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Investigation of Thermal Conductivity of Iron-Silica Magnetically Stabilized Porous Structure

Permanent Link: http://ufdc.ufl.edu/UFE0045600/00001

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Title: Investigation of Thermal Conductivity of Iron-Silica Magnetically Stabilized Porous Structure
Physical Description: 1 online resource (58 p.)
Language: english
Creator: Nili, Samaun
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: anisentropic -- bed -- conductivity -- hot -- magnetic -- magnetically -- method -- msps -- packed -- porous -- stablized -- structure -- thermal -- transient -- wire
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: It is a fact of experience that simulation of thermo-fluidproperties of magnetically stabilized porous structure (MSPS) measurementrequires accurate value of thermal conductivity of structure. Therefore, thereis a critical need for measurements of thermal conductivity of MSPS. The dramaticeffect of magnetic field on the thermal conductivity of MSPS has not studiedbefore. In this study, we have developed a new apparatus based on the transienthot-wire technique to obtain measurement of thermal conductivity of MSPS underdifferent magnetic field orientations. The experimental results show that, whenan external magnetic field of 65 G is applied perpendicular or parallel to ahot wire axis, the geometry of iron particles are constrained, such that themost thermal conductivity decreased 12 % compared to the one without anymagnetic field. Then it was both numerically and experimentally verified thatapplying the magnetic field does not have any significant effect on thebehavior of the propagation of heat in any direction. Therefore, it isconcluded that the change in the thermal conductivity of MSPS is mainly due tothe increase of porosity. Normal 0 false false false EN-US ZH-CN AR-SA /* Style Definitions */ table.MsoNormalTable{mso-style-name:"Table Normal";mso-tstyle-rowband-size:0;mso-tstyle-colband-size:0;mso-style-noshow:yes;mso-style-priority:99;mso-style-parent:"";mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-para-margin:0in;mso-para-margin-bottom:.0001pt;mso-pagination:widow-orphan;font-size:10.0pt;font-family:"Times New Roman","serif";}
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Samaun Nili.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Klausner, James F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045600:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045600/00001

Material Information

Title: Investigation of Thermal Conductivity of Iron-Silica Magnetically Stabilized Porous Structure
Physical Description: 1 online resource (58 p.)
Language: english
Creator: Nili, Samaun
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: anisentropic -- bed -- conductivity -- hot -- magnetic -- magnetically -- method -- msps -- packed -- porous -- stablized -- structure -- thermal -- transient -- wire
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: It is a fact of experience that simulation of thermo-fluidproperties of magnetically stabilized porous structure (MSPS) measurementrequires accurate value of thermal conductivity of structure. Therefore, thereis a critical need for measurements of thermal conductivity of MSPS. The dramaticeffect of magnetic field on the thermal conductivity of MSPS has not studiedbefore. In this study, we have developed a new apparatus based on the transienthot-wire technique to obtain measurement of thermal conductivity of MSPS underdifferent magnetic field orientations. The experimental results show that, whenan external magnetic field of 65 G is applied perpendicular or parallel to ahot wire axis, the geometry of iron particles are constrained, such that themost thermal conductivity decreased 12 % compared to the one without anymagnetic field. Then it was both numerically and experimentally verified thatapplying the magnetic field does not have any significant effect on thebehavior of the propagation of heat in any direction. Therefore, it isconcluded that the change in the thermal conductivity of MSPS is mainly due tothe increase of porosity. Normal 0 false false false EN-US ZH-CN AR-SA /* Style Definitions */ table.MsoNormalTable{mso-style-name:"Table Normal";mso-tstyle-rowband-size:0;mso-tstyle-colband-size:0;mso-style-noshow:yes;mso-style-priority:99;mso-style-parent:"";mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-para-margin:0in;mso-para-margin-bottom:.0001pt;mso-pagination:widow-orphan;font-size:10.0pt;font-family:"Times New Roman","serif";}
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Samaun Nili.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Klausner, James F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045600:00001


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1 INVESTIGATION OF THERMAL CONDUCTIVITY OF IRON SILICA MAGNETICALLY STABILIZED POROUS STRUCTURE By SAMAUN NILI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENT S FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Samaun Nili

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3 To my parents

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4 ACKNOWLEDGMENTS During the time I started my elementary school up to this moment of my graduate stud ies, I was helped and supported by many people which I like to thank them all for helping me to reach to this point where I am now. But I would like to specially thank my parents, which their endless engorgements and supports made this grate moment of suc cess for me. My professors, Dr. Klausner Dr. Mei and Dr. Abbitt, which gave me broad engineering knowledge which shall certainly guide me throughout my future professional courier. I also like to thank supervisor and my friends at the lab, Dr. Ayyoub Me hdizadeh, Amey Barde, Like Li, Nick AuYeung

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF T ABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 NOMENCLATURES ................................ ................................ ................................ ...... 11 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW ................................ ..................... 15 1.1 Literature Review ................................ ................................ .............................. 15 1.1.1 Magnetically S tabilized P orous S tructure (MSPS) ................................ ... 15 1.1.2 Importance of Thermal Conductivity of Porous Structures ...................... 16 1.1.3 Heat Transfer in a Packed Bed ................................ ............................... 16 1.1.4 Previous Analytical Studies on ETC of Packed Beds .............................. 17 2 CLASSIFICATION OF EXPERIMENTAL THERMAL CONDUCTIVITY MEASUREMENT ................................ ................................ ................................ .... 18 2.1 Classification of Measurement Techniques ................................ ...................... 18 2.1.1 Ste ady State Techniques ................................ ................................ ........ 18 2.1.2 Transient State Techniques ................................ ................................ .... 18 2.2 Classification of Hot Wire Techniques ................................ .............................. 19 2.2.1 Standard Cross Wire Method ................................ ................................ .. 19 2.2.2 Single Wire Res istance Technique ................................ .......................... 20 2.2.3 Potential Lead Wire Technique ................................ ............................... 21 2.2.4 Parallel Wire Method ................................ ................................ ............... 21 2.3 Reason for Adapting Single Wire T echnique ................................ .................... 22 3 PRINCIPLE OF ANALYSIS ................................ ................................ .................... 23 3.1 Mathematical Analysis ................................ ................................ ...................... 23 3.1.1 Governing Equations ................................ ................................ ............... 23 3.1.2 Application of Hot Wire Technique for Porous Structures ....................... 26 3.2 Hot wire Apparatus Design ................................ ................................ ............... 28 3.3 Sample Preparation ................................ ................................ .......................... 32 3.4 Measurement Process ................................ ................................ ...................... 33 3.5 Results ................................ ................................ ................................ .............. 36

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6 4 NUMERICAL SIMULATION O F HEAT TRANSFER ON IRON SILICA POURS STRUCTURE ................................ ................................ ................................ .......... 44 4.1 Overview ................................ ................................ ................................ ........... 44 4.1.1 Validating the Experimental Measurements Using the Numerical Simulation of Heat Transfer on Iron Silica Pours Structure ........................... 44 4.1.2 Numerical Simulation of Heat Distribution for Anisentropic Medium ........ 46 5 CONCLUSIONS AND FUTURE WORKS ................................ ............................... 52 5.1 Conclusion ................................ ................................ ................................ ........ 52 5.2 Future Works ................................ ................................ ................................ .... 54 REFERENCES ................................ ................................ ................................ .............. 55 BIOGRAPHI CAL SKETCH ................................ ................................ ............................ 58

