directly to the heat exchange test section or could be diverted back into the storage vessel. A valve at the entrance to the heat exchange test section was used in connection with the valve on the pump by-pass to control the flow of fluid. Valves and piping were provided in order to completely drain the heat exchanger, preheater, cooler and piping to a low level tank. The centrifugal return pump could be used to pximp the fluid from the low level drain tank back into the storage tank or to the sewer.


21 All piping for transporting the fluid was standard 1 i inch k black iron pipe and was insvdated using standard materials. The complete piping layout is shown in Figure 3. Steam was supplied to the system at 130 psi and was reduced to the main header pressure, of about UO psi by a 1 J inch Keckley regulator, type AR . Freceeding the regulator was the main cutoff valve, a strainer, and a continuous bleed-off valve which rid the line of condensate as well as some entrained air. Steam for the storage tank was further reduced to approximately 10 psi, using a one inch Keckley regulator. Type PT. Steam for the preheating heat exchanger was reduced using a i inch Foster regulator, Type 50G2C to approximately 5 psi. Finally the steam used in the test heat exchanger was reduced using another _ inch Foster regulator to pressures lower than atmospheric. In order to provide a method of discharging steam condensate at pressures below atmospheric a vacuum system was connected to the steam condensate discharge line. The vacuum was maintained using a reciprocating vacuum pump manufactured by Worthington Pump Company and driven by a three horsepower electric motor. The vacuum system was connected to the condensate line through a 100 gallon accumulation tank. In order to reduce the load on the vacuum pump the condensate from the steam chest was passed through a cooling coil and then to the condensate accumulation tank. Using this system it was possible to maintain pressures from 8 psi absolute to 20 psi absolute, corresponding to temperatures from 180'' F. to 228^ F. In all, 13 temperatures were measured using thermocouples.


22 These were: (l) storage tank, (2) inlet fluid, (3-10) tube wall, (11) outlet fluid, and (12-13) steam in heat exchanger. Leads from all thermocouples were connected to a rotary selector switch manufactured by the Minneapolis-Honeywell Regulating Compare . Measurement of the e.m.f. output of the themocouplep was accomplished using a Leeds and Northrup potentiometer. Type 8662. This potentiometer was equipped with an automatic temperature compensating mechanism but more reliable results were obtained using an ice bath as a reference junction temperature. The tube wall thermocouples were calibrated before they were installed by checking N3S calibrated themometers. A calorimeter was used to maintain constant temperatures of 32° F., and approximately 100 F. Boiling water was used as a third check point. The values of e.m.f. obtained agreed with those given by Adams in the International Critical Tables, Volume I, within 0.^%, Temperature e.m.f. curves were plotted using the data from the I. C. T. with scales readable to 0.1 degree Fahrenheit. The thermocouples used for measuring the fluid inlet and outlet temperatures were withdrawn from their respective wells and were calibrated in the manner described above. All thermocouples were sufficiently alike to justify using the same temperature e.m.f . curves. Other special apparatus were prepared to measure other quantities related to this investigation; the appropriate apparatus are described in the section devoted to these meastirements. C. ExperiiT-ental Froc^du^e The black liquor used in these experiments was obtained from


23 the Palatka, Florida Mill of the Fi'udson Ftilp and Paper Company, a company engaged in the production of unbleached kraft paper for use in bags and guiuiied tape. The liquor was taken from the last stage of the multiple effect evaporators and contained approximately 55^ black liquor solids (b.l.s.) with the balance water. The liquor was transported in 55 gallon steel drums and remained stored in these containers until used. Since the black liquor was a water solution, liquors of various concentrations could be easily produced by diluting the concentrated material with fresh water. The solids content determinations were made by drying at IO5 C. a sample which was absorbed on asbestos in a porcelriin crucible. In this way no crust was formed and a constant weight was obtained in 2^ hours. In order to avoid usinc excessive quantities of the concentrated black liquor the plan for operations was to start by using the most concentrated liquor and then^by dilution in the stainless steel storage vessel, prepare successively lower concentrations. At each concentration complete sets of data v?ere to be taken so as to eliminate the necessity of repeating a particular concentration. Actually, however, the apparatus was first run using water since it was felt that operating difficulties could best be investitrated and corrected when using a system on which considerable data were available. Following the runs using water, black liquor nins were made using 30.5, 33.0, 25.1, 16.8, and 9.2^ b.l.s. At this point in the investigation it was decided to obt-ain a new sample of black liquor from the Hudson Pulp and Paper Company in


2k order to investip.ate higher concentrations. Experimental runs were made using; this new liquor in concentrations of ^9.3. ^1.9i and 33«0> b.l.s. As a final check on the apparatus and the calcxilations another series of runs were made using water. The procedure vrill be discussed only in relation to the black liquor runs since these areof major imp-ortance in this investigation and since the use of water in the apparatus offered no additional difficulties. Concentrated black liquor was poured into the 80 gallon stainless steel storage tank and sufficient water was added to bring the vol\une of fluid up to approximately 60 gallons. This volvime of material was sufficient to provide fluid to fill the remainder of the apparatus and still leave a safe quantity in the storage vessel. It was necessary to provide agitation to obtain a hcsnogeneous solution of the black liquor and this was accomplished by circulating the fluid through the rotary pump and preheater and back into the tank. Several hours were allowed for this operation. Heat was sometimes added in the preheater and the storage tank to increase the fluidity of the very concentrated liquors and thus improve the mixing. Several samples of the liquor were taken and analysed for solids content. In preparation for a series of runs the liquor was usually circulated through the entire apparatus for a period of from 30 minutes to an hour. The steam to the storage tank and preheater was turned on and regulated to about 5 or 10 psi. The circulation of the liquor served to heat up all piping, pumps, tanks, etc. When the liquor in the


25 storare tank reached the desired temperature the steam to the preheater and stora(7e tank was usually cut off. During the heating up period the potentiometer and ice bath were prepared and the 13 thermocouples were checked for response and agreement. With the fluid circulating through the heat exchange test section the steam was admitted to the annulus and adjusted to about 10 psi. A brass cock at the opposite end of the steam space was opened and steam was bled off for several minutes to rid the steam chest of entrained air. The vacuum pvimp was then started and the valve to the condensate discharre line was opened. Tap water was turned on the coil condenser to prevent flashing of the condensate with accompanying loss in vacuum capacity. A bleed valve on the vacuum rump and the — inch 2 Foster pressure regulator on the steam line were adjusted to give a steam chest pressure slightly below atmospheric. The pressure was used as an approximate indication of the steam temperature. The temperature of the storage tank was allowed to inci-ease to the desired level and then was held at this point by adjusting the fresh water flow in the cooler follov;ing the heat exchange test section. With all apparatus in operation and having been checked, a run was started by adjusting the flow control valves to give a desired flow rate as indicated by measuring the rate of discharge into the weigh tank. With the flow rate fixed, at least 10 minutes was allowed for equilibrium conditions to be reached. Equilibrium could be detected by following the variation of several thermocouples during this period. When successive readings failed to show significant deviation the


26 return pump was started and the fl\:id in the weigh tank was pxomped back to the storage tank in order to make room for 100 to I5C pounds of fluid to be collected during the test period. The pump was then stopped; the quick opening valve was closed to prevent dr&in back through the pump into the v^eigh tank; and the stop clock was started when the pointer on the scales passed a convenient point on the dial. The thennocouples were read and recorded in rapid succession in the follovdng order: (l) storage tank, (2) inlet fluid, (3) outlet fluid, (^-11) wall temperatures, (12, I3) steam space. The timer was then stopped and the weight collected at this point was recorded. During the early stages of this investigation a second set of readings were taken after a several minute interval to serve as a check on the results of the first set. These two sets were found to be in agreement in most cases, thus, indicating that equilibrium had been established before the first set was taken. Therefore, in the remaining exi>eriments, adequate time was allowed for equilibrium to be established and checks runs were made only occasionally. At the completion of one run the flow rate and steam pressure were readjusted slightly and after the necessary equilibrium period a set of data was taken. The flow rate was, thus, gradually increased or decreased to the maximum or minimum flow obtainable in the apparatus. The complete range of possible flow rates was traversed at least twice with each liquor concentration. After all the necessary data had been taken using the highly concentrated black liquor, a portion of this material was pumped out of the system either to the drain or to storage


27 drums. Tne voliime was made up with fresh water and the fluid was circulated to obtain thorough mixing. Samples were taken for solid contents determinations and the apparatus was ready for another complete set of runs at this concentration. Several days were usually required for a complete set of runs to be made at each concentration. Each time the apparatus was started up the procedure outlined above was followed. At the end of one days operation the entire quantity of fluid was pumped back into the storage tank and the remainder of the apparatus was allotted to drain. Each time the liquor concentration was changed, an extra long precircvaation period was allowed so as to prevent the presence of pockets of different concentration in any of the tanks or lines. D. Data Descriptive and experimental heat transfer data for all runs are given in Tables 1 and 2, respectively. The tube wall temperatures as shown in Table 2 are the temperatures at the extremities of the heated length of the tube and are extrapolated values based on the readings of the eight tube wall thermocouples. Plots of the thermocouple readings versus tube length made for each rxin indicated in iiost instances an approximate linear relationship. It will be noted that the point of measur«nent of the tube temperature lies within the wall and that its exact position relative to the temperature gradient through the wall remains to be determained. The avera.^e steam temperatures shown in the last column in Table 2 were not used in the calculations but are given for general


28 TABLE 1 GBIIER/U. INFORM AT ICM OK FLUID SYSTEMS " "Weight per cent Run No, Fluid System Black Liquor Solids 122 Water 2355 Original Black Liquor^ 38.5 5630 Original Black Liquor 33.0, Sl-103 Original Black Liquor 25.1 lOit-131 Original Black Liquor 18.8 132-163 Original Black Liquor 9.2 164-191 New Slack Liquor^ '^9.3 192-202 New Slack Liquor i^l.9 21*4-223 New 'Slack Liauor 33.0 22*^-236 Wat-^r Original Black Liquor was obtained prior to operation of the heat exchange appai;atus and was the material used in all physical property determination's. New Slack Liquor was obtained from sajne source as the original material in order to secure runs at higher concentration of black liquor solids.


<\J H s g :^ (15 3 > W a, r-l i-l <^ 29 ">a3rHfM(\)c^»n(y-ir>c^ vO^O H^MDir»vriHu^ c\i\n vO u^ fM <\i O00 vO lAsO vo ryi(\l(M(MrHr-»'^00 OO «AOOOOW^O OO ^ DO O rHts-OOC^(S)»no [stt, O SO C^ OS 0> O rH W iSU es o^ CTnOsOsOsOOOOC: o r-t l-t H r-i r-^ r-i sD-:tsOsO-:t^ (MOsOfsi OOO rHrH r%C^CO0OCsJ CSJ ^ U-\r^-r_HrH-d--:l-OsOs t-i r4 r-i H r-{ r-i O 00 C^ rH C^ fM fH <\i CM 00 CO (^v OS -3 u^sO -? "" QL O O O O O O O CJs H r4 r^ r-i r-i r-i CX5 ir\ >r\ w-^ o O so (SJ (^ O O^ (N rH C\) r^ 00 (O U-NO r^ rH ^ U^sOf-COC^O -t O C^sO H CSJ (SJ CSJ


30 «> X D O O O <".' -J OO >/^ C^ a^\Ci O Cj Cj O ~i fv C^ a> vc. ofj Q-i 1^ o^ G al^ UN :; a rt a r-*»-lf-irHOOr-tO fxi C\ CM r\i' fSJ ; rj (V CJ CM Ci r-l «^ r-l <^ C r-1 ri H r-l ri r-t f\) (NJ OJ fV fsj CvJ ,3 o <"> u^ O w > u-^ r\ o W\ (\i cv o o o J c^ u-% w^ c^ v/^\ m:i -3 ' ir\ to tt. H P i-l r-l H rH O r-l p fsi r-.' fvj C\J r-H f^ OJ C^t C^ C^ a> O r-l r-( o t> J^ C\ OOOi-trlfHiHOOO fv; r>^ f\J <\) f\i r\! •/> Cj O C«/\ vf ^ c< ' f u\ ci'. i/\ if\ rj r \ vr, r. c^ \.'^c-: U-. -: o c,. ij ,-< f-t r-< r-i O f:!") 0-<-< C' r J '^l fsi Cm rH fH ;\' a.' ^fr-l O C^i f-t f^i (-1 O r\ v/\ u-r (_r) ^1 ,_, iH "% C -d CC' CT' r. C (> r. r, f^ J ^ r cv ,- r\ r-\ r-> ir\^0 vO f\) o,j fj r-j O O ».iJ ('^ CC^ sC' ^' r t-i r^ u \ r^ IC' r.; tv rj •.'M c\ r \ i-i h cH/-(rH/Hr-lrH»-4r-i f-4 ri rH iH r-4 r-t rH r-» r-i f^' co< c O -. si c I '6 .c o ^ O O O u"\ u ^ a? c— rro rrrH ir»c> rH .-1 vc vo a; (. o o r 1 H H M r\ r-\ H iH <^j CJ^ C(j cr; vc (N C» >^^ O V'\ ^ c^i ^ ,H t^ ir> ^ r\ ci .4 cF) rt} \Cu^ rj ,-) fH VI) v£, m5 «-l rH r-l so 1-1 r-l r00 Cj a: aso cr t 1r"\oy (H rH r-» <^' <"»! t£ i *^ C -J iJ-^i si; C ~ CO ON o rj (\: f -i c-j c-j vN c . <^\ r^ r^ c^ rx c"> f^ ^^ < -.^ -4 ^ -J ^ _-? ^


31 C0 '-• O r-" -4 O 4> 'J) M Cv/ <\J CM c\ c^ ^ 0} 4-> ,« to C t' u. ^ •H h a. V H 4 k^\\0 (..» ^ o' 0^ c a^ \C t^ o -vr On o o^o:^ i\> xr> fj vO vi"-"^.J^ ^' ' OC^ r-H rHOOOOi-lrH.-'r-»r-( CJ OJ OJ CV (M <\i (\) CM O r-IO OOOOr-itHfNifS) CvJ C\J Ci OJ .-\ CT ir> C O (-< \C> u-.vii r\ o "^. f^ -3 vr* so fve^ O"; <\' w•^-o r-< •-^ r^ M r-i 0-J O 0(JN Cr> O-. r-l cv '"'J rH o <^^-^l-(r^^-«f^l<^i<^J^s)CV (H CO v£) c •. o o a.i t-y. r-{ O 0> ON (>> 0-. 0\ O O rH cv CM H H iH rH «H M r.J cv CJ : >J'^ r^\C> CM CM r-.' O VTN o o r-V o ro f-H fH fH CM C ^ r . r^ rH « r^ • r-t^ CXD o cr. o 0-CO ,-1 r^ M o CJN C-; f-t r-H iH rH Ovi f\( rj cv H C • J^ rH CS; ^ v/N ^ ^ .J vO CJN (?N On CD « CO O O rH H r^r^r^r^r-^l^cv^vcv<^i CJs cr. i-i ^ ir, 0-. CO vr\vC vTN ir> Cm r^ cvi o > cjn ^' O r^ cxi o vO <>> >A c V if^ c! y. ca CJ (\ Ci C^J^ rj rH f-i M r^ r \ c^ J^ J^ o c r-< 0.' CNrH r-t O J rH J r a • CC-VC o-i ~J r-( CO in tc "^ o o M r vo -J vii ro o H r^ c\ <^\ ov c av C X1 ft s ^— . a> p o • M rH M ,4: *0 VAO cv ^* rc^ V) f .! C-,' cv <»> r-t rctj ON o -T ^ ^ U^ OnDOOO lAVOCOCNJOOO CAC) o w^-Aa) c'^J o cnr-:U C^CO u-\ cvl c; CJ ^ vi") rHCVOJrHpHr-*r-(r-( r-i CnI i'^^ »/^NO JNCO 0-, O u^iA\rviAtrv»r\vriu^ ir\NO V: N£' O r-t re O ^ ^ ^ C^, C-; vi, f, .. \o o. c o ON cr. i-lr-tf-tf-fr-irHr-tr-tHH t^vOOr-jONC^flOC--vOtN•X) Cn; >.C fV w-^, rr-l O fC\] VD O^ ^-^ n£) c^ rN^ 0^ O C^ (H r-< CNi cn; 0'^ r , r-( r-( iH nOvOvDVDnOvDsOnOvCi t^