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7 LIST OF TABLES Table page 3 1 Geometry of apparatus ................................ ................................ ....................... 32 3 2 Material physical properties ................................ ................................ ................ 33 3 3 Thermal conductivity measurement of mixture without magnetic field ................ 37 3 4 Thermal conductivity measurement of iron silica porous structure while there is an 65 G horizontal external magnetic field ................................ ...................... 38 3 5 Thermal conductivity measurement of iron silica porous structure while there is a 65 G horizontal external magnetic field ................................ ........................ 39 3 6 Thermal conductivity measurement of iron silica porous structure while there is a 65 G vertical external magnetic field ................................ ............................ 40 3 7 Thermal conductivity measurement of iron silica porous structure while there is a 65 G vertical external magnetic field ................................ ............................ 4 1 3 8 Average thermal conductivity of iron silica porous structure for different heat fluxes and magnetic field orientations ................................ ................................ 42 3 9 Average thermal conductivity of iron silica porous structure for different heat fluxes and magnetic field orientations and porosity of 59.5 % ............................ 43 5 1 Ave rage thermal Conductivity and the slope of temperature vs. log of time graph with different values of heat fluxes and magnetic field orientations. ......... 52

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8 LIST OF FIGURES Figure page 1 1 Schematic representation of the magnetically stabilized iron silica porous structure ................................ ................................ ................................ ............. 16 3 1 The line heat source analytical problem underlying the transient hot wire method ................................ ................................ ................................ ............... 23 3 2 Schematic representation of the transient hot wire experimental setup. A) Front view. ................................ ................................ ................................ .......... 29 3 3 Experimental setup for THW experiment. Photo courtesy of Nili,S. .................... 30 3 4 Experimental setup while the re is a vertical magnetic field ................................ 31 3 5 The powders and mixture ................................ ................................ ................... 32 3 6 Typical schematic setup for th e transient hot wire experiment ........................... 33 3 7 Thermoc ouples and heat source position ................................ ........................... 34 3 8 Temperature raise vs. time in log scale with 3.9 watts heat flux for different magnetic field orientations ................................ ................................ .................. 35 3 9 Temperature raise vs. time in log scale with 7.3 watts heat flux for different magnetic field orientation ................................ ................................ .................... 35 3 10 Thermal conductivity of iron silica powder while there is no external magnetic field for porosity of 57.8 % ................................ ................................ .................. 36 3 11 Thermal conductivity of iron silica powder while there is a 65 G horizontal external magnetic field vs. experiment number for porosity of 62.9 % ................ 37 3 12 Thermal conductivity of iron silica powder while there is a 65 G horizontal external magnetic field vs. experiment number for 59.5 % of porosity ................ 38 3 13 Thermal conductivity of iron silica powder while there is a 65 G vertical external magnetic field vs. experiment number for 62.9 % of porosity ................ 39 3 14 Thermal conductivity of iron silica powder while there is a 65 G vertical exte rnal magnetic field vs. experiment number for 59.5 % of porosity ................ 40 3 15 Average thermal conductivity of iron silica poro us structure for different heat fluxes and magnetic field orientations ................................ ................................ 41 3 16 Average thermal conductivity of iron silic a porous structure for different heat fluxes and magnetic field orientations and porosity of 59.5 % ............................ 42

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9 3 17 Average therma l conductivity measurement of iron silica porous structure with vertical and horizontal magnetic field for different porosities ....................... 43 4 1 Schematic representation of heat balance for a control volume, advantage of symmetry boundary condition used, half sized meshes used for boundary edges. ................................ ................................ ................................ ................. 44 4 2 Comparison between numerical simulation and experimental measurements for homogeneous mixture of iron silica powder in experiment 1 without ext ernal magnetic field ................................ ................................ ........................ 46 4 3 Frequency of iron silica chains appearance when the sample is exposed to horizontal magnetic field. ................................ ................................ .................... 47 4 4 Mesh independent study of numerical solution for the iron silica chain structure for a/L = 0.015 ................................ ................................ ..................... 48 4 5 The dimensionless temperature as a function of a/L of chains appearance for points 1 and 2 and k 1 /k 2 =3 ................................ ................................ .................. 49 4 6 The dimensionless temperature as a function of a/L of chains appearance for two orthogonal fixes radial positions of points 1 and 2 and k 1 /k 2 =50 .................. 50 4 7 Azimuthal radial heat flux and relative temperature (compared to room temperature) of iron si lica distribution for a fixed radial position ......................... 51 4 8 Temperature contour horizontal chains at 350 seconds and k 1 /k 2 =3 .................. 51 5 1 Average thermal conductivity of iron silica porous structure for different heat fluxes/magnetic field orientations ................................ ................................ ........ 53 5 2 Thermal conductivity vs prosity. ................................ ................................ ......... 53

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10 LIST OF ABBREVIATIONS ETC Effective Thermal Conductivity EXP Experimental MSPS Magnetically Stabilized Porous Structure TC Thermocouple THW Transient Hot Wire

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11 NOMENCLATURE S Variables C Thermal heat capacity [J/Kg.K] d Diameter [m] g Heat generation per unit volume [w/m 3 ] i Electrical c urrent [A] K Thermal conductivity [W/K.m] L Length [m] q Heat flux [W] R Electrical re r Radius [m] T Temperature [K] t Time [s] V Voltage [v] Greek letters Thermal diffusivity [m 2 /s] Thickness [m] Angle [degree] Density [Kg/m 3 ]

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12 Subscripts i insulation l per unit length r radial ref Ref erence w Wire

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13 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science INVESTIGATION OF THERMAL CONDUCTIVITY OF IRON SILICA MAGNETIC AL LY STABILIZED POROUS STRUCTURE By Samaun Nili May 2013 Chair: James F. Klausenr Major: Mechanical Engineering It is a fact of experience that simulation of thermo fluid properties of magnetically stabilized porous structure (MSPS) [1] measurement require s accurate value of thermal conductivity of structure. Therefore, there is a critical need for measurements of thermal conductivity of MSPS The d ramatic effect of magnetic field on the thermal conductivity of MSPS has not studied before In this study we have developed a new apparatus based on the transient hot wire technique to obtain measurement of thermal conductivity of MSPS under different magnetic field orientations. The experimental results show that, when an external magnetic field of 65 G is appl ied perpendicular or parallel to a hot wire axis, the geometry of iron particles are constrained, such that the most thermal conductivity decreased 12 % compared to the one without any magnetic field Then it was both numerically and experimentally verifie d that applying the magnetic field does not have any significant effect on the behavior of the propagation of heat in any direction. Therefore, it is concluded that the change in the thermal conductivity of MSPS is mainly due to the increase of porosity.

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14 T hermal conductivity is measured by tracking the thermal pulse propagation induced in the sample by a heating source consisting of an 80 m n ichrome wire. One E type exposed thermocouple was used to measure the temperature variation in the media.