32 > to •-^ e .ti 'a<^ o -o ^< c-=!^ '~ «4-' »H >-• • 5 P c o o^ JON cT' o ^ u~\ o c^ Cj <.-• o >A-j c\i r-j vo C' O vC O O fv CJ <.l.' Vi.' Uo v-^ f fv fvj M c^ <^ o ooA) rj CJ rH iH Ov rH iH f-4 H C'>r-' CT' c O."f~v CJ >i> ir\ fv, v; <\/ oo IX' o? m o o^ o'j lA r . v: a o cr> 'Ji?^ w"\ H a , r^; o ori o On a: a; c^<\' C\i r-l H H »H r-« r-l d C^ CO 00 CO H iH H c-< O r-> r~u^, vr, vr, ov r> O M o o j r^ a> fv o o rH r-i o 'Tn cr> X v. (vi t^ in \r^^f) oi r~ O O Oa { • r-^ (•-^ c-\ r-\ r-i ^ r r <\; r^ o c^n (v o c^ ri-i f" r% C u-._^ sc. c cr. -3 cn CO vr\ rvo -cf C^ ir\-3M CO c~. c^ <^-i o iNJ Cvi 0,' J COD -H (^ C i-( vO a COD rH r-l rH f-J >-< <\i Cxi C-^, r. (* , CO OO CO 03 r-co v^ o C^ 00 OD ON H CM r^^ (Jv ON Ov On


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34 « 4) t3 B ^^ tt i^ (^ U V l> > en r'C ^ --• f-t r-( CO t!, b. ^ CO r^ ra*i o 'T iH ^ so 0< -^ o r^ r \ c; f j ^^a r^i r^ '^j Cr-7 u 1 0.1 v> -3>-', <^ -J O. Cr-t O C\ O^. U-v CT. C^ O cH r-( -^ r'^ C^^ r•^ o o CO O rH'r-t O O O O O O 0-. iH cj rj w <\i ry (Si r>j CO t-( V OS CO r-t kO C> OS V> OJ f " O 00 O ^' CJ O C r, «?• vA r-* CT' Os 1 C c; r-i o sC su O O 00 fH r-< -T sO sii r-< C -X C^ u"^ r-« r-J O f-l "M O so J C^ C: r i O O sJX, C Si) sO A ^ ^ .3r\ p-\ r--^^^r-^ ^ ^ij r-i t-' :! CJ r--, ^ CO 0\'l C 1^ C J ^ C5S ^ j^ r-t r^o\c\) :^ ri-< ITS r^ C-\ H tH rH Csj CO H ^^i r"-, ^ >A so c^ CD Os o r» O0rHi-«rHrHHHrHi~tr-t r- o C-. ffC' C*^ O C-SO iH (-< fsj rH K rH CO Cs; rs r"\so so ao^ «-) rH CO C\^ xoso C^ c^ eS f'\ c\ r^ cn c"-» ^ r-ir-ir-ir-ir-it-ir-ir-^r-ir-i


35 ba p X> ta fll 01 u 9) J-. c tJ ^ '•) 1 t. f-. COCQrNr^r-4 0C*>-vCCA 0N00O->-tv>r-C^\O c^ O C-Oso sO u-\ WA ^ ^ C \ O ON G-. O O UN aITS O . (.>. r-tr-< r^^^^^^^r^r^lHr^ c\. rvj f . o o M a. Jtw, ONUNONiHOr-tC OOO o o §: _ o^ ir-, o f^ 00 rH IT, ^ \o CnCnCn o CA C-N CNo CO r^ ir> cr. c-v/ > r-i r J CTx On O u", O {nO ^ o cnj c^J nC)^ -J rH Cm c c Ci a,. NL c^. fv CNrC-rfNO nD NO r-t<-< r-lr-r~i rN, r v r", r-, r> C\ r \ r"\ .-HrHHrHrHrHrHrlfHrH (^ O O h'AnO nC C r O NiJ r-\ (»~i f^\ I., (^ r > ^ 47 -:t r'\ r-ir^r-\r-ir-iHr^r-it-ir-i f^ C iS (Tu . CO o r , rH U^, rH r^ cti On ^ VTN cr ^ rv; C-J r-, U-N, rH ^ VA O , NO ^00 4 rH r» J CnrH CG Cn. U~\ vr\ Cx.> t^ r1 rH r^\^^ C^ CN) r \ r\ r-i rH rH rH rH rH CV r^^ vTvv; C^ CO ON C »r\ in vTN lA ko vrv w^ u"\ vTwo r-tr^r-ir-ir^r-ir-ir-lr-ir-i rH H rH rH rH rH H H o C\J o rH r-i H (NJ ?:: i\i a • -;T (NJ CNJ frH OJ f>^^ ^O NO NO NO H rH H rH


36 U 0) > tn a 3: TO a Cm a, ft) t CJ •, c: V.:; m c13 UN C. eCJ f\J (M rM rH iH i-l ;<;k' c P o u", O v^i u> O O t'^ 00 r-" O O O u^ fH J^ w^vo o1-1 i-t (-1 CM CvJ CM CM C^ v£> «-• . vPi ^ JS^ -J -J 00000000 rOJ CM CM CNi CM CJ Csl o rfi • cj c^ j^ Ql"\ C rH Vt' t^ a 0.' tN C^ u\ \t (^ , (• v/^ u-\\o w-\ C> CTv <^ 0C c»\ o> a> c H iH rH f-< rH H r-< -H CM CO CM fvj 00000000 CM C< CM CM rvi CJ CJ CM O i'^ CCO w^ cf.) o c \ o r~K o CM _1 C^ lA O O Csi vr\ Wi-J CM rH O^ O. C. C i CM ^ ^ CO <» OTr O O O O rH H iH CJ CM CM CM J OA CJ C; r-i r-t r-i r-i OOOOOCOO Oj (M CM CM CM CM CM CJ C \ CI t^ O r-' G Cr sOvOr-'t-lsDOf^J'^ M. O^ C , C \ C-'"J O iH rH H -a ^ W~\M3 rH H rH iH rM i-H H cj i-j !M (, (7er; cr^ VO vO M ' \D u"i VA vTn w-\ XT) cT' rV4J C^ r^ C^ C^ f . O QC ^ so VO CC' Os c> «-< 00 f N CVJ C <> , cr. a' CO 0^ 0^ u^ l> VC vi; c\-^ ij >r\ r-t rH H rH p-t i-t i-t H rH »H rH i-l H t-l rH rM CN c:^> (.K C V rM3 v^^ ^ xr\ u> ir\ iTA \r> w^ vr\ u-i i-ii-lrHr-tiHrHrHi-l r-t t-t O rj -1 (\^ ^O V') t^Cn O 5^ y-: rH -J t^ r^ -t CXI rH ^ v<) 3 Q vC O iH r\ -5 00 5 H O^ 0^ N CM rH CM 0^ f-H ^ MD rcr; On O v^vO viT vn ^C r^ • -rH ^ H rH rH r-t oj c>^ vnvO C^CO or: CO CO or. cc cn "O <£


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38 H <\1 ft' t. 4) a. U, r •H t. c?d ^ A CO vO O ri J VO C^ ON C -J'X' v^l Or-l r"\vO rH CM »-( ^ c^ r-1-< c^ u-\ u--, O O G c-l rH f -i i~i O O O CV) (M OJ CV 1 ,' r^l (^j Cm f\l -.•%( V CV O O U00 O '. ^ O O . ON vvJ CV • ^ »''\ Cvl OC f . (-1 CO C rH tO c.y O On O O H O rj C7 H OJ CM rvl CJ Cr\ V.' \ cri o o ^i: C . -J NO s:^ o Cn r-l t^ O 0> O . O^ CO tX" O « 00 C^ C^ Hr-lrHi-fr-irMr-lH'-lrH LfN ^ r-^ On 00 t-CtNCNvi; NO NO r-t H r-) fH rM.iH NO n: no cr j 0) r-t O C-: CNV V C % C {NJ (V CM OJ r-4 r-t »-< H H r-l CC -^ a-) u-\ c, O^ CN O VA CJ r . f^: o> -i CNtrH rH »-t O O O O O C i-l r-lHr-lrHr- r . H r-t t-( (H r-t r-l H r-l r^ r-l H r-l ^ r-l tf C C -n C^ VC ^^ c\_; -3 o o m^ NO a: o • rr~. o c'% cA^ CNo cv -: tn r-« r-< r^l n rH rH .^ r-i CM <•^ J^ ir\MD r-Cr 0» O

39 infornation as an indication of th^ overall driving force. In soine instcinces the steam temperatures are only slif^htly higher than the extr^ipolated tube wall temperature at the outlet. Such a small temperature difference is an unreal condition and resulted from the fact that the straif^ht line used to extrapolate the tube wall temperatures was slirhtly misleading in this region. This condition occurred whenever the plotted tube wall temperatures indicated a slight convex curvature with rer:pect to the horizontal axis. In several instances runs which were actually completed and recorded vrere voided due to known factors which would have made them in error. Thus vacancies appear in the Tables of data for Runs Number 13, 166. 173. and 203-213. E. Samrle Calculations Run No. 184 was chosen for these illustrations since it is typical and showed, in general, satisfactory results. The fluid employed in this ran contained ^9.3^ black liquor solids. The calculation to be presented in this section will include data from Tables 1 ^j^d 2 as veil as the results of the physical property studies discussed in the followin? sections of this dissertation. In addition, other properties detenr.inable from the geometry of the apparatus are necessai^. These properties are tabulated as follows: Inside diameter of tube: D = O.51/12 = 0.0^25 ft. Outside diameter of tube: . 0^= 0.75/12 = O.O625 ft. Thickness of tiike wall: d = O.OlO ft. Heated len?th of tube: L = 6.00 ft.


Inside cross sectional area of tixbe: 3 = C. 001418 so. ft. Total inside heat transfer surface: A = C.SO sq. ft. Total outside heat transfer surface: Aq» 1.176 so, ft. Log mean heat transfer surface: A =C.975 sq. ft. In order to systematize the calculations, a data and work sheet was prepared for use with each run, .'In example of this sheet with the data for Run No. IS^^ is shovm in the ap;)endix. The sheet was designed for the calculation of all dimensionless groups to be used in the heat transfer correlations a? well a« the j factors. As pointed out in the section "Data" it was necessary to determine the exact position of the tube wall thermocouples with respect to the temperature fradient. The thermocouples were located at the botton of grooves milled C.0625 inches deep and C,0625 inches wide, Feened into and completely filling; the groove vas a strip of soft solder. Mathematical calculation of the position of the thermocouple with respect to the temperature gradient was complicated by the goemetry of the cross-section and the fact that the thermal conductivities of the stainless steel (Ty{?e 30^) and the solder are different. Some investigaticHG are reported in the literature wherein the physical position ofthe thermocouple in the wall was taken as an indication of the position of the temrieratui'e measurement. This assumption can be grossly in error, as was shovTi by this study, and it is accentuated when tube walls are composed of materials of relatively low themal conductivity thus causing large temperature drops aci-oss the wall. In order to avoid a complex mathematical analysis of the tube


41 vail temperatuTf^ it vas decided to use a seini-empirics.1 methcxl of attack. A themoco'iple was to be mour.t^d in a flat plats of Type "^Ok stainles? steel in a manner similar to that used in the tube wall ; a temperature gradient v-as to be imposed; and measurements of the vail tem];ierature -inc the two surface temperat^jres were to be made. Having* in this way, determined the thermocouple position relative to the temperature gradient in a flat plate a m.athematical treatment could be used to locate the thermocouple measurement in the tube vrall, A groove C.0625 inches deep and C.06^5 inches wide vas milled two-thirds of the way acr-oss a h inch by ^ inch piece of Type 3^^ stainless steel C.125 inches thick. A copper-constantan thermocouple vas installed in the same way the tut>e vail thermocouples had been done and additional thermocouples were soldf^red to the surfaces a1x)ut 0,25 irches ax^'ay from the groove. Rubber hose was used to direct atmospheric steam on the grooved side of the plate in the area of the thermocouples. A stream of water was directed at the opposite side of the plate. The three temperatures v.'ere read over an extended period of time and average values tcere determined. The temperature drop from the wall thermocouple to the cooled surface vas found to average 80% of the total temperature drop across the wall. This is in contrast to the fact that the thermocouple was physically located very close to the center of the vail. Most of the difference can be attributed to the difference in thermal conductivity between the stairless steel (9.^) and the solder (19. C), Additional effect is caused by the fact that the bottom of the groove is at the midpoint of the wall and therefore the thermocouple


42 which is aMJ,-c.-=^rtt to the bottom is actuall;/ somevhat off center. The rrrblera of deteminine; the ther.riocouple locc.tion in the tube ^Tilx bri5c»r' on infor-TTiHtion gainf^u on the fl^t piste tests is simj-lified by a.^svnninp; that the v;all is of uniform composition find that the effeetivs physical locition of the thennocour.le is one-fifth of the way throuf;h the vhII. In order to deteri-.ine the proportion of temperat^jre drop from the thermocouple at this loc^ition to the inside surface it is necessary to devel \o an e -iTeso-ion for the temperati:re distribution th.rough the tube wall when heat is flowing throo.-h th<=wall at a steady rate. For a lonjj tube of the dimensions used in these' experiment's, let t , t , and t be the temperatures at the radial dist5nces r , r , and O v S O VJ Tg respectively (see Fipiire ?)• Vnen the tube has length I, the he£t transiaitted in unit time, c, is given by the expression q = 2TrrL.„fi =. 2iru:„3fi; (10) where k., is thennal conductivity of tho wall. Int-^gration of this equation betveen the limits r and r and between t and t gives so so q = ?1TLkw a, t^^ ^^^j Inr^ Inr^ Integration betv/een the lirnits r and r and between t and t gives s w s w '^ q = 2TrLk ,(t, .-t^) (^2) Inr . Inr . 3 W Since the v.'.lue of q in the equations 11 and 12 are equal, the equations •"nay be solved si.-aultaneously to give


Figure 7 Cross Section of Heat Transfer Tube


Wf t„ t. Inrg . Inr^, (13) ( Using r = 0.235, r^ = C'.375 and r =0.351 there results so w -2 Si , 1:!= 0.83 (1^) *s ^o ln°» 255/0. 375 Therefore to calculate the actual inside tube surface temperature the overall temperature drop must be multiplied by 0,83 ^^d this value subtracted from the temperature of the tube wall as indicated by the thermocouples. As shou-n by Figure 8, a plot of the tube wall temperature versus the tube length, the data are well represented by a straight line. Over the small temperature rise encountered the thermal properties of the black liquor may be assumed constant. Thus the variation of the fluid temperature through the tubs may be represented by a straight line between the inlet and outlet bulk stream temperatures. Since the heat being transferred is proportional to the overall temperature difference it is obvious that different amounts of heat are being transferred in different sections. However, a mean value of the temperature drop across the tube wall may be calculated from the dimensions of the tube, the total heat flowing and the conductivity of the tube '>;all. Thus from the basic heat flow equation At. = t„ t, = ^^oJ^Zl („) "•A where A^^ is the logarithmic mean of the inside and outside tube and (r r ) is the thickness of the tube wall. o s areas


^5 0) c c o +> * 1 1 O -P H O -P r ! 1 ' •o 1 1 l' 1 1 1 ill to| H p P3 1 11 i ll 1 1! 1 1 c o IT) f-< 0) ^ X 4J n r^ <2^ «T1 ^ m 0) •H H J-. ^ as > e m V Jh o (i> c (0 S +j

1*6 A^ = ^o " ^ = 2Lir£ojJs) (16) lnf2 In '^o A r A (2) (6.0) (3.lh) (0.0312 0.0212) ^ ^ ^^^ ^^ 2 ' In 0-031?^ 0.0212 Using a value for the conductivity of the tube wall of 9,k BTU/(ft.^) (Fr.) (°F./ft.) there results from equation (15) (0«0312 0.0212) ^*w = *o "^s ' ^ O.k) (C.975) = 0.00109 q (17) Conbiniup; ecuations (1^) and (1?) and solving for (t t ) an ' w 3 expression is found for the mean temperature drop between the tenperature Indicated by the wall thermocouples and the inside surface temperature . t„ tg = 0.83 (to tg) = (C.83) (0.00109) q = 0.000905 q (18) The quantity of heat transferred per unit time, q, may be found from the mass rate of flov, W, the heat capacity of the fluid at its average bulk stream temperature, Cp, and the increase in temperature of the fluid from inlet to outlet, AT = (T^ T ). Therefore, t t = 0.000905 WCp (T^ T^) (19) For run Mo. IS^, the mass rate of flo^: from Table 2 was 2632 Ibs./hr. The inlet bulk stream temperature T, was 159.8° F. and the


^7 outlet bulk stream temperature To was l6?.l F. and these gave an average bulk stream temperature, T , equal to 160;95 F. The values of b the fluid heat capacity for various concentrations and temperatures are given by Figure 13 . At the average bulk stream tempera tur-e and concentration of this run a value of Cp equal to C,738 was found. Thus, t t = 0.00905 (2632) (0.738) (162.1 159.8) VJ s = ^.1 °F. Based on the assumption of uniform heat flux along the length of the tube, the inside tube surface tempera tur-e at the inlet and outlet of the heated section may be found from the extrapolated wall temperatures at these points. These extrapjolatcd wall tempera txxres, as shown on Figure 8, were found to be 202.5° F. at the inlet (t ) and 2QU.

At ^^2 A ti (200./+ 16?, 1) (198.U 150.8) , , Zit, (198.^ 159. S) Actually, in this cass the arithmetic Average temperature difference would have been satisfactory since the ratio of the terminal ter^peratura differences does not exceed 2, The avera^^e coefficient of heat transfer bet\veen the tube wall and the fluid v/as calculated directly from the rate of heat transfer, q, the mean temperature difference. At , and the area across which the tn heat flowed, A. Thus by definition, q a hAAt =• WCpAT (21) w where h is the coefficient of heat transfer based on the inside surface area . Thus , h . '"^'Cp AT AAtj^ (22) (2632) (0.738) (2.3a) (0.80) (38.i^5) h = liii5.0 3TU/(hr.) (ft.^) (^F.) , The Stanton number, St, was used in the correlations to be presented in later sections of this dissertation. This number can be calctilated from the heat transfer coefficient, h, the heat capacity, Cp, and the mass velocity, 0, which is equal to the mass rate of flow divided by the cross-sectional area. Thus,


49 h h ^' ' WhT] ' Sfl <23' A more corivi^nient method of ralculatinr the Stanton nunber is four.c by rearrn-ietif^rt r.f equttion 21 after multiplying each side "by .'5. CpVv CpG A ^!>t„ JL = 0,»-Ci:;l8 ^_ ^ C.OCI77AL (,r..) CrG C.eO At„ At It i^ evident that >.e Stcnton nun-^er r.:ay be calculated directly from the two te.'nperature diff'^rences. Thus, _h. ^ (0.00177)^ (::,30) = 0.0001058 The Prandtl number, Pr, barbed on the bulk mean fluid tejaoeratare was calculated fron values of Cr, k and/* obt.^.in«d from Fij^ures 1;, 2C, and 22. Tliese values are Cp equal to 0.73'', >U equal to 18.1 contlpr^ise, and k equ-al to O.306 3TU/(hr. )(ft?)(°F./ft,) . a corrvf^rsion factor of 2,^2 vas .T.ultipliod tines the viscosity in centipoises to obtain viscosity in consistent unit'. ir -. Bi^= (p-?3:-) (rM) (2.^2) (26) k C.3O6 = 105.5 Th« Reynolds number. Re, b3.-:ed on the bulk mean fluid temperature v:a2 found to be.


50 . Pe = ^ = Lpi (,7) (la.l) (2.42) = 1800 The Oraet* number, Gz, can be evaluated from the Reynolds and D L Friindtl nuonbers and the — ratio as follows: ' if) m (r) (?) '^ 0. = («,, «.,(£|5«5) (..) Gz = (Re) (^Y) (O.OO56) Gz = (1300) (105.5) (0.00556) Gz = 1057 The ratio -^^ is fcind by dividing the fluid viscosity at the average surface terror era ture by the fluid viscosity at the bulk mean temperature. The avera^^e of the tube surface tejnperatures at the inlet and outlet was found to be 19^«'+ F. and the viscosity at this temperature u'as found from Figure 22 to be 9.05 centipoise. Thus, ill = il25 = C.50 M 18.1 Tlie coefficient of cubic'*! expansion, j3 , may be calculated from density or specific gravity measurements. By definition.


51 ^ _ ^ exnan.^ion (30) (31) /-. ... ^^ In terms of density this may be written 1 1 y5 = p2 Vi (S-^n) 1. In tenns of tre specific ^Tsvities of the flui^^ at the terminal bulk temperatures ^ 2 (T . T ) 3 3 ^^'"^ 2 112 The values of specific gravity at various temperatures and concentrations may be obtainetJ from Figure 23. Thus, /3 = (1,2590)^ (1.2582)^ 2 (162,1 I5G.P) (1.2590) (1.2582) fi = 0.000288 ^/*^. The r.rashof number, Gr, is calculated from the inside diameter of th? tube, D, the density of the fluid £t the bulk mean temperature, fi , the gravitational constant, f, the viscosity of the fluid at the bulk me&n temperature, ^a , the coefficient of cubical expansion y5 , and the temperature difference betv.-een th'^ tube surface and the bulk of the fluid, Atp^. The equation ''or the Grashof namber with all constants and conversion factors includ*^.-! becomes. Or


52 = 2.13 (10^) ^'/^ ^Sn (33) At th*=» bulk mean fluid temperature, the specific gravity from Figure 23 was 1.2S66 and the visco^3ity from Figure was 18.1 centiroise. Thus, ^ _ 2.13 (10'') (1.2586)^ (0. 000238) (JS.'-^) (le.l)-^' Gr = lli+O F, GalculatH'd , Re3ult s The complete calcul-ntea results for all experimentdl runL^ are tabulated in Table 3, The variables tabulated and their ranges of values are as follovs: Hest Transfer Rate, a: JU-'C U52OO 3TU/Hr. Log Mean Tempemture Difference, Lt^: 13.9 ica.50^. Hea* Transfer Goe^'ficient, h: SO 33M? 3Ti;/Kr., Ftv.

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57 4-» -H W ^ . O +J •H t> CO •n »< »-i c c .o a. 7 c o u *^ a. 00 vo vr\ ^ On a^ 0-5 VTN O cj a> o'^ ct^ jvr53 o o iH CM to o^o cvjcvicvjoococoj-r, cooj (Nifvj vnvr\cor^ocj-;f c^ r^ c^ ct^ c^ cr «• CO r r c^ 3 3 I c\ c \ ct CO r^ fNc^ CNCNa cc CO CO 00 oc ai o.": 00 00 Cn-Oni^OOOOvOOCO CC C^ r-O C^ r-l (-1 C" Cv4 (>; VA «^ CO C-\ <^ O -d^ O O O O H O O OOOHHHfHOfHH ^0 CO H f-IMfHiHHrMrHOJ OcnOHNO'-^tN.oCNjjs^ C^ O OJ M -^ »''^ u^ C^ C^ f^ O O O O O O C:) O O O C O O O O O Cj Ct' ir\ O On riJ". C^ iH C^ w/\ fvJ Oc~ C^ O ^ C^ CNr-l ^^ CTn nQ Ni/ Oj C-\ C\ C^J

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59 o ^1 to JD C.-4 O H-> o eg to O J I o f-4 c O ti e o u 4) 0) G b U -• 60 fl) ' . O C<.i «) n cg.^ C^ O r'^ C-J • • * * o o o o -d^ r 1 r-N cj :^ • • • • o o o o o o on ny ffS a"* C^ t-i r-t C^ t^ C0\ 00 . . CO cn m u^\D cO f\' O O-i CO NO f^ r^tv o Cv rvi <\j cj o o o o oooooooooc o o o o o O O Cj o w^ O VO C^ f-l O SO J^ l-t r-i ,-1 0" -^ OO' O r-i or 7?-,^: O 3 C^ NO O vjA vr, i-j ^J ir-. U^ rH iH iH iH 0^ to o o o o w-\ u\ \r\ >s\ O c^ r^ O C^ rs; r-.f f, CJ fKj r; o W'x.-J r-< CO O; ITS U'y W , W , U^ U ^ U-, ^ (Ni QC' r '. CO On C^ iH c^ <->j fvj u;5 J ^ vO O 00 CV.O o o o o o c »r\o ccVi> k-^ ^ 1»AC' o rO rxcv vu CO arH O .-O t^vO O c"\ c-i 0^ CO (^ PI • ('>0 VO VO lAr-i ^^^o C^ O 0-. -J r-l t'\rH (M ^ -^ (N C^ r-( r-. fH H r-< iH ri r-H r-< iH C) u-\ c>,' u\ CO Cn f'j w^ <\i kA ^ o iH <^; vo o M H J"'O C' C^ C \ (-1 H o fJ C-r^ u^ >rv t-^ v.'\ c> vo crr^ -;t w 1 r>.-« t: r-1 rH rH O O CO o >r( c•^ o ,-4 CJ CJ o o o o VL.' l^ -J vi^ oj H vo rH H iH I-) O O O O O G C-. O r-i r-i rl C^ o iH H cs; o^ c'l f'^ f ^ i-l rH rH f-t OOOOOOOOOO O O O O O O O O O O CO O C> C^ Q O O <\) ..-: rH r-J ^ ^ OJ J(^J rH O t\i ^ o"", r'N r\ H r-j c'\ f-. c^. c^ o•^ rH eg f^^ ir\sO C»-CO C^ O u^ u-\ iTi lr^ u \ u> u> »r> \r\ 'Xi r^r^lHHr^r^^^^-tHr^ ooooo oooo o o o rj c\i Jv\oc c^ ' t^ lA c^ :;:> o V) c 00 ./•\ CO o -o ^ r~ so c;n o < r-( f\> rA^ W^N3 t^ CO On O vOvOvO'-X^sOvOsCsOsD C^ i-itHHHrHfHr-fi-tiHr-1


60 O CD « H or"' ^ CO U o «; -H •v> W O 01 w ^ III c <^ K .•n t.-. f-. u: H C o 4/ « 3^ J) +-> <. C :-< fH w t.,1 0) c. ^ 1^ 0) it « <-> o c >^ x CO u; tg^; <^^ ^^ H vi> o f ; rH rj r(J^ DC! (V H r . ^ ^ S O O -3^ VO o H c o o o o «i) On OrH <5 \o UN r''* >A O O O O O O f-« O O O O 00 <'\ O -* C><^^ C^ O T) o f^, vr\ c\ c'\ H M r ( /-^ 1-1 ^ r-i -^ <--l rH isi i^ u~ >-i c^ > N-v k » OS M v^^ k.^ c ,<^ CO ^-i 3 O w N fv. crj o -;; ja o en c\ rH W \ v/ > vCJ -3C^ O CO t^^ J^ 'JT C 'Cn rH O r-1 H O O C O O r-< vO O CO CO 00 fV r-t H CV -t r»r, CM C ; C ^ r*v l'-\ O N --t 000(HHr-trHiHf:'0 OCVlO-OU^CVJCMOvOC^ u:'» o o> c: en cr. vo vO >n »n ^ J--r vr> _t_-+ ^ ^ ^t .-t o o o o o O H vO C-< _> CV r-l c' ^ c^ r\ c ;S o o o o c:> o o CO c^^r\^ cAco CM (^ H ^ ^ o r>j _j vTv rw^ 3 -^ cC' O O C. Cj O O CJ o i>j ^ mo o-N o 00 t>CT) o fv' .J c: r% («^ 0s vr^ r-) o o o o o rH fNi {X. ^ O C O O O r-t O f-ir-ir^r-tO-tt-^r-irir-i rH r-( O C I CO >^\CJ ^'^"^r1 » 4 J VO «A ^'^ H > r^< r. rH r-l H f-l C^cX; C"i NO fACX) 00 •X) O 0-C rH CNJ \C i-» «-« O CnI r fvj ,-( CJ O O CJ H rH r^ H a ^ C^ f1. UN rH «-< r-l rH rH H rH rH H rH r. ^ a' rHrHHHCiOOrHrHrH vO rH H C^ ""N rH CM rH VO CO r-t cv (^, W^, rH O O O O C O O CO ^ rH rH <"n1 00 rH t^ rNvO O O Ct; rH H H rH rt rH H OOOOOOOOOO SO P\C"J iPi rH r. NO nO CM CO O CM cn; ^ vrjNO -d^ r> r^-.O O O O O rH 1'^C) rH -4 rH rH H rH rH i-"A o o o 'r\ $f:' ON V '^i J rH O V"^ r-i CT' O O w->0 u-s t-u^ c^ vr-, ^ ^-c: '.. r-i O O-vC r r£»vr> vr C" ^? ^^. c CC r^ CNJ cn. -:i r \ C^ f . ^ -:r -:! JJ '"\ 3 cnI^ r-co o c» o o o o o O C' O r-NONrH C^ H O: rH 00 \f\ tV N c; r~c^ -:t ^ (^ o> H OOQOOOOOOC5 OOOOO C~cv ^ co cn( CN ctn -yo) NO r , ir> NO c> ^ Ox rH -^ <«^ 0-^ (-N -f ^ u^ ^ ^ ^ u-^ 3CO C^ C^ On rH . CO On O o: ?. o; cc cjC 00 oo CT. CO oc H r-i r-i r^ r-i r-t r^ i-t r-i rH CV C^^ •A UN cr> (7N ijN 0-rH rH rH rH H


61 t g ^ (!' »\ CO o I'J OC. cs .1) <> f -r 'X' c c^ fN .-^ f C; t>e o f JIh ri r~i « • • • • o X O O iH r-l rH o c 6-< C 9) V c *•• ^ ia p c O ii. <.^ t) a H li f-o c> o * k • On o O, on u? ov O c^' (I rj r\? r\ C; Vf , 0> r'\ tM vv r-t ^vo o; CM t«. i-t o 00 H r » vr> .;ju^ ^ to (M «n r-c Jt ^ t^ c^ vo c^ r^L (.J o o o IM r-l r-t VQ C^ V) t-i <"^ nO a. r-^ Ow <. o; > . o c; o c. c> ooooooooo (• _i ir\ \j~\^ r-u. m o «• CO w-^ , u'\ vr\ C^ CO r^ o u^vO »^^ <\t oT CN PJ C^ <^> V N r-i -3 f , vr> OJ _i -J CO vO vA -1 o o o o o crN >AvO CO rH f-t pH fv. u> u"\ u"^ ir\ u^, O C; O CJ CJ O o COO»-^l-^^HlHr-t^-! uA C\ "v; -y vr\ c'\ ^v; c^ o CO t.rr o o c^^ r o < > o o o o o o o o 0) c ctt U' * r. -•-1 On r^ C\ cu fA C-rA rj a« (~CC o IT! '•I rt; H ^4 o C> c:> r-l C'> (, (V v^^ r-, M 0.. -J vO or. i-, '.n s: rH rH iH . O ON aN vi"ON o r^ H H l-( fNJ O O O H r-l H f-l H r-( o; in: t\i (\i i\i fv: iNj o.'•J r< (M c^ NO \o r • r \ ^ -y cN c ^ o o o o o c> o o VN. vo t^ OJ vo '-f vO r-t cC5 c o r\ V tNi ^ ^ ^ (\; rvi 0^ c^i r-*

o u ^3 f^ r r> r^ r^ cc o o C^ CO ^ H f' O — * CO C^ ^ ^ C> O'.C^l C-i r-i r-i r-* r-i r-{ r-t •f^ V 1 C tk: o t^ o cj CO f-. i. kTN C^C^ (J^ O O ^. m a: ^ (^ c-1 r^ f'v ^ -a H C • ^ aa oS Cvl (\» CM f^j cvj Ovj eg