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15 CHAPTER 1 IN TRODUCTION AND LITERATURE REVIEW 1.1 Literature Review The p orous media enhance s fluid flow mixing by increas ing the contact surface area, so porous structures are an effective heat transfer enhancement technique. Due to importance of the application o f porous structures, there is a huge motivation to study of the heat transfer characteristic in porous media. Catalyst and chemical particle beds, micro porous heat exchangers (solid matrix), p hase array radar systems, cooling of electronic components such as mirror in powerful lasers, industrial high temperature furnaces, packed bed regenerators, micro thrusters transpiration cooling, spacecraft thermal management systems fixed bed nuclear propulsion systems combustors and many others [ 2 6 ] can be consi dered as the application of these structures 1.1.1 Magnetically Stabilized Porous Structure ( MSPS ) Ayyoub M. Mehdizade and James F. Klausner in 2012 [ 1 ] have investigated on enhancement of thermochemical hydrogen production using iron silica MSPS. The MSPS is u sed as the reactive substrate for two step water splitting, hydrogen production process. The reactivity of the material has been kept intact by controlling and constraining the geometry of matrix particles inside the structure in a desirable manner by appl ying an external magnetic field (Figure 1 1). Their hydrogen production is higher than those who reported in open literature for two step water splitting process [ 1 ] Their experimental and analytical study of reaction kinetics of the laboratory scale magn etically stabilized iron silica porous structure and they indicated that, MSPS is very suitable for the industrial applications where the enhanced reaction rate is desired, and their proposed model can be used for the design of larger scale reactors [ 7 ]

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16 Figure 1 1. Schematic representation of the magnetically stabilized iron silica porous structure [ 1 ] 1. 1. 2 Importance o f Thermal Conductivity o f Porous Structures Recently, the porous structures have gained tremendous attention due to their wide industria l applications. Thermal conductivity is one of the major thermodynamic coefficients in the study of energy transport through porous Medias due to its applications in thermal energy storages devices, high temperature furnaces, bed catalyst, weather control, artificial heating and cooling of buildings, in geothermal operations, thermal exchange in heat pumps and energy conservation in buildings. Effective thermal conductivity (ETC) has been investigated extensively using both experimental and theoretical appr oaches b y various scientists in detail [ 8 ] 1. 1. 3 Heat Transfer i n a Packed Bed The complex heat transfer phenomenon in packed beds with co current gas liquid up flow has been extensively investigated in the literature and several models have been develope d in order to describe heat transfer in the bed. However, the

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17 proposed correlations are valid in specific flow regi mes only, for example: Nakamura, Tanahashi, Ohsasa and Suguyama (1981) studied the thermal conductivity of in pulsed flow, Sokolov and Yablok ova (1983) studied the thermal conductivity of bubble flow, Gutsche, Wild, Roizard, Midoux and Charpentier (1989) and Lamine et al., 1992 and Lamine et al., 1992b studied the thermal conductivity of separated flow. Besides, most of these studies related to water (coalescent liquid) and air (or nitrogen) flow [ 9 13 ]. 1.1. 4 Previous A nalytical S tud ies o n ETC o f P acked B eds Numerous analytic models have been created and modified for achieving the ETC of packed beds in the presence of a static gas. As the examp les, the models by Hall and Martin [ 1 4 ] referred to as ZBS. Three recent evaluations of a number of these models have been accomplished by Tsotsas and Martin [ 1 5 ], Fundamenski and Gierszewski [ 1 5 ], and Xu et al. [ 1 7 ]. The first two studies achieved that a reformed form of the ZBS model [1 3 ] did the best job of presenting the experimental data. The third study found serious absences with all three analytic models tested, and concluded that the UCLA two dimensional, finite element model [ 1 8 ] gave the most rel iable predictions using reasonable parameters.

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18 CHAPTER 2 CLASSIFICATION OF EXPERIMENTAL THERMAL CONDUCTIVITY MEASUREMENT The value of thermal conductivity depends on temperature, compression, chemical composition, physical structure, state of substance. Mo isture content also affects the thermal conductivity of a material. In fact there are many different techniques for measuring thermal conductivity. For limited range of materials, respecting to medium temperature and thermal properties, the proper te chniqu e has to be determined. A distinction can be made between steady state and transient state techniques. 2.1 Classification of Measurement Techniques 2.1.1 Steady State Technique s W hen the material which is analyzed is completely at equilibrium, the steady s tate techniques are generally performed Requiring a long time to reach to equilibrium is one of the main disadvantages of this method. However, the signal analysis would be very easy since the steady state implies constant signals. In t his method, therma l conductivity of medium is determined using temperature change and amount of heat flux across the surface. Thermal conductivity measurements using the steady state method are classified as a) h orizontal flat plate method, b) v ertical coaxial cylinder method c) s teady state hot wire method d) m ethod of concentric spheres, and e) a bsolute and relative methods. 2.1.2 Transient State Technique s Basically t ransient state techniques are used when the thermal conductivity of the medium can be determined form the temp erature response to heating. After an initial transition period, the raises in temperature of area close to the heater depend on just the thermal conductivity of the surrounding medium, and no linger on the heat

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19 capacity of the wire. In transient methods t here is no necessity of reaching a re al thermal equilibrium while the medium is heating up. Transient state techniques are fast and they are appropriate for quick measurements and they are suitable for field uses, as well. Typically in this method the temp erature measurement is taken from ( few centimeters away of the heater ). In other transient hot wire techniques t he temperature rise of the heater is measured in order to calculate thermal conductivity Transient state methods are classified as a)continuous line source (hot wire) method, b) c ylindrical source method, c)spherical source method, and d)plane source method. The present study is focused on the continuous line source method. 2.2 Classification of H ot W ire T echniques The THW is the well established as the most reliable, robust and accurate technique [1 9 ] for evaluating thermal conductivity of fluids [ 20 2 2 ] and solids [ 2 3 ]. The difficulty of determining the establishment of the steady state condition the difficulty i n preventing natural convection, this transient hot wire method has been chosen in this study In the transient hot wire technique i f free convection is present ed it is easy to be detect ed because it will affect the linearity in the graph of temperature rise verses the logarithm of time. Transient hot wire techniques are basically classified as the flowing: 2.2.1 Standard Cross Wire Method On this technique, thermocouple is soldered or spot welded at the center of the wire which is already suspended in through the medium. An electric impu lse passed through the wire and consequently, temperature rise due to the heating of the wire. The temperature rise in time is recorded by means of a thermocouple connected to the center of heat source Typically, this method mostly used to measure thermal conductivity of solids, powders and rarely for fluids. Wild temperature measurement

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20 range and proper temperature sensitivity are stated as the advantages for this method [2 4 ]. Due to the thermal contact resistance of the wire and thermocouple, some non li nearity errors occur during the measurement. When the direct current is applied to an asymmetrically arranged thermocouple, an error occurs to the temperature measurement, resulting in an increase or decrees of thermo electric voltage, respecting to the po larity applied. These errors can be prevented by taking the mean of the primary and reversed applied DC voltage polarity measurements or either applying an alternative current. 2.2.2 Single W ire R esistance T echnique In this technique, a single wire can act as a both temperature sensor and heat source which has been submerge to the sample. The temperature rise in the wire is measured by the change of the resistance, caused by the heat source. The influence of local non homogeneities is eliminated while measu rement of the hot wire mean temperature along its total or partial length [2 5 ] In this method, c ooling down of the wire by support, due to the finite length of the wire and finite axial boundary is suggested as a one of the mai n sources of error The fini te radius of the outer boundary, finite thermal conductivity of the wire, finite wire radius, and the finite head capacity of the wire can be classified as the other sources causing measurement error on this technique. However, these errors can be diminish ed by choosing an appropriate selection of hot wire and dimensions of the wire cell. This could be stated as a straightforward technique for measuring thermal conductivity of electrically conductive material, if the above mentioned errors are compensated. This method has been performed for measuring the thermal conductivity of magnetically stabilized iron silica porous structure in this study.

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21 2.2.3 Potential L ead W ire T echnique The potential lead wire technique is a modified version of single wire resistan ce method, in order to prevent the errors which are caused by the end effects. Two potential leads are connected to the hot wire in a proper distance from the ends on this technique. The current of heating is passed through the ends, while the potential dr op in the wire is measured across a known length using the potential leads. The measure lead wire are maintained at a smaller cross section compare to that of hot wire, in order to avoid any influence of connections [2 4 ] This is inappropriate method of me asurement for electrically conductive materials for the following reasons. First of all, difficulty in attaching the potential leads to the hot wire at the required distance from the ends du e to having insulation coating [2 6 ] The other reason is that, a d ip in the axial temperature profile of the hot wire caused by an alternative path for the heat flow created by the potential leads [2 7 ]. 2.2.4 Parallel W ire M ethod In this technique, in order to compensate the end error effect, two hot wires of different l ength are incorporated in the opposite arms of the bridge [2 8 ] The measurement section is considered by difference between the lengths of the two wires. Thus, this configuration allows us to have an absolute measurement by experimental elimination of the end effects. The end geometry of short and long wires should be match in order to have an accurate measurement. This considered as a major problem of this construction, since attaining to an ideal end connections is difficult. The other problem, though in significant, is that the two wires should have identical uniform cross section. Since the wire from the same wire spool may not have uniform cross section,

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22 t hus, improper cancellation of the end effects due to the different heat dissipation of wires occurs [2 7 ]. 2.3 Reason f or A dapting S ingle W ire T echnique In the present study the single wire hot wire method has been performed as the measurement instrument for iron silica magnetically stabilized porous structure thermal conductivity measurement. Simplicity of operation and low cost of construction is one of the reasons for adapting this method. Moreover, we need a very uniform insolation coating on the metal wire, which is difficult to attain in the case of cross wire and potential lead techniques due to co nnections on the hot wire itself. In the two wire parallel technique, it is difficult to construct identical end geometries. In case of the single wire method, only one hot wire is used I nstead of using the hot wire as a temperature sensor by itself, a th ermocouple in a reasonable distance from the hot wire was used to monitor the temperature on this study C onnections are easily attainable. Moreover, end errors can be minimized by optimizing the cell design.

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23 CHAPTER 3 PRINCIPLE OF ANALYSIS 3.1 Mathemati cal Analysis Thermal conductivity is measured by tracking the thermal pulse propagation induced in the sample by a heating source consisting of an 80 m n i ch rom e wire. One E type exposed thermocouple was used to determine the temperature in the media (Figu re 3 1). The heat impulse transferred to the wire between two observed times gives a temperature increment of 9 C in 350 seconds which is depend on thermal conductivity o f the structure. The line heat source solution for the problem of conduction in a sin gle phase fluid or solid is well known and classical. Let us consider a wire of finite diameter and infinite vertical extent embedded into the target single phase sample. Figure 3 1 The line heat source analytical problem underlying the transient hot wire method 3.1.1 Governing E quations The finite diameter is considered initially because it is more convenient to convert

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24 although very thin, wire diameter. Eventually the heat flux resulting from such a finite diameter wire will be evaluated in the limit when the wire radius tends to zero, thus converting it into the line heat source. The radius of this thin wire is taken as r w and the amount of heat generated per unit length (l) and of the n ikrom e wire by an electric current i [A] passing through the wire is [W.m 1], Where V is the voltage heating can be converted into the corresponding amount of radial heat flux from the wire to the surrounding fluid or soli d in the form Equation 3 1 : ( 3 1) Where q r at r = r w is the radial heat flux from the wire. The mathematical model for the hot wire method is based on an ideal, infi nitely long and thin continuous line source dissipating heat, of heat flux, per unit length, applied at time t = 0, in an infinite and incompressible medium. The general assumption is that heat transfer to the infinite medium of thermal conductivi ty k and thermal diffusivity is by conduction alone and thus increases both temperatures of the heat source and test medium with time. It is also assumed that the line heat source has uniform instant temperature everywhere, but is transient in time (virtually achieved with small diameter and long wire with large thermal conductivity and/or small heat capacity). dimensional (1 D) transient heat conduction in cylindrical coordin ates (Equation 3 2). ( 3 2 )

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25 Where, T = T 0 T is the temperature of the medium at any time t and arbitrary radial distance r T 0 is the initial temperature of the source and medium, and T is the temperature difference between the medium and initial temperature. Equation 3 2 is the subject of the following boundary conditions (Equation 3 3 and Equation 3 4 ), ( 3 3) at and ( 3 4) Where and C are density and specific heat capacity of the test medium, respectively. Solving for the radial heat conduction due to this line heat source leads to a temperature solution in the following closed for m that can be expanded in an infinite series as follows (Equation 1 5) which is outlined by Carslaw and Jaeger [ 2 9 ]. (3 5 ) Where represents the exponential integral function, and After initial, short transient period (i.e. t >> r 2 /4 ), except for the first term containing time t th e higher order terms could be neglected, resulting in a very good approximation as Equation 3 6 For a line heat source embedded in a cylindrical cell of infinite radial ext ent and filled with the test sample ( 3 6 ) Equation 3 6 reveals a linear relationship, on a logarithmic time scale, between the temperature and time. Thus, one way of evaluating the thermal conductivity is from the slope of the above relationship evaluated at any fixed radial position. However, the latter needs the knowledge of thermal diffusivity of the sample.

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26 There for, f or constant sample medium properties and a fixed and arbitrary radius r differentiation of Equation 3 6 shows that all dependence on radius r is lost and the following relation is obtained (Equation 3 7 ). ( 3 7 ) There for, the thermal conductivity can be obtained by rearranging Equation 3 6 as below (Equation 3 8 ): ( 3 8 ) Therefore, if temperature of the medium is measured as function of time at any fixed radial position, including at the point of contact with the line source (i.e. the temperature of the thin line source) which can be found by measuring the ch anges of the electrical resistance of the line heat source, the thermal conductivity of the test medium, k is proportional to the source heat flux and inversely proportional to the temperature (or temperature difference) gradient with regard to the natura l logarithm of time 3.1.2 Application of Hot Wire Technique for Porous Structures Typically, a bare metal wire which is centered in a sample is used for thermal conductivity measurement of the samples. Since the sample contains iron particles which are el ectrically conductive, there for ambiguous results in the measurements will appear due to application of bare wire. Some common problems which identified by Nagasaka and Nagasahima [ 2 6 ] in the application of ordinary transient hot wire technique to electri cally conductive liquids are: Resulting of ambiguous measurement of generated heat in the wire due to p ossible current flow through the liquid Polarization of the wire surface

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27 Distortion of output voltage signal due to the conducting liquid cell Using an e lectrically insulating material in order to overcome these errors is recommended. The study of thin insulation on temperature distribution has been performed by Nagasaka and Nagashima [ 2 6 ] and outlined by Yamasue et al. [ 30 ]. The temperature rise of hot w ire is given as Equation 3 9, ( 3 9 ) Where A 0 B 0 and C 0 are defined as below (Equation s 3 10 3 11 3 1 2 ): ( 3 10 ) ( 3 11 ) ( 3 12 ) Where, r 0 is the sum of the radius of the wire r w and the insulation thickness Su bscripts w and I represent wire and insulation, respectively. Comparison between equations 3 7 and 3 9 shows that the term is because of the existence of the insulation on the wire. Thus, the plot of verses wi ll shifted without changing the slope by the constant of A 0 if the term is negligibly small in comparison with the Electrical insulation coating to bare metal wire has been recommended for electrically conduct ing fluids. Nagasaka and Nagashima have coated the platinum wire (diameter