63 the log me.m temperature difference are not tainslated since only the end result is of significance and the procedure is straight forward.Q« Anal / sis qf Result s The discission in this section vill be limited to the general reasonableness of the calcjlatarj resi'lts and a complete analysis of the interrelationships of the data will be presented in the overall discussions at the end. A^ stated previ(''ui5ly the consistency of the data will be indicitted by the def^ree of applicability of the well established methods of correlation. In res^arr! to the experimental accuracy involved in these measurements it can be stateii that effort was made to obt'iin a reasonable ntimber of significant figures at all times. It is well established that even under ideal conditions and vdth extreme care heat transfer correlations may have deviations on the order of 20%, This cannot be interpreted as legitimate reason for careless e>:i>eri-'nental technique but does justify the use of slide rule accuracy in computations and measurements. However* particular care roist be exercised In measurements that involve detennining small differences of relatively large numbers. Thus temperature measur«anents were accui*ate to four significant figures or a tenth of a degree fahrenhelt. Temperature differences of 10 to 100 were thus accurate to three significant figures while those below 10 vere accurate to two significant figures. '^?o temperature differences were encountered sirallsr than approximately Z'^F, It is in the evaluation of the tube surface tenperature that the greatest error may occur, firrors are introduced due to the tmcertainty


6U of the position of the wall thermocouple with respect to the ternperatm-e gradient. The teraperature drop across the tube wall was relatively large riue to thp lov thf^rmal conductivity of the stainless steel and varied from 3° F. to as hirh as *-^C° F. Corresponding differences between the tube surface temperature and the bull: fluid temperature were perhaps ^4-0° F. and 20° F., respectively. Since the tube surface teir,peratvu-e u-as found as a function of the total wall temperature drop and the drivin'-' force temperature difference vas then found by difference betv.'een the tube surface temperature and the fluid temperature, it is evident that any error in tbe tube vail texperature v/ill produce an error inversely proportional to the ma^itudes of the temperature drops. Thus, an error in the 3 ?" vail temperature drop would produce an error only T^ as great in the kO F. driving force temperatiire difference. On the other hand an error in the ^C*^ F, wall temperature drop would produce an error -^ or 2 times aj great in the 20*^ F. driving force 20 temperature difference. Efforts were made to ef.taibli.'sh the possible error in the location of the wall thermocouple with res.-^ect to the te.-iiperature gradient. It was concluded that the maxi-num exi^ected error was on the order of 5.0'^. Thus, under the most extreme conditions the maximum error to be e?rpected in the temperature difference beti/een the tube surface and the fluid v^'tjij) was 10.0 >, An approximate evaluation of the error in each run may be made by dividing the heat transfer rate, q, by 221 times the log: mean temperature difference. Usin

65 transition region the error varies fror. t 1,0;^ up to t 3.5-;^ and in the turbulent repion the possible error may increase to 1 IC.O^ at the very high Reynolds na-nbers. The fluid flow measm-enents v;ere accurate to = pound and ~ 2 10 second. The weight of material collected wa.> usually around 100 pounds but at very low rates was occasionally as low as 20 pounds. Thus, the weight measui^enents had a maximum error of pound in 20 pounds or 2 2.5:^. but was usually on the order of 0.5^. The time of collection of the fluid was never less than ICO seconds. The maximum error in these measurements was therefore 0.1^, Usinp; the exioerimental heat transfer coefficient on the fluid side, the thermal properties of the tube and the overall temperature difference, values of the steam side coefficient were calculated and found to be on the order of 1000-2000 3TU/(Hr.) (Ft?) (°F.). Such values were considered ouite reasonable.


CHAPTER III SiECIFIC '-EAT irrViSTIOATIOXS AND R^^SULTS A. Backgrouq H The specific heat as well as the other properties of the black liquor should be known as a function of temperature and solids content in order to have sufficient information to use in conjunction v.lth heat transfer equations. The literature contains v^ry little inforrriation on the specific heat of sulnhate black liquor. Kobe and Sorenson (l?) determined the specific heat of sulphate liquor from the of western hemlock. They used liquors of four different solids content over the range of 77 to 200 F. The results were correlated as mean specific heat as a function of solids content only, there being no api>arent correlation with temperature indicated by their data, Stevenson (3I) gives a value for the opecific heat of black licuor solids as 0.23. The same reference also gives values of specific heat of black liquor solutions of various solids cont°nt. These values are equivalent t*-> the sa-n of the component parts on a weight fraction basis wherein the srecific heat of black liquor solids is O.5O and water is 1.00. At least one other value for black liquor solids is in common use, namely O.^k, 66


67 The literature contains nvunerous methods of determining the specific heat of liquids, many of vjhlch are modifications of the classical methods. The jnethod chosen for this work was similar to thst given by Williams (32) and was selected because of its simplicity. This method is ba-^ed on the mensurement of instantaneous rates of heating and cooling' during alternate heating and cooling periods of a sample in an insulated vessel. Kobe and .Sojrenson (1?) measured the average rates ov^^r a 10 interval in a similar apparatus. B. Arparatus The apparatus is illustrated in Figure 9 and is shown diagramma tically in Figxire IC. The sample vas contained in a 2C0-ml, Deuar flask fitt.-d with a cork stopper which was covered vith aluminum foil to prevent '.%'ater absorption. The heating element was; a coil of 20-gage Chronel "A" resistance wire, ihis v.-as contained in a small ^-lass tube bent to form a horizontal circle of 1 -^ in. diameter with tho two ends of the tubing ext -ending up into the bottom of the cork stopper. The external copper wire leads extended all th-; way into the heatinf^ coil in the circular portion of the tubing. A glass stirrer vas centered just belov' the he.itinr element and rotated in a glass tube bearing in the cork, A 3C-^are copper-constantan thermocouple was held firmly between the cork and the flask and extended into the center of the sa^mple. Sealing wax was used to seal arotmd the heating element and stirrer bearineopenings in the aluminum foil. Although it softened during each use it remained in place and formed a vapor-tight seal. The entire api aratus vas set up in a room maintained at the constant temperature of


cd o •ri O « 0\




70 72° F. i 1.0° F. This enabled equilibrium conditions to be established v.'hich otherwise woxild have been im}-)Ossible v/ithovit the use of an additional insulated vessel surroundinr the Dewar flask. The heating current ivas supplied by a 6-v. lead stora^^e cell of which usually only two cells v;ere used giving slirhtly less than ^ v. The voltage was measured by a calibrated General Slectric voltmeter accurate to C.Ol v. The current was measured usinga General Electric tnillivoltmeter across a j-^i^I • • 200-rTv. s?unt, s<.nd was accurate to 0,006 anp. The temperature v;as measxu'Hd using a Leeds snd Northrup potentiometer. Type 5662, and plots of temperature ver.sus e.if.f. taken from the datci in the I.C.T. by Adams (l/. The temperature measurement? vjere accurate to 0,05° ^« C. pe rivati on of E q ua tions The ba.'dc equation of calorim.etrj' foi* a batch system is, Q = WC AT, where Q is the heat added to a sample of weight, W, refiulting in a change in tenperstur*-, AT, and where C is the heat capacity or the specific heat referred to vmter at 60 F. Since the heat camcity of water at 60° F. is 1.000 3TU per pound per °F., the specific heat is numerically equal to heat capacity but has no units, IVlien heat i« added to a syster.1 which includes a calorimeter vestjel a portion of the heat is absorbed by the vessel and some is lost to the surroundings due to the teiTi]>erafure elevation of the apparatus above ambient. The equatlc^n beccxneii Q = f^ + (C.K.) ] AT +F^ (34)


71 v:here C. T. is the calorimeter equivalent and includes all the heat requirefnents of the system other than the substance uncieistudy and H, is the heat loss.. Eqvuition (3^+) expressed differentially as a function of tLTie beccxnes where TT" represents the rate of heat loss to the suiro>jnding.«r , Rnd is dependent on th*-teniperature of the deten-iination. Thus at any temperatuj-e level, if the heatir.<; is discontinued, ~ = 0. and — h may b« d© dO ' deterr^ined as §'KM=..,]t (36) where the subscript o designates the no-her.t poriocS. Therefore,;] [S. .||] (3,) de wherein C*K» is detomint^d using in the apparatus; a material of known specific heat, the rate or" heating is determined from acciu-fxte electrical ir.easuranents during the heating period, and the rate of change of temperature for the heating and coolin.^ peiiods is deterrdnec^ from the slopes of accurately plotted temperaturetime data. D. Ex^-.erin^ ental I^-or-edurfi Samples of various solids contents were prenarf^d by dilution of a concentrated liquor sa;-aple and v;ere e->ecked by drjdng at 105^ C. a STTuall quantity which vas absorbed on asbestos in a porcelain crucible. The procedure followed in makire a test consisted of the


72 following steps: (1) A sample of knovm solids content was added to the tared flask and accurfttslj weighed. (2) The apparatus was assembled and the heating current was turned on to bring the entire system up to the desired tempers. ture T. The heating current was reduced and a half hour was alloved for the system to attain equilibrium at T. (3) The terr.pere ture was allowed to drop to 3 to 4*^ below T and the heating current was a

73 / / / / / J / / \ / ?. ^ O o 1 ^, 1 ^ \^ 1 ^ N, 1 / *^ \ / 1 / r / / / / * \ \.. 1 V ^ V u V ^ — ^ ^ ^ <§ 0) a to u 5 w pl a> C^ cv p 3 to c c •H ^ o Si: •^ * o c o F CO •H Tl H H c 05 vn c H •H •H •^ 'aan^jBJsdwax


74 The slopes of the heatinc; and cooling curves were determined and average values of the most consistent slopes were used in the calculations. Ej« Data Table k contains the tabulated average heating and cooling curve slopes and the rate of heating for rmis made at solid content percentages of h,n^ 9.?, 13,h, 21.6, 32.2, k2,h and 52.6 and at ter.iceratxares of 100, 125, 150, 175 and 200° F. The data used to plot the heating and cooling curves were considered too voluminous to be included. F, Sample Calc\)lations A typical calculation for a 270.0 gram (O.596 lb.) sample containing 52. 6::^ solids at 150*^ F. is shown as follows: The rate of heating by the electric current was found from the equation 4i« 0.05692 3 I (38) where E is the voltage, I is the amperage and the constant is the nunber of BTU/min. equivalent to one watt. Thus, with 3.6^ volts and 1.53^ ampers the rate of heat \ras ^ = 0.05692 (3.64) (1.534) = O.3I8 .3TU/min. de The rates of tempersiture change during haating and cooling at 150° F. were deterrdned from the slopes of the curves plotted in Figure 11. Thus,


75 -.9 '".2 la.v 21.6 32.? t T^rar'eratur :• ^ :r;F: . V » / (Ib.s.) ICC O.i.85 ICO n,US5 1.-5 C.Ufis 125 C.U35 15C C A% 130 C.'iBS .500^ 100 < .^S5 100 o.iic.5 125. O.^fH l'-5 0.'.'".5 150 O.ic. 130 0.'495 175 0.-95 375 O.J^95 200 O.Un^ • 2C0 O.ifS-5 100 0.319 100 0.519 135 0.519 125 0.519. 100 c .508 100 C.5O8 125 C.5C9 125 0.503 150 0.503 150 C.<08 175 C.5OS 200 C.5C8 200 :.508 100 C.'iOO ICO 0.^30 125 c.^30 125 0.530 150 C.530 150 0.530 175 C.5-5O Heatinr 'e-^tisr ^olin?(:3TI/Jiin.) 0.3295 C.3;:?9 C.3252 0.3250 0.3230 C,?2''0 0.3135 0.3i;56 0.3'^ 56 C.3^5 :. ?U3 c.3iilP 0.3-'j56 0.3^56 0.3^132 0.3/11? C.3309 0.3239 0,3270 C.3250 0.3516 C.35I6 C.3403 O.'i^CS 0.3393 0.33Q3 C.3357 C.3337 0,3357 0.-607 C.3609 0.357^ 0.3579 0O537 C.3537 C.3523 C^F./Min.) (^F./Hin.) 0.5^5 . '•6'*. 0.^56 C.35C C.3bl 0.122 0.5r>i,0.591 C.527 c.530 C.Clj 0.:.21 C.32I C.316 0.182 0.130 0.571 0.567 0.';35 C.'-67 0./-3 0.'>.6 0.530 C.5';2 C.ii26 0.^'«2 0..?f6 C,12C 0.139 0.669 0.662 C.56C 0.564 0.i;70 0.459 0.352 0.053 C.O53 0,1^--: C.ii,3 C.230 . >*') ?. C.058 0.057 0.128 0,130 cay 0.221 0,31.-:; C.326 0.46^ C.C50 0,060 0.1-^2 C.I35 :.05if o.O';6 C.1U5 0.142 0.234 C.231 0.36I C.513 0.5I8 0,054 0.056 C.152 0.144 C.2i42 0.234 0.350


!(> TASL'^ : — Continued 5c 1 id:" Content Temoerature ''.-ISf, of Sanrle Hfstinr Rate of Ter' Heatinr; rer^ture Change (.0 ^2,^ ',1.1 171200 2CC 100 100 123 l.':5 15c 15c 175 175 200 200 100 100 125 125 15c 150 175 175 200 200 (Lbs.) .' .530 C.53O :.552 C.552 C.552 C.552 0.S52 c.552 c.552 c.552 c.552 c.552 C.596 C.596 0.596 C.596 0.596 C.596 0.596 c.596 c.596 0.596 (3ru/Mip.) C^F./Min.) C.3523 c.350t| C.3504 0.3075 o,30?3 0.3666 0,3652 C.3658 0.3658 C.'^639 C.3639 C.363I C.3623 0.3329 C.3266 0.319^ C . 319'i C.3I82 0.3170 C.3I55 C.71J0 0.3109 C.^103 0.350 0.199 C,223 0.567 C.578 0.623 C.6^2 C.525 0.529 C.^Oi* 0./il5 r.263 C.2S1 0.61^4 C.632 C.5it2 0.539 C.ii52. 0.3^6 C.339 0.202 0.203 (^./Kin.) C.357 C.ii6C 0.05'0.057 0.129 0.125 0.220 0.216 0.328 0.31a C,0h6 C.QhS C.I23 0.121 C.2C3 0.203 0.298 C.295 0.419


d0 77 = O.V+i4 °F./min. fis = -0.203<= F./min. de The calorimeter equivalent, C.&., was determined using pui'e water in the system. This valtie was 0,0655 3TU/°F. Therefore, by substitution into equation (37) 0,318 = (0.596 Cp + 0,0655) (O.WW; + O.203) Cp = 0.717 3TU/(lb.) (°F.) at 150° F. G« Calculated Results and Discussion The calculated resxilts are tabulated in Table 5 for the range of solids content from ^.9 to 52, 6y^ and for temperatures from 100 to 200® F. The values of specific heat in the table are averages of two determinations. The maximum weight loss due to evaporation was on the order of 0,2^ of the original weight of the sample and did not affect the results. The data are shown graphically in Figure 12 v/hich is a plot of specific heat versus the per cent solids with temperature as a parameter. The specific heat was found to increase with increasing tenperature and to cecre&vse with increasing solids content. This is entirely consistent with the nature of all the organic and inorganic constituents of the black liquor and shovild, in fact, continue in similar manner beyond the range of temperature and concentration studied. An empirical equation was sought to fit the data and relate the


78 © 0-. o 00 ^ vr\ r\ r\ be n $ § CO E^ ^ M * • t • • * • «J c:.' O o o o o o ^ u"^ it o-> CM r^ vn, O o so , ^ ^ g: r ? fM • • • • « o o o o o o • H H l-l CO C^ U^ •^ ^ «\i CO H IV r. (7^ o 00 t^ IN ^^ tj\ H • V » o O • o o o O o «: H H .J Q S J H E•*» g| to o >r\ ^g o P^. C^ * CO o o cv • 4'.^-^ Cd (X. ft. ccr • m GO • ^ ^f 5 ^U C-o • o o o o o bJO a, <: C r-» H CO tn fc5 -J•O 1 ^?; u-> OC' o Fl K^ 00 o o H o c^ o S rj oa OS OC re rr -3 ^^ t-. iH • • • * « • • c o o o o o o o o o o (ti • §^ O n s^ s ^ H cS o o CO •> X O c aCO CO CO c^ f^ ^ >>o r-» « • « • « * ^ C' o c> o o o c; o 1/! tt « Tj a Oj ^ vD CV} ^ t^ o S II r-i « • • * * • • -;! fH J (?N 00 ri ir>( r\. (SJ o <8 l-i OJ f^ ^ \r\ o H > a,


•H (^ o % P n) c 0) c ffi o «M (X, O CM o H r\ a> ^^^11 3Tfjfoads


80 specific hf?at, Cr , to noth tempers ture, T^ F. , and the solids content as the weight fraction, C. This eouation was found to be Cp = C.9^C 4S.C X 10"% (C.<39 6.i. X 10" 't) C . (39) and is shovm a^ the solin li^ie • '..n Figur-? 12. In dealing ^;ith a series of calculations wherein the tcnperature range is not too large or if for si.T.plicity an av^rare value is desir?id at a particular temper'j ture level the equation may be sL-nclified. For iniitance, at 200*^ F, equation 39 reduces to %C.O^ F. = ^'^^^' ' (".511) C (kO) wherein Cp is a function of solids content only. The equation for Cp as a function of T "nd C has been used to errtrapolate the data to the lOC,^ solids axis as shov/n in Figure 12 by brokt^n lines. These values of Cp are tabulated in Table 5 as a b . 1 . '=^ . function of ter.perature. The method of calculation used in most of the kraft mills consists of assvrniin.q; a str^ir^ht line relation between pure vater v.ith a Cp = 1.0 and black ] iquor solids of an asruned Cp, , valu?. This b.l.T. relation is Cp = l.OC (1 Cp^^^-^^„^) C (iil) and is used irrespective of t-^nper.^ As stated abovr-, Stevenson (3I) gives two values for Cp, , , namely C.P.8 and C.5C. These values are o . i . s . in use in the mills as veil a? another value of C.3i.. Equ&tion 41 is


81 plotted in Fi^re 12 for the Cpj.^^-j^,^^ values of C.28 and C.'j'.. The line for Cp^^i^.,^ of O.5G falls approximately on the 200° F, line of the present data and was left off the jlot to maintain clarity. The results of these experL^-ient-i indicate that at the temperatures u.3ed in evaporators (I60 to 265° F.).only the value of Cp, , = 0,50, of the ones currently in use, gives nearly accurate results. However, this yields values wnich are too low at the higher temperatures which are necessary at the higher concentrations. The eri-or involved in using one of the lover Cp, , values will naturally increase even T.ore at the hicher concentrations. The data of Kobe and Soren'^on sre plotted in ?igurs 12 using their equation, Cp = C.98 0.52c (42) This sins;,le line represents the average of data obtained over the range 77 to 200 F. Their data indicated no correlation with tempera tui-e and pave considerably lower value? than the 130° F. line which is the approximate 'avera^^e of the present data. On the ba-is of the present data the corr&lat.-on of Kobe ; nd 3orenson gives values much too iovfor the temperature conditions used in evaporators. If equation 3?. which relates Cp as of function of T and C, can be assumed corr-ct over the ra.-e of temperature studied, it may b, used with due reservation, to extrapolate the data beyond the ran^e obtainable in the laboratory apparatus at atmospheric pressure.


82 The straight lines in Figure 12 indicate that the specific heat i? linear with the solids content when temperature is fixed. It follows, that these data can be represented on a line coordinate type nomograph. Figure 13 is such a praph and may be U5;ed more conveniently than Figure 12.


83 1.02 T1.00 . .98 _ ,96 . .9^ .92 .90 _ _ .88 . .86 . .m . .82 . .80 . _ .78 .76.72 .70 .68.66.64 Speci fie Heat ,0° Temperature, °F. ^60 --50 --40 --30 --20 --10 lo Per Cent Solids Figure 13 Nomograph for Specific Heat


CHAPT2R IV THiiH'IAL CONDUCT IV ITY IW^STIOATICIB kim R^,3ULTS A» Backgro^jnd >. thorout-h search of the literature revealed a complete lack of therr.ial coriiiuctlvity inforrrLation or. sulphate black liquor. It is necessary to know values of thermal conductivity at various temperatures aad solid concentrations Ln order to interrel^ti--* the heat transfer data. Sakiadis and Coat=s (2?) surveyed the literatijre and compiled all the available thermal conductivity data on or|-anlc liquidT, inorganic liquids and solutions of various liquids. They critically evaluated the data and gavn ratinp-s of excellent, very g'X>d, fair, etc., based on the methods used, the precision of measureiT,?nt and the general aj^reement with other data. Although these data do not include black liquor it was rossible to determine the freneral range of val-ues to be exi:>ected» Most organic and nonmetallic inorganic liquids have ther-nal conductivities in the range of C.C5 to '-"..IS 3TU/(Hr.)(Ft?)(°F/n.). Notable exceptions ar6 antnonia and water which have values around -.3O to O.i+0 3TU/(Hr.) (Ft;)( F./^t.). Jakob (13) states that in general aqueous solutions conduct heat less well than water and that their conductivity decreases with increasing concentration. The data compiled by oakiadis and Coates for aqvieous solutions indicates that this is usually true. Hov/ever, 84


85 aqueous solutions of sodium compounds freouently show the reverse tendency. Thus, solutions of sodium hydroxide, sodium carbonate, and sodiun sulphate shov; increasing conductivity with increasing concentration. Other soditim compounds showed either constant or only slightly decreasing values of conductivity with increasing concentration. All aqueous solutions of organic materials had conductivities which decrea.-^ed rapidly with increasing concentration. The effect of temperature on tlie conductivity of various cowpounda cannot be generalized. However, water has a positive temperature coefficient up to approximately 260° F. Stevenson (31) states tliat most of the alkali in the black liquor is present as sodium caroonate or as organic sodium compounds with chemical properties very similar to sodium carbonate. The greater part of the organic matter removed from the wvX)d in cooking is combined chemically with sodium hydroxide in the form of sodium salts of resinous and other organic acids. In the sulphate process, appreciable amounts of organic sulphur comjx>unds are present in association with sodium sulphide. The rest of the alkali is present as free sodium hydroxide and sodium sulphide. There are also small amounts of sodium sulr.hate, silica, and minute amounts of other impurities, such as lime, iron oxide, alumina, potash and sodium chloride. The proiX)rtlon of total organic matter varies but will generally be within the limits of 55 to 70 per cent of the total solids in the black liquor. The black liquor used in these experiments was analyzed and foiand to contain 7C.3/J organic matter in the total solids present. From the above considerations it was apparent that the themal


86 conductivity of black liquor '.-rould begin at low concentrations at the conductivity of water. Further, since black liquor is largely organic, but since the inor?:anic material i:3 composed largely of sodium compounds it was supposed thst the conductivity would decrease moderately with increasing concentration. The literature was' studied in an effort to find the best available method of determininfr the conductivity. This study failed to reveal any unanimity in the methods ns^d in the past. Sakiadis and Coates (28) have reviewed all of the published methods and have investigated the various factors in the c'e.dgn of therm^J conductivity apparatus. Their survey disclosed that mo:-.t investif;'£tion.s reported in the literature were made— . . . with apparatus involvint; heat transfer through thin films, of the order of a few hundredths of an inch, to eliminate development of convection cur-rents. However, this practice limits the accuracy of the deterr\ined coefficients. A scirvey of investicrationr. i-elating to heat transfer mechanism indicated th&t the development of convection curr^-nts is dependent on the direction of heat flow, temperature drop across the film as well as liquid film thickness. Their experiments x^ere designed to determine the existance of convection currents in horizontal thick liquid layer? when heated from the top. Their results proved: . . . that no convection currents develop in V.orisontal thick layers, of the ord?>r of one to two inches, heated dounward, . . . Convection currents were found to develop during heat transfer in thick liquid layers when heated from below by horizontal surfaces, and by vertical surfaces. An apparatus w^s desic-ned incorporating the alxjve conclusions and the best features found in other apparatus reported in the literature. (2, 2, ^, 12, 2

87 moderately thick horizontal iiruid layer. A layer thickness of one eighth of an inch vas considered to be well vithin the safe limihs for pure conduction and \^as also thick enough for exierimental accuracy. Thennal conductivity is expressed aa qusnlity of heat floving through a unit thickness of material per >jnit time per unit area and per Uiiit tc.Trerature gradient. Tho quantity of heat flowing is the only factor that causes any real lifficulty in rnr-asurf-.Tient. To avoid the actual meisure-nent of ih^ he^.t flotin:it vas decided to use the temperature drop caused by a quantity of heat fioving through a material of known th-rinal conductivity as ..n indication of the rate of heat flov. 3y arranging the heat flov^ in series tlrou^ih both the material of known conductivity and the test materi-d the s^me Quantity of heat would flow through both. The ratio of the thennal conductivities could then be ex-pressed as functions of the temper-iturs drops acrors the two I'^yers. Very reliable data are available on the thermal conductivity of water at t^mperatur-s from 1;:0 to 200" F. This material w^ns chosen as the standard and all therm.-^l conduct Iviti-:. v.erc determined with reference to it. 3, Apparati^.q Th.? assembled conductivity apparatus is sho:^ in Fjgure 1'^. The large box in the center of the i icture contains the thermal conductivity apparatus which is shov,-n in Figure If. A dia?rainatic view Of the assembled apparatus is shovn. in Firura 16. The apparatus shown in these illustrations consists, of an infra-red la.T,p which served as the


•H I


Figure 15 Themal Conductivity Apparatus out of Insulated Container


90 f> n * TJ r-l « ^ 3 m 3 « CO cr c »-H M OP ^ ^ m +> o » 0) oJ cam e a> J3 X H to .g m "O B 0) m oi 0) JQ a n h < «M


91 heat source, the insulated box which contained the main thermal conductivity apparatus, an internally cooled plate on vhich the apj:.arc'tus rested, a constant teTm-erattjrft ^J.-i^p^ or oil batl-, a circulating piunp, thermocour-'les and a poti^ntiometer. The radiation from the infr^-red bulb var. absorbed by a brass disk six inches in ciarneter and -4 of an inch thick which vas attached to the lid of the inj-xlated boy. It vas coated vith black crackle paint and thus had a high absorptivity and was of such thickness that a uniform temperature on its under yide could be assumed. The under side of this disk reradiatec to the toi. disk of the thermal conductivity apparatus which was approximately three inches away. Both of these s'jrface.'; were also coated with black crackle raint . Thus a uTiiform tempei'aturft of the top disk of the main apparatus was vertually assured. The irain apparatus was embedded in foara glass insulation with the exception of the t^p disk whirh had to "see" the under ride of the heat source The main apparatus which is shown in Fip;ures 16 and 1? was constructed of brass which was heavily coated v.ith nickel to prevent corrosion. The apparatus consisted of three brass disks, the lower two of which were actually bottoms of shallw^ cupy. The sizes, which are show in Firnire 17, were adjusted so that the three tieces would nest vith one eirhth of an inch clearance all around. The sides of the cu]>s vere made of very thin brass and served to retain the liquids in the spaces betvreen the disks. The sides were made higher than necessary, for retention of the liquid in order to provide insulating air spaces which would retard possible heat loss from the sides. Small pieces of plastic were used as

PAGE 100


PAGE 101

93 spacers to adjust lh» vertical distance between the surfaces to one eighth of an inch, ''oles were drilled fror. one side into the centers of each disk and snail brass tubes were inserted just large enough to receive the "O-^aupe copper-con stantan therniocour-los which vere used. The thjree assembled disks rested on top of a core'' briss plate through which a fluid of regulated temperature was circulated. Good met:d-tometal contact was insured by very accurate grinding and lapping of the two surfaces. The pattern of flovr of linuid throunli the cooling plate was so as to insure a imiform temperature at ever;^' point on the surface. This was accomplished by havinf the fluid circulate toward 'he center and out apain in concentric spirals. The coolinc fluid wa^; circulated with a sm^ill laborstory pump. A constant temperature bath was u<^ed to maintain a supply of cooling fluid. The fluid used was either water or oil depending on the temperature to be maintP.ined. • C. Df-rivation of Sgu^tions The relationships used to calculate the thermal conductivity of an "unknown" liquid v.ere derived from a knowledge of the thermal conductivity of water which was used a? standard, the dimensions of the apparatus and the thermal conductivity of the brass. Denoting the areas per]: encficular to the heat flow at tne oottcan of the top disk as A^. at the top of the middle disk as A„. at the "bottom of the middle disk as A^, and at ths top of the bottom disk as A. and letting Xg, X^ and X^ be the respective disk tydcknesses and X and X, the upper and lover liquid layer thicknesses; an ex^^ression can be

PAGE 102

9^ wri tten for the heat flow across each liquid. Thus, \2 = "12 \2 ^\2 (-1^3) and q34 = '3U ^U ^V (M) where q. and a. ,^ are the rates of heat flov. "12^^ ^'^ are the overall coefficients of heat tran; fer, h2 and A^^ are the mean heat flow areas and At^^ ^"t^ ^S^ ^® "^^® temperature drops across the liquid layers plus hilf the thicknesses of the two adjacent brass disks. Those equations may be rearranged and written in terns of the in-Ji-zi Ju..l heat conduction coefficients based on the mean ar^.as. ^1 o U 12 ^12 ^2 •^a h ^M \2 \ ^ '^ + ; f~ + _— J2 (^5) At„, 1 (0.5) X^ Xi (C.5) X — — --'''+ •: + — ., .... . — X -^ 34 3^ b 3 ^ :i^ c "; Using the dimensions given in Figure 1? the follov-i.v-r values were determined : \ '^ h ^ ^'^^5 in. = O.OlUl ft, \ ~ ''b " ''c ~ '^•3125 in. = C.C2605 f., A^ = 19.63 s^;. in, = 0.136it sq. ft. Ag = 21,60 so. in. = C.I5OO sq. ft. A^ = 22.08 so. in. 0,153^1 sq. ft. A^ = 2.1 ,20 sq, in, = 0,1681 so. ft, i „ 0.1'(6i, + O.lcAO \2 = '—J *"" ^ °*^^^'' ^''' ^^' A^. 0.15?^ + r .i6fiT „ T,-Q /*3il ^ , = 0.1603 sq. ft.

PAGE 103

95 The exact conposition of the brass was unknov.-n but a reasonable value for its thermal conductivity (23) was assumed. Thus, ^a = ^b = ^c = 65 BTU/(HrJ(Sc. Ft.)(*'F./Ft. ) It was assumed that all the heat passing through the upper liquid would pass through the lower liquid. This was reasonable due to the insulating effect of the concentric nickel plated sides of the cups and the surrounding foam glass insulation. The fluid used in the cooling plate was also circulated through tubes located in the insulated space so as to maintain an insulation temperature near the desired temperature of operation which at tines was 100° F. above ajTibient . Based on the foregoing discussion, q,2 was assumed equal to a^. Dividing equation ^5 by equation ^6 and inserting all known constants there results, (C.5) (c. 02605) 0.5 (0. 02603) ^\2 ^ (65) (c.i:'64) "^ k^ (C.1M3) "^ (65) (C.15C0) ^^34 (C,5) (C.02 605) ^ c.oiUi ^ (c.5) (c.02603r (65) (C.]53^) k3^Tc.l608) (65) (0.1681) 0.098^ ^^12 _ 0.001U68 + k^ + 0.001334 '^*^-C. 001306 + 0.0878 + 0,001192 3^ ^1 At 0.0984 ^12 0.002802 + — iT— " 34 0.002^498 + 0.0878 This equation can be further simplified by consideration of the relative sizes of the two terms of the numerator and denominator. Assuming a value for the liquid thermal conductivities of C.30 the

PAGE 104

96 eqxiation becomes, ^^1? _ 0.002f}02 + 0.323 At^i^ ^ 0.ro2i^93 + r,.293 " * By neglecting the smaller terms in the numerator and denominator the ratio becomes ^^12 _ C028 At3^ " 0.^92 " '*'''' Therefore the terms in eouation i*7 representing the cr;-,dv)Ction through the brass may be nerylected and the simplified equation beco»nes ^!H = l!l^8^L^l = 1.122^2. (48) ^V (0.0873T\ \ D» Syt'rimental frocediire Sauries of "olack liquor of various solid contents were prepared as before hy dilution of a concentrated sample . Before each run the nickel plated sxirfaces of the three i>arts of the main apparatus were polished in order to maintain similar fiL-n properties and emlssivities. A measured quantity of one of the liquids to be used in the apparatus was added to the lover cup. The amount was just sufficient to cover the three small plastic iriacers. The middle cup was carefully placed in position in such a v;iy that no air coiild be trapped underneath. A similar procedure was follov;.>d in adding the other liquid and the top disk. The level of the liquid in the annular spaces was checked and any excess was withdrawn if necess iry to prevent the level becoming deeper

PAGE 105

97 than between the plates. For high tender ^tvrs runs more liquid was r'-;moved '"ror. the annular srace so that \fter h.»atin3 the expanded liquid Wv-^uld have: a depth of approrrimntply one elf nth of an inch. The top of the mnulir spaces was partially sealed by nreosing alutninutn foil over the openings. precaution was t:'ken to prevent evaporation of any of the liquid siimple-. If evaporation did occur it would soon result in hir bubbles betv;een the plates v/ith .i correspondingdecrease in the conductivity across the licuid. Such an occurence would be rapidly detected in the temperature measurements. In sone of the earlier runs it v.'^:; noticed th£it even when little or no evaporiition occ-orred air bubbles were formed in trie water layer if the water had not been properly deairated. (^oneequently, the water was always boiled just prior to u.^ing it in the JAr bubbles were never found in the black liquor layer. The thermal conductivity assembly was placed in the insulated box on top of the con'=;tant temperature platen. The insulation was arranged, the tVu-ee thennocouples were installed, the top was placed on the box and the infra-red heat lamp was positioned vertically aVx)ve the black brass disk in the box lid and was turned on. A cylinder of anbestos paper enclosed the i^th of radiation and prevented convection currents across the face of the disk. The constant temperature bath was regulated to a ternperature lust bolow the temreroture to be maintained in the test liquid and the circulating puiT-p was started. The values of e.m.f. produced by the thermocounles at the centers of the three brass disks were measured over a period of time until equilibrium was established.