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28 aqueous NaCl solution [ 2 6 ]. While to form an electrically insulating layer of tantalum peroxide (thickness 70 nm) [ 31 ], Yu et al. have used on a platinum in order to measure thermal conductivity of nanofluids [ 3 2 ]. Jwo et al. [ 3 3 ] insulated a Nickel Chromium alloy wire with Teflon to measure thermal conductivity of CuO nanofluids. Recently Ma in his thesis has utilized a platinum wire for measur ing t hermal conductivity of various combinations of nano crystalline material and base fluids [ 3 4 ]. 3.2 Hot wire Apparatus D esign The present design has been conceptualized to provide a flexible method to easily replace the sample and disassemble the cell to cl ean the parts. Some of the important design factors that have been considered are: flexibility in handling and cleaning, centering of the platinum hot wire, connections of the leads to the hot wire, electrical wire routing, temperature measurement of the sample, and electrical and signal wiring connections. The main design parameters are: (a) material of hot wire, (b) radius of hot wire, (c) insulation tube, (d) length of hot wire, (e) radius of the test sample outer boundary, and (f) length of the sample. Nichrome has been selected as superior hot wire material. It has higher thermal conductivity (TC) compared to the tantalum, also used as hot wire. Along with the material, hot wire radius is one of the most important parameters for the cell design. Among commercially available sizes, 80 wires have been selected

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29 for the present application, since smaller 12.5 cleaning and handling of micro particle samples and it also provide a desirable value of res istance in compare to the internal resistances. A 1/16 inches ceramic tube has been selected as insulating material, as it is highly resistant to electric conduction, chemical reactions, corrosion and stress cracking at high temperatures. An 80 nichrome wire with a ceramic insulation tube of 0.44 mm thickness, has been used as the hot wire. In this design, the length of the nichrome hot wire (L w ) was taken as 0.15 m. The hotwire cell outer boundary radius was determined as 49mm. The overall sam ple volume V c after fabrication is calibrated to be 246 mL. A cross sectional view of the newly designed hotwire thermal conductivity apparatus is shown in Figure 3 2 a b Figure 3 2 S chematic repre sentation of the transient hot wire experiment al setup A) Front view. B ) T op view of the hot wire cell which represents thermocouples and heat source position.

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30 Figure 3 3 Experimental setup for THW experiment Photo courte sy of Nili, S. where r 0 d 0 r w d w T 0 R w ,L and q represent the radius of the cell, diameter of cell, radius of the thin wire, diameter of the thin wire, distance between the magnets room temperature, electrical resistance of the wire and heat flux, resp ectively. The major assembly components of the apparatus cell are: base plate, outer shell, and cell caps with hot wire. The cell base plate with five threaded holes at the center and corners of the plate is used for convenient assembling and disassembling the outer shell. The outer quartz shell with 46 mm inner diameter acts as the sample test particles reservoir. The Teflon cell caps, designed and fabricated to slide fit into the outer shell, are hollow inside. The inner three thermocouples, mounted on th e inside of the tube, monitor the test particles temperature. Even though in this technique only one thermocouple is required for evaluation of thermal conductivity, the second thermocouple is added to the system in order to crosscheck the calculated ther mal conductivity from the temperature history. The third thermocouple, orthogonal to the second thermocouple is added as well in order to see whether there is uniform heat flux in azimuthal direction.

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31 All temperature measurements are controlled using the L abVIEW 2011 user interface and NI USB 6211 data acquisition with a hot wire power supply (14602ps MPJA) as and a multimeter (T&M ALLIANCE) for measuring the amp and voltage of the hot wire with the resolution of 10 mV and 1 mA. All thermocouples are calib rated using a high resolution thermometer and we used a thermistor glass 10K OHM D0 35 AL03006 5818 97 G1 as the cold junction compensation in order to have more accurate measurement. Three E type thermocouples are embedded in the 9.1 mm and 18. 3 mm in the mixture of the iron silica particles with the size range of 63 75 and 75 respectively. Table 3 1 lists the dimensions of the experimental set up while Figure 3 4 experimental apparatus. The therm al conductivity under two different magnetic fields orientation has been investigated (Figure 3 6). Figure 3 4 Experimental setup while there is a vertical magnetic field Photo courtesy of Nili, S.

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32 Table 3 1 Geometry of a pparatus R w d w r w d o r o r 1 r 2 L mm mm mm mm mm mm mm 20.631 3. 1 1.5 45.7 22.8 9.1 18. 3 300 The fixture in Figure 3 4 was made in a way to provide three degree of free dom for each magnet Thus the desire magnetic field properties can be easily achieved. 3.3 Sample P reparation The 63 75 micron 99.65% purity iron particles mixed with 75 105 micron silica particles with volume ratio of has been used for this experiment. Two magnets have been used in order to stabilize the structu re while it was being fluidized. Table 3 2 shows the sample physical material properties before and after mixing The iron silica chains can be easily detected in Figure 3 5 D A B C D Figure 3 5 The powders and mixture. A ) S ilica particles B ) I ron particles C ) I ron silica parties before stabilizing D ) magnetical ly stabilized iron silica packed bed Photo courtesy of Nili, S.

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33 Table 3 2 Material physical properties Size range Material density Powder ap parent density Mass powder Porosity Thermal heat capacity mm g/cm 3 g/cm 3 g % J/g K Iron 63 75 7.87 2.81 275.80 63 0.703 Silica 75 105 2.65 1.55 230.00 41 0.450 Mixture 1.89 505.8 53 0.565 a b Figure 3 6 Typical sche matic setup for the transie nt hot wire experiment A ) With horizontal magnetic field B ) With vertical magnetic field 3.4 Measurement Process All temperature measurements are controlled using the LabVIEW 2011 user interface and NI USB 6211 data acquisit ion with a hot wire power supply (14602ps MPJA) and a multimeter (T&M ALLIANCE) for measuring the amp and voltage of the hot wire with the resolution of 10 mV and 1 mA. All thermocouples are calibrated by using a high resolution thermometer and a thermisto r glass 10K OHM D0 35 AL03006 5818 97 G1 was used as the cold junction compensation in order to have an accurate measurement. Thermal conductivity measurements of the sample under each condition have been repeated 2 times. The time range from 250 to 750 s has been de termined to

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34 be l inear ( Figure 3 8) The reference temperature T ref at which magnetic field orientation measured, is evaluated as the process average temperature ( Equation 3 13) ( 3 13 ) Where and are corresponding to temperature rises at t 1 and t 2 respectively. The powder temperature are measured by three E type thermocouples with respect to time is shown in Figure 3 7 Due to the transient nature of the experiment, thermal conductivity is measured using exposed thermocouples. It is expected that the results of the exposed thermocouple are more accurate due to its smaller time const ant. After passing a transition region, the temperature rise falls in a linear fashion for both of the thermocouples ( Figure 3 8 and Figure 3 9 ). Next, measurements were repeated for different heat fluxes and as expected the ratio of the heat flux verses the slope of temperature log of time remains constant. Then the same experiments were repeated while the system was exposed to the vertical and horizontal magnetic field s hown in ( Figure 3 8 and Figure 3 9 ) with a magnetic flux density of 65 gausses. Figure 3 7 T hermocouples and heat source position Photo courtesy of Nili, S.

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35 Figure 3 8 Temperature raise vs. time in log scale with 3.9 watts heat flux for different magnetic field orientations Figure 3 9 Temperature raise vs. time in log scale with 7.3 watts heat flux for different magnetic field orienta tion

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3 6 3.5 Results For 2:1 silica/iron mixture ratio, the experimental results showed that, when the magnetic field direction was perpendicular to the hot wire axis, the maximum therma l conductivity reduction was 12 % in comparison to the case without any mag netic field. It was suggested that the magnetic field organized the iron chains in the normal direction of hot wire surface a nd repulsive force between chains, increases the structure porosity. Both of these effects will limit the heat flux penetration fro m the hot wire to the media and results in a lower thermal conductivity. In the other hand, when the magnetic field switched to the parallel direction to hot wire axis, the radial thermal conductivity decreased by 1 1 % due to decreased contact between iron particles in the radial direction Table s 3 3 to 3 5 and F igure s 3 10 to 12 show the calculated value of thermal conductivity of the material with/without magnetic field The raw experimental data was recorded from exposed E type thermocouple for two di fferent amounts of heat fluxes. Figure 3 10. Thermal conductivity of iron silica powder while there is no external magnetic field for porosity of 57.8 %

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37 Table 3 3 Thermal conductivity measurement of mixture without magnetic field Experiment number mass (g) Power (W) Porosity (%) Thermal Conductivity (W/m K) 1 439.3386 3.77 57.8 0.211 2 439.3386 3.77 57.8 0.208 3 439.3386 3.78 57.8 0.211 4 439.3386 3.77 57.8 0.216 1 439.3386 7.36 57.8 0.216 2 439.3386 7.34 57.8 0.219 3 439.3386 7.35 57.8 0.220 4 439.3386 7.34 57.8 0.220 Thermal conductivity of the sample without any magnetic field f or two different heat fluxes are shown in Table 3 3 and Fig 3 10 for fo u r measurement set s Figure 3 11 Thermal conductivity of iron silica powder while there is a 65 G horizontal external magnetic field vs. experiment number for porosity of 62.9 %

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38 Table 3 4. Thermal conductivity measurement of iron silica porous structure while there is an 65 G horizontal external magnetic field Experiment number mass (g) Power ( W) Porosity (%) Thermal Conductivity (W/m K) 1 402.1074 3.76 62.9 0.188 2 402.1074 3.72 62.9 0.192 3 402.1074 3.76 62.9 0.191 4 402.1074 3.76 62.9 0.181 1 402.1074 7.36 62.9 0.194 2 402.1074 7.36 62.9 0.192 3 402.1074 7.37 62.9 0.189 4 402.1074 7.3 1 62.9 0.198 Figure 3 12 Thermal conductivity of iron silica powder while there is a 65 G horizontal external magnetic field vs. experiment number for 59.5 % of porosity

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39 Table 3 5 Thermal conductivity measurement of iron silica porous structure wh ile there is a 65 G horizontal external magnetic field Measurement set mass (g) Power (W) Porosity (%) Thermal Conductivity (W/m K) 1 439.33 3.8 6 59.5 0.217 2 439.33 3.82 59.5 0.206 3 439.33 3.8 1 59.5 0.207 4 439.33 3.79 59.5 0.206 1 439.33 7.3 8 59. 5 0.217 2 439.33 7.3 8 59.5 0.221 3 439.33 7.35 59.5 0.223 4 439.33 7.32 59.5 0.219 Thermal c onductivity of the sample wi t h 65 G external horizontal magnetic field fo r two different heat fluxes and porosities have been shown in Table 3 4 Fig ure 3 11 Table 3 5 and Figure 3 12 report the measured data for fo u r measurement set s Figure 3 1 3 Thermal conductivity of iron silica powder while there is a 65 G vertical external magnetic field vs. experiment number for 62.9 % of porosity

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40 Table 3 6 Thermal conductivity measurement of iron silica porous structure while there is a 65 G vertical external magnetic field Experiment number mass (g) Power (W) Porosity (%) Thermal Conductivity (W/m K) 1 402.1074 3.84 62.9 0.19 1 2 402.1074 3.84 62.9 0.1 90 3 402.1 074 3.84 62.9 0.190 4 402.1074 3.83 62.9 0.19 1 1 402.1074 7.45 62.9 0.194 2 402.1074 7.45 62.9 0.197 3 402.1074 7.4 5 62.9 0.197 4 402.1074 7.42 62.9 0.195 Figure 3 14 Thermal conductivity of iron silica powder while there is a 65 G vertical exte rnal magnetic field vs. experiment number for 59.5 % of porosity

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41 Table 3 7 Thermal conductivity measurement of iron silica porous structure while there is a 65 G vertical external magnetic field Measurement set Mass (g) Power (W) Porosity (%) Thermal C onductivity (W/m K) 1 439.33 3.77 59.5 0.206 2 439.33 3.97 59.5 0.211 3 439.33 3.76 59.5 0.195 4 439.33 3.78 59.5 0.197 1 439.33 7.3 4 59.5 0.206 2 439.33 7.35 59.5 0.202 3 439.33 7.3 4 59.5 0.210 4 439.33 7.32 59.5 0.209 Thermal conductivity of th e sample with 65 G external vertical magnetic field for two different heat fluxes and porosities have been shown in Table 3 6 Figure 3 1 3 Table 3 7 and Figure 3 14 report measured data for four measurements set. To summerize in Figure 3 1 5, Table 3 8 F igure 3 16 and Table 3 9 the average of four experimental measurement s of thermal conductivity in different heat fluxes porosities and magnetic field orientations are shown respectively. Figure 3 15 Average thermal conductivity of iron silica porous s tructure for different heat fluxes and magnetic field orientations

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42 Table 3 8 Average thermal conductivity of iron silica porous structure for different heat fluxes and magnetic field orientations Heat flux (W) Average thermal conductivity without magnet ic field (W/m K) Average thermal conductivity with horizontal magnetic field (W/m K) Average thermal conductivity with vertical magnetic field (W/m K) 3.8 0.21 2 0.188 0.190 7.4 0.21 1 0.193 0.196 In Figure 3 13 and Table 3 6 we have the porosity of 57.8 % and 62.9 % for the case that there is no external magnetic field and while there is horizontal/vertical magnetic field respectively. Figure 3 17 compares thermal conductivity of magnetically stabilized silica iron powder for two different porosities an d magnetic field orientations. Figure 3 16 Average thermal conductivity of iron silica porous structure for different heat fluxes and magnetic field orientations and porosity of 59.5 %

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43 Table 3 9 Average thermal conductivity of iron silica porous struct ure for different heat fluxes and magnetic field orientations and porosity of 59.5 % Heat flux (W) Average thermal conductivity with horizontal magnetic field (W/m K) Average thermal conductivity with vertical magnetic field (W/m K) 3.8 0.209 0.204 7.4 0.220 0.207 Figure 3 17 Average t hermal conductivity measurement of iron silica porous structure with vertical and horizontal magnetic field for different porosities. A) 3.8 watts heat flux B) 7.4 Watts heat flux

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44 CHAPTER 4 NUMERICAL SIMULATION O F HEAT TRANSFER ON IRON SILICA POURS STRUCTURE 4.1 Overview I n this chapter magnetically stabilized iron silica porous structure has been numerically simulated in order to validate the experimental measurement results and also confirm there is a uniform r adial heat flux in our sample. Thus, a computer code y using Fortran 90 has been created and developed and the results have been shown by utilizing the Tec plot 360, 2012 software 4.1.1 Validating the Experimental Measurements Using the Numerical Simulatio n of Heat Transfer on Iron Silica Pours Structure In this section a numerical curve was fitted on our experimental data to validate our measurements. For this purpose, an energy balance equation is used for each element by using explicit finite volume meth od for iron silica pours structure once we do not have any external magnetic field and for the case which there is a horizontal external magnetic field perpendicular to the hot wire surface (Figure 4 1 and Eq uation 4 1 ). Figure 4 1. Schematic representa tion of heat balance for a control volume, advantage of symmetry boundary condition used, half sized meshes used for boundary edges.