PAGE 106

98 The time for equilibrium varied from a half : our to tvo hours depending on the tempera tiire of opera-tion. Once constant readings were obtained over ? period of 5t least an hour the run was comv-leted. The relationship between temperature and e.T. r. for the thermocouples was approximately linear over a short tempera L'-ire range. Therefore, the ratio of e.r.f. differences wis used in equrition k8 instead of temperature differences. This procedure eliminated the introduction of errors due to conversion of e.n-..r. values to temperatures. CalibratiDn of the apparatus was a.ccompli>3hed using water as the upper and lovjer liquid and with ethylene glycol and glycerol in conjunction with water. Values of thermal conductivity predictec using equation k3 showed maximum variations on the order of 2,0,?^. No difference wa=5 found in values by interchanging' the upper and la»rer liquids. Thus, for consistency, water was used as the upper liquid and black liquor was the lovjer liquid. E. .. Data The experiniental thenaal conductivity data are shown in Table 6. In columns two and three are tabulated the average temperatures of the black liquor and water layers, respectively. Column four shows the average of the ratios of the e,y.r. differences ror the water layer over the black liquor layer. The averages in these columns are for all measurements; taken durinn the period of equilibrium which may have been an hoMT or more. Column five has tabulated the values of the thermal coriductivity of water at the average temperatures of column three. These values were taken from a graph in the Appendix which represents

PAGE 107

99 T.^SLS 6 EXPERU-ffiNTAl, /J.'D CALCLXATSD TFEff'.fil, CONDUCTTV'ITy DAT. Avei-sge Temperature Avert re liilio of ry .ermal Sclirtc of Lic,uid Layer 6,%,f, Differences Watnr/Bl^ck Liruor Conuuctivitv Content 31ack Lifucr Vtater Water Black Liquor (°rj ('^-) (BTU/Hr , 3r.Ft.*^F/Ft.) 12.68 101.3 lOi^.l l.OiiO 0.3636 0.337 126.0 128.1 1.064 0.3730 0.35^ 1?P..6 13^.^ 1.052 C.375O C.j52 15<^.9 156.3 1.074 0.3v820 0.365 15".'+ 156.1.074 0.3320 ':.365 151.6 I'^'^.'i 1.123 0.3315 C.382 165. 7 16^.1 1.047 C.3352 C.359 175.6 17^/.'' 1.06? 0.3330 G.367 '3.55 101.6 i::>h,h 0.^69 0.3638 0.314 10i>.2 IOC . C.037 C.366O 0.322 1?5.6 12^,.-) c.^98 0.3730 C.332 12^^.7 127.7 l.OOB 0.3730 0.335 153.2 IS'.3 1.013 0.3825 C.146 15^.3 156.3 I.OU C.3A20 0,344 17'-. 3 176. i^ 1.019 0.3870 0.351 3?. 60 1^1.8 155.8 0.Q68 O.38I5 0.329 176.7 1^0.5 0.969 0,3880 0.335 19'^,^ 202.0 1.003 . 3930 0.353 :3.75 101.7 10i*.3 0.924 0.3640 0.300 12^.6 127.7 0.952 C.37'^0 O.3I6 153.3 15^.3 0,922 o,^?:z^ 0.^15 15:^.3 15?.^ 0,^31 0.3823 0.313 h2,oO IC1.6 lOii.6 0.890 0.-'639 C.289 12C-.0 12*^.4 0.^02 C.^730 0.300 153.3 IS?.^ 0.887 C . '>325 0.102 151-7 155.^ 0.919 0.3815 C.3I2 176.5 17^.9 0.^31 C.388O 0.322 •^-^ . :?0 lO-'.O lO-i.l C.S29 0.3644 0.269 105.2 111.7 0.825 C.-^672 0.270 126.5 12^.4 C.811 0.3735 0.270 126.4 12<^.3 . 827 0.3735 0.276 126.6 12^.7 C.328 0.3735 o.^76 12fi..U 13"^. 6 0.^55 0.1750 C.286 l^-'.h 15P.''+ 0.S21 0.3825 0.280 151.3 1*1=;. 4 0.866 O.38I5 0.295 176. U I8C.3 0.385 0.3880 0.306 19B.3 200.1 0.907 0.3925 0.317

PAGE 108

100 the mean value.3 of all of the food quality data on water reproduced by oakiadis and Coats (2?). F. Sample Ca l cula tions The run using black liquor with U<; .QO)l solids at 126.0° F. will be used to illustrate the method of calculption. !Lcuiliorium concitiona were maintained over a period of approximately two hour?. Over this period minor fluctiuitions occurred in the e.m.f, readings v-hich were taken at ?0 to 30 minute interval?. The e.r.f. differences across the liquid layers vere evaluated and the average ratio of these differences for water over black liquor was found to be C.902. Individual values of the ratio varied by a maximum of t 2.5^. The thermal conductivity of water (k^) at the averSf^e temperature of the water layer was found to be 0.3-^30 BTU/(Hr.) (3a. Ft.)(°F./Ft. ) , The thermal conductivity of the black liquor (k, ) was evaluated using equation ^^8 when the ratio of e.-n.f. differences was assumed equal to the ratio of temperature differences. (0 "^730) (C '/OZ) ^l = *'' /322' "" ^'^^^ BTU/(Hr.)(Sq. Ft.)(^./Ft.) G. C a lculated Results and Discussion The calculated values of thermal conductivity oi" clack liquors containing from 12.68 to 53.20.^ solids at temperatures from 100 to 200° F. are tabulated in the last column of Table 6. These data are represented graphically on Fi^urp If, which is a plpt of thermal conductivity versus per cent solids v.-ith temperature as a parameter. It is noted that the temperatures of the sanples varied slightly froni the dei-ired tenperatures.

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101 O.i+0 eg* i? 0.35 g 0.30 0.25 ko 50 20 30 Per Cent Solids Figure 18 Thermal Conductivity versus Per Cent Solids 60

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102 of Tnea-jrement {ICO, ]2 = , I5O, I75 and 2C0° F.). A cross flol of theirmal con(5uct.ivity versus temnercitiire was prepared ^nd vslues of the thermal condiictivity at the dfisirnd temreraturrty weie re-d frcm the smoothed curve.s. These values wfr<3 uaed to locate the line*-, in Figure 18* The slopes of theae lines were found to varjlinearly with tenpertture according to the foliowinp; relation. Slope = 0.2096 0.000:338 t (®F.) (k9) Interpolfition of the 3 ires of Firure IS was accomplished using knowr* values of thennal conductivity of water at intermediate temperatures and the relation of eouation ^9, The interpolated grapih is shown in Figure i"^-. For convenience these data are presented in the form of a line coordinate chart in Figure 20. There were no published data with which to compare the results of the?-exp^^rinenti'. However, the values were considered consistent with v;hat night be er-Tcected from aqueous solutions of the materials in the black liquor.

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103 20 30 Per Cent Solids 40 50 60 Figure 19 Thermal Conductivity versus Per Cent Solids

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104 0.i42 -r 0.40 -0.38 0.36 -0.34 0.32 -0.30 -0.28 -0.26 -0.24 -L Temperature, F, t60 -50 --40 -30 --20 --10 Per Cent Solids Thermal Conductivity BTU/(Hr.)(ft?)(^/ft.) Figure 20 Nomograph for Thermal Conductivity

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chaptf:r V VISCOSITY A. 3ack;;r9un a The literature contains only two references on th« visco&ity of sulphate black liquor. Kobe and McConaack (16) reported valuer for soda, sulphite and sulphate liquor obtained from pulj-ing westei-n hemlock, Fedluiid (11) reported vali:es of viscosity for black liquor frctn two diiferent raills-»one a typical kraft black liquor and the other low in organic matter. Kobe and KcCormack reasoned that since the viscosity for all types of waste liquors was due largely to the dissolved si^g&rs and colloidal lignin molecules some general relation might erlst for all thru^e. This vas substantiated by their results vhich sho^v-ed that the three licuovr, could be represented on the same corr«lntion v;ith an accuracy of 5^. They reported that the liquor.'., even in low concenti-ations, possessed a certain amount of gel-like properties below 63° F. They used the Cstwald viscometeifor their determinations oveithe temper? t\u-e range of 32 to 200<^ F,, but did not indicate whether tubes of different capillary sizes were used. Thus it was not possible to determine whether their results showed any differences in viscosity with different rates of shear. Such differences could be displayed by gel-like materials. 105

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106 I-t was nssvmec, th^r^forp, thst the liquors which they exarsin»^d at tempera t'a*ep above 63 F. were Neiwtcnian since they did not i-eport anything to indicate other..'ise. Hedlund reported that especially at lovr tempera tureo there was a difference in viscosity at the sane concentration betv'een the lienors of different org&nic content. However, ht» did not indicate any differenfe>' of viscosity with rates of shear. The Hoppler type viscometer was eir.j-loyed in these experiments over the teTnpei-o.tur'f» ranje of 65 to YjO F, KoV>fc and McConnc,ck used an Cthmer (Zl) plot to correlate their data. In this net> od tie logarithm of viscosity was plotted against the logarithjn of t)ie vise )sHy of vi^ter at th" same tenperature. Straight liner, were produced in t.hia way for each concontiction, Friwj this diagrajr. and an A. --.T.M, Standard viscosity-temperature plot they interpolsted their data and plotted it at; the logarithm of viscosity ve^Tus temperatiire. This method of plotting resulted in lines whicn had slight curvature at the lower tenperat'.;re;;. Thus the temperature axis was modified so that the lines were .straight ovei their cntirfId-npth, When the data of Hadlunci were plotted on the diagram pr^par' ' •'/ Kobe and McCormack straight lines showing fair agreerient were found at concentrstions below 50^' At higher concentrations the linos reprei-entinfthe data gradually became curved. Considering the differences in wood and the probable differences in the cooking process it was renarkable that even suc'i close agreement should be found. 3« Apparatus and rpocecUure The values of viscosity were deterrr.ined at various temper?. txares

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107 using Cannon-?enske-Ostwald type vlsccsneter tubes in conjunction with a constant temperature bath controlled to C.l*^ F. The tubes were precalibrated at 100*^ F. and 210^ F. V-ilues of the calibration constant for intermediate tempers turec were determined by interpolation. Viscosity tubes of the ICO, 200 and 3^0 series were used in order to cover the entire ranc^e of viscosity without excessively long efflux times. Standard procedures were follo^^ed and the average of several consistent readinc-s was determined. The average efflux tine was multiplied by the appropriate constant to obtain the kineniatic viscosity In centistokes. The kinematic viscosity was then converted to absolute viicosity in " centipoises by multiplying: ^y the density or sp-ocific gravity. The calculations are illustrated using the data for a mn using 1?.6S% black liquor at 100° P. An efflux time of 83.2 seconds was found as an average of 10 runs on 2 samples. The calibrs^tion constant for the 100 series tube was 0.01^06 cent 1 5 per second, Thu5, Kinematic visco:..ity = (33.2) (0.01406) = l,l69 centistokes The specific gravity found from Table 8 or Figtire 23 was 1.060. Therefore, Absolute viscosity = (1,169) (1.060) = 1.24 centiix)ise C. Calculated Rej ults and Discussion The exTJerimental data and calculated results of viscosity' of

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108 black liquor are tabulated in Table 7. Usually the viscometer tube was used which gave from 100 to ?.0Q seconds efflux time. However, in two instances two different size capillaries were used vrf-th thp same concentr£tion of black liquor. Thus values of viscosity wpr= obtained for a sample containing 33.7,c solids at two different rates of shear. Close agreement was observed for these values. F\irther. no discontinuities were found for any of the samples on which more than one size viscraneter tube was used. For ir.stance, if the data for the 53,2!h sample had indicated a different straight line for the points determined using the 200 series tube than for the 3OO series tube the obvious conclusion would be that the viccosity varied Tvith the rate of shear. Such was not the case and the conclusion was drawn that over the range of variables studied the black liquor behaved as a Ne^rtonian fluid. Thus apparent agreement on this point exists between these data and the data of previous investigators. The data of Table 7 were plotted on a modified Othmer(£l) diagram similar to that used by Kobe and McCormack. The viscosity was plotted vertically on a standard logarithmic scale. The tempera tui-e was plotted horizontally on an arbitrary scale so that a straight line resulted when the data for water were plotted. A cross plot of the loparitl^jti of viscosity versus solids content was prepared and lines of slight curvature resiilted. From this graph values of viscosity at even increments of solids content were determined and plotted on the modified Othjner diagram (See Figure21). Straight lines resulted for all concentrations over the temperature range

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109 TABLE 7 5XP5RIMETTTAL IND CAT cri. 4t-^:d V. 3(^0.SITY DATA Sol'.r • Vi .^'T Absolv>9 -r,::1...,v,t Sc rl-?s Mo. Viscosity (') (Cent incises) 12.68 100 100 1.2ii0 1?.5 100 C.953 150 100 0.763 175 100 0.639 200 100 C.5^3 23.55 100 100 2.I185 1?5 100 1.819 150 100 I.U09 175 100 1.121 200 . 100 0.9 23 33.75 100 100 (.27 100 200 t.l9 125 100 ^.22 135 200 h.ZZ 150 100 3.06 175 100 2.31 32.6 200 100 1.68 i^2.9 100 200 21.89 125 200 1^.00 150 200 S,k6 175 200 5.37 200 100 h.2k. 5?. 2 100 300 245.20 125 300 97.90 150 300 i*6.80 175 200 26.00 200 200 15.92

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no ^ N ^~ ~~~ 1 — X \ N \ s 100.0 \ \ \ \ s ' V ^ \ \ ^ s — X -^ — ^ ^ v N s ^ X \ \ -^ N nJ "^^ \ \ V \ ^ ~""\ 1.,. \ ^ ^ \ \ \ ^ .K ^^\, »,^_^ -^ "^ \ -> \^ \ N s. ^ ^ ^ ^ \ ^ V, \ \ X \ \ k. ^^ !^ "-v \ ^,^/^\, ^ xK \ 10.0 ^ ^ ~"^--^^ \ ;;^ ^ X ^ ^ X \^x ^ ^ ^ ;~~^ " ^--^^ -^ 1 ^ '•^^^ ^ 1 =--= L^^"-0^ =^:^^ ^ ^ ^ ...j^^^ "^ ^''**" ^---, ~" '-~^"~~>.^"^-> ^ "" 0) -~-^ ..^^ -O ^ >-cS\~^ -^^ "^Ctn --^ k (0 cr~~-Cr ^-^^J^ k^ -~^ ^"*i*ki?"~--S^< ^ -;^ ^ c 0) o ^^5 ::;^ ^ -^ :^ ^^=3=i --.^^_l^'">« :::: =^ ::; •H ^^^ ^ $ ^ ^ ^ :::;;;;;;; $ O U > 1 ?~s ^ j § ^ ^ § s 1 1 1 1.0 ::r~^ i 5 -crrt;--;: =::^ §^^=^=?c^^ ^ — . ::::::;:: ~~~-i:^ s ^^^::5~^ g "^^^^ ^-^^^^^^^^^ -=:; ^^ rr^::5^;;;^ 1 ^ — — , . , " ^^^^f^^^^^ ^ -— ..^ — ^ = "~^ ,^^ 55 50 ^5 100 125 150 175 Figure 21 Viscosity versus Temperatvire 35 ^5 2C 15 10 200 °F.