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45 (4 1) Where q i (i=a,b,c,d), dx, dy, dt, g are representing the amount of heat flux which is comes through the element from each dire ction, element size, time step, amount of heat generated per unit length respectively and previousTemp and currentTemp are regarding to the element temperature in two different time steps, m and n subscripts are representing the element location. Figure 4 2 shows the analytical solution from equation 3 5 and a numerical curve fitted on our experimental data and we can see that all our measurements falls on a straight line in logarithmic scale for first 750 seconds which is enough time for having reliable me asurements. After passing this time, the numerical curve departs from the experimental measurements, indicating that the transient method is no longer valid and the temperature distribution is approaching to an asymptotic steady state condition. The analyt ical solution in Figure 4 2 also shows lower ( t >> r 2 /4 ) and upper bound (750 sec) for valid measurement and it can be seen that the upper bound for both analytical and numerical simulation are the same. Therefore, this model is valid only for the first 750 seconds in our experiment.

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46 Figure 4 2. Comparison between numerical simulation and experimental measurements for homogeneous mixture of i ron s ilica powder in experiment 1 without external magnetic field 4.1.2 Numerical Simulation of Heat Distribution for Anisentropic Medium Now we investigate the heat f lux and temperature distribution along the azimuthal direction while the media is anisotropic and consisting of two arbitrarily materials with different thermal conductivities of k 1 and k 2 It was initially expected that the heat flux and temperature distr ibution are not identical at the location of thermocouples 1 and 2 (shown in Fig ure 4 3a) due to different thermal resistances when two different materials with conductivity of k 1 and k 2

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47 appeared frequently in the structure (Fig ure 4 3a 4 3b) Note that in all Fig ure 3 4, the total volumes of material 1 and 2 are kept unchanged and the only difference in the structure is their frequency of appearance The mesh study is performed in order to ensure the high accuracy of simulation is achieved Fig ure 4 4 sh ows the temperature as a function of time with different grid resolution s for the highest frequency of appearance in our study It shows that the results are grid independent when more than 200 uniform grids are used in each direction for the highest simul ated frequency of the appearance; the material 1 and 2 include 3 and 6 grids, respectively Figure 4 3 F requency of iron silica chains appearance wh en the sample is exposed to horizontal magnetic field.

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48 Figure 4 4. Mesh independent study of numerical solution for the iron silica chain structu r e for a/L = 0.015 In Fig ure 4 5, the dimensionless temperature of thermocouples of 1 and 2 (see Fig ure 4 3a) is shown as a function of the ratio a/L where a and L represent the material 1 thickness and the cell radius respectively. A decrease in a/L value corresponds to an increas e in the frequency of the appearance of material 1 for a fixed volume of the sample. Figure 4 5 shows that as the a/L decreases (or frequency of appearance increased) the thermocouple 1 and 2 measurments merged to each other when a/L < 0.042 These results suggest that at high frequency of appearance for k 1 /k 2 =3, the temperature field is insensitive to the anisentropic media. Thus, an average thermal conductivity can be used to simulate the heat distribution within the media

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49 Figure 4 5. The dimensionless temperature as a function of a/L of chains appearance for points 1 and 2 and k 1 /k 2 =3 In order to ensure that this conclusion can be generalized for all the cases, the same numerical si mulation is performed for different thermal conductivity ratios (k 1 /k 2 ) Figure 4 6 shows t he dimensionless temperature as a function of of a/L at the same radial position at =0 and 90 when the thermal conductivity ratio is 50 In this case, the similar trend is observed where the temperature measured at points 1 and 2 merge together for high frequency of appearance of material 1 and 2 when a/L < 0.025

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50 Figure 4 6. The dimensionless temperature as a function of a/L of chains appearance for two orthogo nal fixes radial positions of points 1 and 2 and k 1 /k 2 = 50 Figure 4 7 shows the simulation results variation of the heat flux and temperature for different angles at the fixed radial to the heat source. This figure shows that, f or high frequency of iron si lica chains appearance (see Figure 4 3 ) there is no significant change in radial heat flux and temperature distribution along the azimuthal direction (Figure 4 7 and Figure 4 8 ).

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51 Figure 4 7 Azimuthal radial heat flux and relative temperature (compared to room temperature) of iron silica distribution for a fixed radial position The temperature contour has been also plotted after 350 second in Figure 4 8 Therefore, as was discovered in previewed figures, for high frequency of appearance of material 1 an d 2 the isothermal lines are located on circles where their distance to the heat source are unchanged Figure 4 8. Temperature contour horizontal chains at 350 seconds and k 1 /k 2 =3

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52 CHAPTER 5 CONCLUSIONS AND FUTURE WORKS 5.1 Conclusion The experimental results showed that, when the magnetic field direction was perpendicular to the hot wire axis, the maximum thermal conductivity reduction was 12 % in compar ed to the case without any magnetic field. It was suggested that the magnetic field organized the ir on chains in the normal direction of hot wire surface a nd repulsive force between chains, increases the structure porosity. Both of these effects will limit the heat flux penetration from the hot wire to the media and results in a lower thermal conductivit y On the other hand when the magnetic field switched to the parallel direction to hot wire axis, the radial thermal conductivity decreased by 1 1 % due to decreased contact between iron particles in the radial direction. Table and Figure 5 1 show the average calculated value of thermal conductivity of iron silica porous structure with/without magnetic field measured by exposed thermocouples for two different amounts of heat fluxes value s and Figure 5 2 shows the thermal conduct ivity of iron silica powder while the porosity was changing. Table 5 1. Average t hermal Conductivity and the slope of temperature vs. log of time graph with different values of heat fluxes and magnetic field orientations. Heat flux (W) Average thermal co nductivity without magnetic field (W/m K) Average thermal conductivity with horizontal magnetic field (W/m K) Average thermal conductivity with vertical magnetic field (W/m K) 3.8 0.21 2 0.188 0.190 7.4 0.21 1 0.193 0.196

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53 Figure 5 1. Average thermal co nductivity of iron silica porous structure for different heat fluxes/magnetic field orientations Figure 5 2. Thermal conductivity vs prosity. A) 3.8 watts heat flux. B) 7.3 watts heat flux Also the numerical simulation shows that, the temperature of u nchanged radial positions from the heat source merges for anis e ntropic m edia, if the frequency of appearance of materials is high enough. Moreover this study suggests that, for simulation purposes, we might use the average conductivity values ( reported in Figure 5 1) to find the temperature distribution inside the media. It was both numerically and