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Ill investigated. These data were replotted on a line coordinate nOTiograph as shown in Figure 22. The data of Kobe and McCormack were checked against these data by plotting on Fi^re 21. The overall aa:reement was found to be on the order of l.O'^. General agreement of their data with those of Hedlund has already been pointed out. Mo analytical data were available for comparing their black liquor to the one used in these exi>eriments which contained 70.8^ organic material in the solids. However, considerable evidence exists upon which to draw the conclusion that sulphate (kraft) black liquors exhibit similar viscosities irrespective of the nature of the wood used and the normal variances in mill operation.

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112 100.0 -5C.0 -10.0 — 5.01.0-0.5-Per Cent Solids Viscosity, Centipoises Figure 22 Nomograph for Viscosity 220 -210 200 190 190 170 160 150 140 130 --I20 --U0 --100 Temperature, F.

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CHAPTER VI SPECIFIC GRAVITY A. Apparatus and Procedxire The specific gravity of black liqvor was determined over the complete range of peicent solids and temperature used in these experiments. The procedure used was to measure the veight of black liquor contained in a IOC ml. volumetric flas!-; and divide this by the veight of water cont-tined in the same flask at the same temperhture. The flask was first filled with black li nior up to the line and immersed in a constant temperature bcith controlled to i 0.1° F. .\fter the flask and content.*? had assumed the ter.perature of th*? bath the level in the flask was adjusted. The flask was dried and wei?h<>d aft^r arrain immersing in the bath to recheck the level of the liquid and the temperature. The flask was then filled with distilled v:ater and a similar procedvire was followed. The weieht of the contents in the two cases was determined by subtracting the weight of the flask. The specific gravity was then detemined by dividing the weight of black liquor by the weight of water contained by the flask. 3« Data and Calculated Results The specific gravity measurements are tabulated inTable 8 for the solids content range of C to 53,20^ *nd at temperatures from 100 to 113

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11^^ TABL?; 8 SFRCIFIC 'l^ATV^ D.i^A .;>oii.ds .-'cific Content Temperatur-? Gravity {D (^.) C 100 C.Q93 125 C.987 150 0.930 175 0.972 200 0.963 1?.68 100 1.060 1?.63 125 1.033 1?.68 15C 1.01^7 li:.58 175 1.038 12.68 200 1.030 2?.. 53 100 ia?3 2?, 55 125 1.116 23.55 150 1.109 23.55 175 l.iOO 23.55 200 1.092 3^75 100 1.184 ^3.75 125 1.177 33. "^5 150 i.i6a 3:^.75 175 1.159 32.60 200 l.ii*5 U2.O0 100 1.2iil h2,9C 125 1.233 k2,9Q 150 1.225 ^2,90 175 1.217 ^^2.90 200 1.208 53.20 100 1.304 53 . 20 125 1.297 53.20 150 1.285 5^.20 175 1.277 53-20 200 1.268

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115 200 F. These data are plotted in Figure 23 as specific gravity versus per cent solids with temperature as a parameter. A cross plot of specific gravity versus temperature was prepared (not included) and a linear relationship was found.

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116 1.30 1.20 V. 1.10 1.00 10 20 30 kO 50 Per Cent Solids Figure ?3 Specific Gravity versus Per Cent Solids 60

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CHAPTER 711 INTERRELATION OF THERMAL AND PHYSICAL PROPERTIES AND THE HEAT TRANSFER COEFFICIENTS The diniensionless ntunbers calculated in Chapter II and tabulated in Table 3 were employed to detennine the j factors as given by equations 4 and 6 for all runs. The calculated j factors are tabulated in Table 9 for runs with Reynolds numbers f^reater than 3000 and in Table 10 for runs below 3OOO. These values are plotted in Figure ZU as log j versus log Re. , , From equation ^ it is evident that by this method of plotting the predicted J factors in the turbulent region should be linear with a slope of minus 0.2. Inspection of the data in this region of Figure 2U shows it to be in substantial agreement with the Sieder and Tate line (equation 4) which is also plotted. It is to be noted, however, that the data show some divergence at the high values of Reynolds number and that this divergence increases with the solids content of the black liquor up to a maximum of 33^ in a few cases. Also, close examination of the data for any one concentration shows that it falls on a line vrith a smaller angle of inclination than the Sieder and Tate line. In effect, the results indicate higher rates of heat transfer than are predicted by equation h at the high Reynolds numbers. From a practical point of view these results are considered 117

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118 TABLE 9 HEAT TRAJTSFER j FACTORS— REYNOLDS NU>raERS A307E 3000 Run Rejiiolds j' Factor, Eq. 4 Run Reynolds J 'Factor, No, Number (lo3) No. Number Eq. 4 (103) 1 IO96O 3.75 68 4230 3.^9 2 II36O 3.90 69 3380 2.23 3 15860 3.5s 73 3880 3.19 k I586O 3.62 74 3I8O 2.79 5 24270 3.52 77 4290 3.78 6 24270 3.33 78 6290 4.40 7 31720 3.29 79 8370 4.28 8 3278O 3.31 80 8530 4.46 9 41940 3.15 31 7100 4.11 10 42560 3.17 82 7470 4.21 11 20000 3.^9 85 4690 3.90 12 20330 3.^3 36 5700 4.11 Ik 56430 3.04 87 7260 4.21 15 59670 3.12 88 9130 4.19 16 59050 2.32 89 11180 4.25 17 3356O ?.09 90 13640 4.24 18 43560 3.01 91 16810 4.26 19 78O5O 3.05 92 19550 4.03 20 3068 5.00 93 23910 4.24 21 7080 3.37 94 24320 4.18 22 13260 . 3.55 95 12400 4.34 27 7490 5.18 96 15150 4.22 28 8040 5.1^ 97 I825O 4.27 47 3500 2.79 99 5290 4.71 48 3600 3.23 100 8300 4.11 ^9 5020 4.64 101 11590 4.34 51 33^ 3.05 102 16200 4.23 52 4830 3.79 103 21990 3.99 53 53^0 4,16 104. 11240 4.18 54 5804 4.20 105 11790 4.23 55 7360 3.'30 106 81 30 4.27 59 .3300 2.61 107 8220 4.39 60 4140 3.53 109 5/J40 ^.60 61 4170 3.53 no 5500 4.42 62 5120 3.91 111 13260 4.05 63 6000 4.02 112 13260 4.10 64 7610 4.22 113 14/^90 4.1c 65 9980 4.42 114 16260 4.13 66 10400 4,11 115 16320 4.14 67 4590 3.70 116 20150 4.32

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119 TABLE 9— Contijnued Run Reynolds J 'Farter. Run Reynolds j' Factor, No. Number Ec. 4 (IC') No. Number Ec. 4 (lo3) 117 20720 4.46 152 55100 3.69 118 2231c 4.10 153 55100 3.76 119 26390 4.?1 154 3870 4.22 120 27840 4.50 155 10410 4.21 121 32570 4.26 156 I69OC 4.18 122 32670 4.70 157 I796O 4.10 12ii 3545 3.76 158 18940 4.06 125 9093 4.19 159 24170 3.91 126 l>,o6o 4.11 160 27890 3.93 127 14540 3.92 161 33340 3.77 128 17720 4.20 162 41770 3.87 129 21490 4.08 163 49350 3.91 130 25240 3.89 201 3350 3.57 131 39990 4.^5 202 3650 4.23 132 4220 3.95 214 3580 3.96 133 3550 4.21 215 4700 4.50 13^ 6350 4.22 216 5180 5.40 135 6250 4.19 217 5840 4.43 136 10020 4.12 218 6770 4.43 137 10020 4.12 219 7850 4.55 138 14520 4.03 220 •9650 4.45 139 14230 3.39 224 29000 3.41 1^+0 18210 3.98 225 29300 3.37 141 I836O 3.79 226 11300 3.83 1U2 2O86O 3.86 227 17620 3.63 1^3 2O86O 3.76 228 24550 3.^^! IkU 25I8O 3.76 229 29100 3.30 145 25250 3.35 230 32100 3.24 146 3O86O 3.76 231 37700 3.25 147 3O66C 3. 80 232 42800 3.24 148 35500 3.77 233 52300 3.02 149 35670 3.62 234 58900 3.02 150 42780 3.36 235 67900 3.03 151 43150 3.86 236 75500 2.98

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122 f) iA n O • r ON n -o iS^ ^ G ^ y j!=; o 08 c +> Ix, CO o x> o § 5^ •H -tJ CD V i) • tS' •o CI c nl Ih H 0) (0 Si ;3 ^5 ;z; s o ^H (0 CJ •a V t-> II 5^ .§;§ C^0JO(nOHH C\jr\U>,C^fVr\OOt^COOrHr-'Cvir-lr-ir-'OOOa^O^C^OOOC>OCT> Hr^^^r^l-^^-lHf^^^C^J(^J^^l-^^^^r^f-^^^r^OOO^Hl-ll^r^OO vOON>n<»CJ"^OOONOOOOOOOOOOOOOOOOO «a^g>ONpvO>oiy>iHgocga.>opc5gj^o2ooc050ooTOooap (7\ CT^ oo o> a^ (jv o cr^ o oo oo oo <>: CO CO 00 or. CO 00 a S 00 00 00 OOOOOOOOOOiHOOOOOCJOOOOOOOOOOO t^C^HrHr-IONvO''^OOJ004«^C^vO»^HCOC^C^N">OJC^»^-:tO"^ ^ O O^CM^O H^OnCNJO >A^ rHSD^ O CJnC>^"^0 C^C^(JsC^\J*AC^0 00 0-. avtH(»a-OC>OrHMOr-«OOOC>\C7NC7Na\QOOroOOCy^COCOOO OOOrHOOi-HOrHHHHHHrHr-tOOOOOOOOOOOO j*ao^c>ioc7vOvOw^^-3-c\i ir,\0 >?\H C^\v£)vOvO-:t CM f^Csl C^OOCOOO 3--:t^^^cO0O0O CvJC^C^vOvOCOOOOr-CVrHOJO 00C^f^00C^^C^OH«Hr^f^C^ oooooooocnooor. a^a>cjNC7>oa> H r-l H H H iH(-(r-tOOOOOOOOOOOOOOOOO rH»?\---(^C\JvO\DNO>ACOO^ C^OCOHC^ fv. C^ r^ (V. o c^ r"\ r\ r^ rA c\' (v c \ c^j h cn' rc?oo cvj c^ cn' vr\(\lC^vQNOODC^r-tC30jNOOOOOOOO H iH H c^ c»^ OOOOOOOi-tHf-1 w^u^c^c^Hoo»^^c^Joooo^or-l^-r^NDr-icv(\ja:jr-oir\vf)Hocot^o(jsHONCJcsi^ " .-.a^ r\ cv> c\' Jc^ vc (Mc^J-:}^^cMr^-:tl^J-3f^•^OOC\Joc^ir^oc^C^-3C^^""^>Avr^cnoJOJ fH t-i t-t r-i r-i r-i r-t H 5OC.W>m»AO<\iC^00O«Hv£)r^CVC^^iH00 r-l CVJ ^^-:J r-( (-" CNJ M CvJ r^ CM O (^ r-l O 0> OO OC C^ vO ""> ^ >AvO v£) JT'. C^ CD O Cv. CO CM C\J oooo"^JrHC^r^cvHcoc^^r^^r^cooo "o5rHOCTsC^JrON0N0O^00O-:tv0C0r^CMC^HN0 C^CMvO'A'AC^OOOOC^OCMHHCMCMCMCMC^^ iAC^lO. CM rH H CM rH CM CM Q CM CM ^ 5 00 O CM CO O r-l CM vrwO f^^00C0r^-^^nC^00OxOH<^-* "^^ C^OO Os Q H £J U^C^C^^-C^C^OOOO OnO CMvOvOMDvOvO C^-b^C^C^C^C^C^C^C^OOOOCJO HrHrHHHHHHrHrHr-li-trH«HrHi-tH«-Hf-(

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I I I I I M I I I I I I I I I 123 I I I I I I I I I I I O.OIO 3B.S% Water before Black Liquor Runs Water after Black Liquor Runs 9.2^ Original Black Liquor IB. 8^ " " " 25.156 " " 33.C 38.5:^ " " " ^9'3lt> New Black Liquor 41.9^ II M n 33. ( Equation k J I I I I I I I I 600 aoo 1000 I I I I I I I ll J \ I I I I I I I I I I ill 2000 4000 (,000 aooo 10000 , RejTiolds Number Figure Zk j Factor versus Reynolds Number (roooo 00000 looooe

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12k satisfactory since general agreement with the theoiy is demonstrated plus the fact that, for design purfioses, equation i^ would yield "safe" values. Frcwi an academic point of view some discussion of the divergencies should be offered. Examination of the data in Table 3 shows that the quantity of heat transferred to the fluid, q, increased directly with Reynolds number. Likewise, the deviations of the calculated J factors increased directly with the Rejmolris number. It is recalled that the pipe surface temperature was calcxxlated from a knowledge of q, and thus the magnitude of any error in this calculation would increase with Reynolds number. In the "Analysis of Results" section of Chapter II the error in the pipe surface temperature was evaluated at IO5S based on an assumed possible error in the thermocouple location of 5»^'^An error in the pipe sxirface temperature would also cause an error in the viscosity ratio term in the same direction. However, this error would be very amall since it would be raised to the C.lit power in equation ^, Thus, these factors would not account for all of the deviation found at high fieynolds niunbers, nor do they seen probable since the data for water are in good agreement with the Sieder and Tate line. The only other possible experimental cause of variation in the tvirbulent region j factors would be errors in the thermal and phj'sical properties or the temperature at which they were evaluated. Over the entii^ range of these experiments the specific heat and thermal conductivity varied no more than about 30^, whereas the viscosity varied 100 fold. However-, in the turbulent region alone, the viscosity variation was only about 3 fold and about the same variation was found in the

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125 Prandtl nvunber. On the other hand, for a single rur the maximum variation of the viscosity and Frandtl number from inlet to outlet was about 15:*. The inlet to outlet variation of the specific heat was no greater than Z%. Thus the J factor deviations cannot be rationalized on the basis of using an incorrect temperature for the evaluation of properties in equation U, Errors in the properties themselves of such magnitude as would be necessary to accoxint for the j factor deviation seem highly improbable . 3y elimination it would seem that the only possible expjlanation unaccounted for lies in the fact that equation k does not apply equally well to all materials. However, from the engineering view point, it is desirable to have only one equation which represents a mean value for a variety of materials. The Sieder and Tate line (eqtiation U) is therefore accepted as representing the data for black liquor sufficiently well in the turbulent region. Referring again to Figure 2^ it is seen that the experimental points plotted in the viscous region are considerably scattered. The solid line drawn in this region represents the Sieder and Tate equation 6 for the particular ^ ratio used in this work (= liil), A close analysis of the data showed that the gresitest deviations occttrred when using a material of low viscosity at a low velocity. Also, it was observed that the greatest deviations were all positive, thus indicating higher rates of heat transfer than predicted by equation 6. The deviations could be easily explained as due to natural convection, since the occurrence of natural convection currents is favored by low velocities

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126 and viscosities. Also, any increase in the circulation rate would result in a higher heat transfer rate. In Table 10 the predicted J factors (equation 6) are listed along with the calculated ones. Also shown is the ratio of the calculated to predicted j factor values. Examination of these terms will indicate how many times greater is the j factor or heat transfer rate when natural convection occurs. These terms are therefore the desired values for the S and <^ natural convection factors of equations 7 and 8, The natural convection factors, (^ and (|> , proposed by Sieder and Tate (3) and Kern and Othmer (15), respectively were evaluated and are listed in Table 10. The "tentative" equation of Eubank and Proctor (9) was rearranged to have the same form as equation 6 and a corresponding natural convection factor, (t , was calculated from it. These values are also listed in Table 10. The data in the viscous region were replotted using the natural convection factors ' , and ^ in Figures 25, 26, and 27, respectively. Inspection of these plots in comparison with the uncorrected data in Figure Zk revealed that the Sieder and Tate factor was the most effective in rectifying the data with the line of equation 6. The factors of Kern and Othmer and of Eubank and Iroctor both resulted in elevating the j factors consJ.derably above the Sieder and Tate line. The values of (p varied from 0.738 to 1.150 and (|)*'varied from 0. 871 -to 1.010 with the higher values being associated with the r\ms with the greatest natural convection effects. Therefore, the net result of these two corrections was to increase the j factors for runs with little natural convection up to

PAGE 135

127 I ' I ' I ' I ' I I I ^ [ o u o c + r-i CO O n u c 1 (4 1 r; ^ ^/ f

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128 X! u c .it tn v^ H U C 0) ^i & 0) I .1 I I I I P/ f

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130 the rims vdth appreciable natural convection. On the other hand, the Sieder and Tate factor,^, which varied from C.876 to I.634 effectively lOT-rered the data for runs with appreciable natural convection down to the line of eqtiation 6 and did not cause much change in data which were already near the line. The fact that these corrections yield values less than 1.00 in some instances does not propose a hypothetical flow condition with less than zero natural convection. It does propose that in these instances there is less natural convection than was present in the data used to establish the constants of the Sieder and Tate equation 6. Therefore the correction factor,^, must be less than 1.00. The differences in the effectiveness of the natural convection factors can be explained by the different pipe diameters used by the various investigators. Actually, it is the | ratio that is important but the length, L, has not been varied over as large a range as the diameter. D. Sieder and Tate used a length of 5-1 feet, Kern and Otlimer used a length of 10 feet, and a length of 6 feet was used in these experiments. Sieder and Tate used a 0.62 inch diameter tube as compared with a 0.51 inch diameter pipe used in these experiments. Kern and Othmer used pipes with diameters ranging from 0.622 inches to 2.^4-7 inches and Eubank and Proctor based their results on works of other investigators with pipe diameters ranging from 0.i;94 inches to 2.4? inches. It is not surprising, therefore, that the Sieder and Tate natural convection factor should be effective with these data. The fact that the other convection terms were less effective suggests that the pipe diameter, or

PAGE 139

131 more correctly the t ratio, is not entering into the expressions in the D proper way. Further evidence in support of the above was found in the work of Kern and Othmer, When they applied the Sieder and Tate correction to their data they found that while it did fairly well on the small diameter runs it grsatly over-corrected the large diameter runs. On the other hand, their correction was designed to more acctirately correct the large diameter data wherein the greatest natural convection effects are encountered and thur, the greatest corrections were necessary. Their result yielded corrections which were only slightly too large for the large diameters and had little effect with the small diameters. Referring again to Figure 2k and examining the data for the various concentrations separately it was noted that the data fell on different lines for each concentration and that these lines apparently converged around a Reynolds number of 3OOC, It was further noted that the data for the most concentrated liquor fell generally about the Sieder and Tate line and the more dilute liquors fell on the lines in a clockwise direction from this. The Grashof ntmbers were found to have only moderate variation for the runs of any one concentration. Therefore, the Grashof number alone coxild not be counted on to apply the proper correction over the full range of Reynolds numbers. Since for any one concentration the necessary correction factor increased as the Reynolds number decreased, it was logical to conclude that some function of the Reynolds number should be included. These same observations were made by Kern and Othmer in their

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132 experiments and thus lead to their inclusion of the log Re term in the natural convection correction. The applicability of the Kem and Othmer type correction factor to the data of these experiments seemed logical. To test the method specifically for the pipe diameter used in this work it was decided to evaluate new constants and see how close the corrected data could be made to agree the Sieder and Tate line. The log Re times the desired values of ^ ( =— ) were plotted Jp versus the one-third power of the Grashof number. A linear regression line was determined for these data and the new natural convection factor of the Kem and Othmer type was found to be, 3'^3 ._ 2.ip (1 ^ 0.0;342 Gr '''') , ) t" log Re ^^ ' Values of ^ were calculated and are shown in Table 10 . The data in the viscous region were recalculated using this factor and were plotted in Figure 28. Both from theory and inspection of the Figures it is obvious that the use of this factor gives the closest agreement with the Sieder and Tate line. The essential difference between this factor and the original Kem and Othmer factor is that the coefficient of the Grashof number is approximately 3.^ times as large. This added weight given to the term containing the Grashof number is necessary due to the difference in diameters for which the factors apply. It is possible that if the way in which this coefficient depends on diameter could be determined an 1 . Ill The standard eri-or of estimate using ^ was found to be 0.000629 for the range of j values from 0.00170 to 0.01200.

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l'3^ equation equally effective for all diameters would result. The region of viscous flow was found to extend somewhat beyond a Reynold number of 2100 which usually marks the beginning of the transition region. In most instances viscous flow was maintained up to about 3000 Re::,'nolds number. Beyond this value a sudden change to the transition region was noted and the j factors increased rapidly and then finally leveled off and became asymtotic to the data in the turbulent region. This behavior, in the transition region, was entirely as expected and needs no further amplification. Additional support to the occurrence of viscous flow up to a Reynolds number of 3OOO can be found in the literature. Kern and Otlimer (15) found viscous flow in some instances at Rejmolds numbers as high as 38OO. Bosworth (5) states that the viscous flow may exist at a Re^Tiolds number of JQOC for cases of undisturbed flow. McAdams (19) cites data indicating the beginning of transition at a Reynolds number of 25CO or slightly higher. The general agreement of the calculated and predicted j factors over the entire range of experiments is considered to be prima facie evidence in regard to the reliability of the thermal and physical properties as well as the applicability of the interrelationships of the variables used in this work.

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CHAPTER VIII CONCLUSIONS The results of the foregoing investigations have lead to the conclusions which are itenized as follovrs: 1. Complete data on specific heat, thermal conductivity, viscosity and specific gravity of sulphate black liquor were determined over the range of to 6O5S solids and 100 to 200*^ F. 2. The specific heat data for sulphate black liquor found in the literature were neither complete nor consistent and the new data give for the first time the specific heat as a function of both per cent solids and temperature. 3. No thermal conductivity data were found in the literature for sulphate black liquor, therefore, these data represent an important contribution. ^. A thermal conductivity apparatus suitable for aqueous solutions and other relatively non volatile liquids was developed. 5. The viscosity data were found to agree with data for sulphate black liquors from widely different origins. They were also in substantial agreement with soda and sulphite liquors. 6. The general use of the thermal and physical data is recommended, in the absence of specific data, even though they have been 135

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136 determined using black liquor from only one mill. This is possible since specific heat, thermal conductivity and specific gravity would not be expected to vary much with different liquors. Also, from number 5, above, viscosity can be assumed the same for liquors from various mills. 7. The calculated j factors were found to be in substantial agreement with the values predicted from the Sieder and Tate equations in both the viscous and turbulent regions. For engineering design purposes, the Sieder and Tate equations yield "safe" values. 8. The j factors in the transition region increased according to predictions and became asymptotic to the txirbulent region values at a Reynolds number of 10000. 9. Natural convection became appreciable in the viscous region for fluids flowing with low velocities and with high Grashof numbers and caused as much as 100'^ increase in the j factors. 10. The Sieder and Tate natural convection correction was found to be more effective than the other factors given in the literature. 11. The Sieder and Tate natural convection correction was best probably because it was developed based on data frcm a heat exchanger similar in size to the one used in these experiments. Other natural convection factors found in the literature were based on data from larger diameters and different lengths. 12. The Kern and Othmer type natural convection correction was very effective when the constants were reevaluated by the least squares method based on these data.

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137 13* Further work is necessary in order to develop a correction for natural convection equally valid over a wide range of diameters and lengths. 14. All of the data in these experiments were determined using an — ratio of 141. It can only be assumed that si:nilar results would be obtained at different values. The effect of different h values is predicted by equation 6.

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BIBLIOGRAPHY 1. Adams, L. H., Int. Grit. Tables . Vol. I., (1926), 58. 2. Bates, K. 0,, "Themal Conductivity of Liquids", Ind. Sng. Chem, » 25, (1933). ^31. 3. Bat-^s, K. C, "Thermal Conductivity of Liquids", Ind. En?. Chem. . 28, (1936), i^9^. 4. Bates, K. 0. , Hazzard, G. , and PaL:ner, G., "Thermal Conductivity of Liquids", Ind. Eng. Chem . Anal . Ed. . 10, (1938), 31^. 5. Bosworth, R. C, L. , "Heat Transfer Phenomena", Jolin Wiley and Sons, Inc., New York, (1952). 6. Colbum, A. P., "A Method of Correlating Forced Convection Heat Transfer Data and a Comparison with Fluid Friction", Trans. Am. Inst, Chem. Engrs .. 29, (1933). 17^. 7. . "Mean Temperature Difference and Heat Transfer Coefficients in Liquid Heat Exchangers", Jnd, Sng. Chem. . 25, (1933) » 873. 8. Dittus, F. W. and Boelter, M. K., Univ. of Calif.. Pubs. Eng. . 2, (1930), ^3. 9. Eubank, 0. C. and Proctor, W. S., S. M. Thesis in Chemical Engineering, Massachusetts Institute of Technology, (1951) • 10. Graetz, L. , Ann. Physik . 25, (I885), 337. 138

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139 11. Hedlund, I., "Indtmstad Svartluts Viskositet vid Hoga Temperaturer", Sv ensk Papperstidning . 12, (1951). ^08. 12. Hutchinson, E. , "Oi the Measurement of the Thermal Conductivity of Liquids", Trans . Far. Soc .. Ul, (19^5). 8?. 13. Jakob, y. , "Heat Transfer", Vol. I, John Wiley and Sons, Inc., New York, (19^+9). 1^. Kern, D. Q. , "Process Heat Transfer", McGraw-Hill Book Comp&ny, Inc., New York, (1950). 15. ., and Othmer, D. F., "Effect of Free Convection on Viscous Heat Transfer in Horizontal Tubes", Trans. Am . Inst. Chem. Engrs. . 39, (19'^3). 517. 16. Kobe, K. A., and McCormack, E. J., "Viscosity of Pulping Waste Liquors", Ind. Enp. Chem. . 41, (19^9). 284?. 1?. . , and Sorenson, A. J., "Specific Heats and Boiling temperatures of Sulphate and Soda Slack Liquors", Pacific Pulp and P aper Ind. . 13, No. 2, (1939). 12. 18. Latzko, H. Z., Natl. Advisory Comm. Aeronaut.. Tech. Memo , (19^). 1068. 19. McAdams, W. ". , "Heat Transmission", 3rd ed., McGraw-Hill Book Company, Inc., New York, (195^). 20. Morris, F. H. , and Whitman, W. G., "Heat Transfer for Oil and Water in Pipes". Ind. Entr. Chem. . 20, (1928), 23^. 21. Nusselt, W., Ver. deut. Inc. . 6? (1923), 206. 22. Othmer, D. K. and Conwell, J. V/. , "Correlating Viscosity and Vapor Pressure of Liquids", Ind. Eng. Chem. . 37 (19^5). 1112.

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11*0 23. Perry, J. H. . (Editor), "Chemical Engineers' Handbook", 3rd. ed., McGraw-Hill Book Company, Inc., New York (1950). 2k, Prandtl, L. , "Eine Beziehung zwischen Warmeaustausch Stromungs widerstand der Flussigkeiten", Phvsik Z. . 11, (1910), 1702. 25. Reynolds, 0., Proc. Lit. Phil. Soc. of M anchestp^r. Vol. 14, (I87U). 26. Rumford, E. T., "An Experimental Inquiry Concerning the Source of Heat which is Excited by Friction", Essays: Political. Economic, and Philosophical . Vol. 2, No. 9, (1796-1802). 27. Sakiadis, B. C. and Coates, J., "Studies of Thermal Conductivity of Liquids, Part II", Bui. Enp. Eb q^ . Station. L ouisiana State University . 35, (1953) 28» • and . , "A Literature Survey of the Thermal conductivity of Liquids", Bui. Eng. Exp. Station. Louisiana State University. 3k, (I952) 29. Schmidt, R. J. and Milverton, S. W. , "On the Instability of a Fluid when Heated from Below", Proc. Ray. Soc. . I52, (1935), 586. 30. Sieder, E. N., and Tate, G. E. , "Heat Transfer and Pressure Drop of Liquids in Tubes", Ind. E ng . Che m.. 28, (I936), 1429. 31. Stevenson, J. N., (Editor), "Pulp and Paper Manufacture", Vol. I., McGraw-Hill Book Company, Inc., New York, (I95C) 32. Williams, G. C, "Specific Heats of Volatile Liquids", Ind. En^. Chem. . 40, (1948), 340.

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142 «> V \ C 00 \ O ctf (0 «] \ 1 ' ^^ N \ ^ \ \ \ \ \ \ \ p U ct It Eh H J^ ?R (•^i/*iQ)(n£*bs)CJH)/aia • 'C^xat^oupuoo iBuixeqx

PAGE 151

1^3 i.uo 1.30 1.20 :^1.10 cl.OO .90 ,80 .70 \ \ ^ \ \ Data from ! IcAdam, (19) \ 100 120 l-l+O 160 180 200 Temperature, F. Figure 30 Viscosity of Water

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1^44 Run No. (SHMaterial ^9.3 7a S.L. Date t/^'^^^Q 2/, 'f^• Flov; Rate Remarks Lbs. /QO Sec. I3(^-S w, Lbs/Sec. 0.121 — W, Lbs, Hr. ^^^2. 1. Temperatures 2. /^%S 3. /C2J h. J^^2.iS :io3.z 6. 7. 6. sos.s c 31^5-^ 10. So^.l 11. 12. 12. sc^s:/ G ^ I f3o3ac> \ _Z£^ ^1 AT ISf.g 2-3 t^ tg = 0.000905 W CuAT = ^/_ t 207^ t 20^ k T^ ^.7^^ b /// 0.3 OL tj, ^-7^^ /^^ 0. 3m ^s f:c^5 r-vM\ =_Zf£^_/£p^j = 7/.7r /d7^7 /y^s'\ _ ao^ / wcp N lyubj IFl^ /D G] = /SOO / D G \ = ^^^^ Ji = 0.001770 ^ = g> OOP /OS? Cp G At„ Cp G I k /b V /tbi i = h / Cp>u\^ /3 _ o.Ooc/oS'S 17.Z = O.oo/fl, Cp G I k if Figure 31 Sample Data and Work Sheet

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BIOGRAPHICAL ITEMS The author was bom in Louisville, Kentucky on October 15, 1922. He received his elementary education in Louisville public schools and was graduated from the duPont Manual High School as Second Honor student, in 19^. He per sued his undergraduate studies at the University of Louisville from which institution he received the degree of Bachelor of Chemical Engineering in 19^3* The following year he received the degree of Master of Chemical Engineering from the same University. During his graduate studies he was engaged in research work on synthetic rubber for the Office of the Rubber Reserve. For the next three years he was employed by the University of Louisville Institute of Industrial Research and did research for the Quartermaster Corps. In 19^7 the author accepted a position as Assistant Professor of Chemical Engineering at the University of Florida, where he has also persued a course of study leading to the degree of Doctor of Philosophy. The author is a member of Omicron Delta Kappa, Sigma Tau, and Theta Chi Delta honorary fraternities and Triangle social fraternity. He is also a member of the Technical Association of the Pulp and Paper . Industry. 145

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of the committee. It was submitted to the Dean of the College of Engineering and to the Graduate Council and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. January 29, 1955 (^ D^'n, Cdilege of'^ngineering Dean, Graduate School SUPERVISORY CO^'^IITTSE: Chairman f'^t-i /I a~ C<.A.*itit/\, .^ '£j^

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UNIVERSITY OF FLORIDA 3 1262 08666 940 4

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