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54 experimentally verified that applying the magnetic field does not have any significant effect on the behavior of the propagation of heat in any direction. There fore, it is concluded that the change in the thermal conductivity of MSPS is mainly due to the increase of porosity. Further investigation s need to be done for the same structure at high temperature to evaluate the sintering effect on the thermal conductiv ity. 5. 2 F uture W orks To further explain these below items can be studied in future studies : 1. Investigation on effect of higher temperature on thermal conductivity of the sintered pours structure 2. Investigation of effect of different orientation/flux magneti c field on thermal conduct ivity of the packed bed reactor 3. Investigation on effect of higher temperature on thermal conductivity of MSPS 4. Computing the convective heat transfer coefficient by a similar method and investigation of the influence due to magneti c field presence 5. Validating the re sults with numerical simulation

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55 REFERENCES [ 1 ] Ayyoub M. Mehdizadeh, James F. Kl ausner, Amey Barde, Renwei Mei, Enhancement of thermochemical hydrogen production using an iron silica magnetically stabilized porous structure, International Journal of Hydrogen Energy, Issue 11, 2012;37: 8954 8963. [ 2 ] Subbojin V.I. Haritonov V.V Thermophysics of cooled laser mirrors. Teplofizika Vys. Temp. (1991); 29 (2) :365 375 [ 3 ] Jeigarnik U.A Ivanov F.P Ikranikov N.P Experim ental data on heat transfer and hydraulic resistance in unregulated porous structures Teploenergetika (1991); (2) : 33 38 [ 4 ] Lage J.L Weinert A.K Price D.C Webe R.M. r Numerical study of a low permeability microporous heat sink for cooling phased ar ray radar systems Int. J. Heat Mass Transfer 1996; 39 (17) : 3633 3647 [ 5 ] Chrysler G.M Simons R.E An experimental investigation of the forced convection heat transfer characteristics of fluorocarbon liquid flowing through a packed bed for immersion co oling of microelectronic heat sources, in: AIAA/ASME Thermophysics and Heat Transfer Conference, Cryogenic and Immersion Cooling of Optics and Electronic Equipment, 1990 ASME HTD 131 : 21 27 [6] Kuo S.M Tien C.L Heat transfer augmentation in a foam material filled duct with discrete heat sources, in: Intersociety Conference on Thermal Phenomena in the Fabrication and Operation of Electronic Components, IEEE, New York 1988 : 87 91 [7] Ayyoub M. Mehdizadeh, James F. Klausner, Amey Barde Renwei Mei, Enhancement of thermochemical hydrogen production using an iron silica magnetically stabilized porous structure, International Journal of Hydrogen Energy, Issue 11 2012 ; 37 : 8954 8963 [ 8 ] Singh Ramvir, Bhoopal R.S Kumar Sajjan, Prediction of effective thermal conductivity of moist porous materials using artificial neural network approach, Building and Environment, 12, December 2011 : 46; 2603 2608 [ 9 ] Nakamura M.T Tanahashi D., Ohsasa T.K Suguyama S Heat transfer in a packed bed with gas liquid con current upflow Heat Transfer: Japanese Research, 1981; 10 : 92 99 [ 1 0 ] Sokolov V.N Yablokova M.A Thermal conductivity of a stationary granular bed with upward gas liquid flow, Journal of Applied Chemistry USSR (Zh. Prikl. Khim.), 1983; 56 : 551 553.

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56 [ 1 1 ] G utsche S Wild G Roizard C Midoux N & Charpentier J. C Heat transfer phenomena in packed bed reactors with co current up flow of gas and liquid. Proceedings of the fifth conference on applied chemical unit operations and processes, V eszprm, Hunga ry, 1989: 402 408. [ 1 2 ] Lamine A.S transfer in packed bed with cocurrent upflow, Chemica l Engineering Science, 1992;47: 3493 3500 [ 1 3 ] Lamine A.S mics and heat transfer in packed bed with cocurrent upflow Chemical Engineering and Pro cessing, 1992;6: 385 394 [ 1 4 ] Hall R.O.A Martin D.G The thermal conductivity of powder beds. A model, some measurements on UO2 vibro compacted microspheres, and the ir correlation] referred to as HM, and the model of Zehner, Bauer and Schlnder [Effective radial thermal conductivity of packings in a gas flow. Part II, Thermal conductivity of the packing fraction without gas flo w, Int. Chem. Eng 1978 ;18: 189 204 [ 1 5 ] Tsotsas E Martin H., Thermal conductivity of packed beds: a review, Chem. Eng. Process,1987; 22 : 19 37 [ 1 6 ] Fundamenski W Gierszewski P Heat transfer correlations for packed beds Fusion Technol 1992; 21 : 2123 [ 1 7 ] Xu M Abdou M.A Raffray A.R The rmal conductivity of a beryllium gas p acked bed Fusion Eng. Des,1995; 27: 240 246 [ 1 8 ] Adnani P Modeling of transport phenomena in porous media, PhD thesis, University of Cal ifornia, Los Angeles, CA, 1991. [ 1 9 ] Hammerschmidt U. and Sabuga W Transient Hot Wire THW Method: Uncertainty Assessment, Int. J. Thermophys., 2000: 21 ; 1255 1278. [ 2 0 ] De Groot, J. J Ke stin, J and Sookiazian, H Instrument to Measure the Thermal Conductivity of Gases, Physica Amsterdam, 1974: 75 ; 454 482. [ 2 1 ] Healy J. J de Groot J. J and Kestin J The Theory of the Transient Hot Wire Method for Measuring Thermal Conductivity, Physica C, 1976: 82 ; 392 408. [ 2 2 ] Kestin, J and Wakeham, W. A A Contribution to the Theory of the Transient Hot Wire Technique for Ther ma l Conductivity Measurements, Physica A, 1978: 92 ; 102 116. [ 2 3 ] Assael, M. J Dix, M Gialou, K Vozar, L and Wakeham, W. A., Application of the Transient Hot Wire Technique to the Measurement of the T hermal Conductivity of Solids, Int. J. Thermophys. 2002: 23 ; 615 633

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57 [ 2 4 ] Vozar, L A computer controlled apparatus for thermal conductivity measurement by the transient hot wire method. Journal of Thermophysics and heat transfer ,1996 : 13 (4) ; 474 480 [ 2 5 ] Tye, R.P.(ed), Thermal Conductivity, 1969: 2. L ondon: Academic Press [ 2 6 ] Nagasaka, Y and Nagashima, A Absolute Measurement of the Thermal Conductivity of Electrically Conducting Liquids by the Transient Hot Wire method, J. Phy. E: Sci. Instrum., 1981: 14 ; 1435 40 [ 2 7 ] Johns, A. I Scott, A. C., Wa tson, J.T.R F erguson, D., and Clifford, A. A Measurement of the thermal conductivity of gases by the transient hot wire method. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1988: A 325 ; 295 3 56 [ 2 8 ] Roder, Hans M A transient hot wire thermal conductivity apparatus for fluids. Journal of Reasearch of t he National Bureau of Standards, 1981: 86(5) ; 457 493 [ 2 9 ] Assael, M. J Chen, C. F., Metaxa, I and Wakeham, W. A Thermal Conductivity of Suspensions of Carbon Nanotubes in Water, Int. J. Thermophys., 2004: 25 ; 971 985. [ 30 ] Yamasue, E Susa, M Fukuyama, H and Nagata, K Nonstationary Hot Wire Method with Silica Coated Probe for Measuring Thermal Conductivities of Molten Metals, Metal lurgical and Materials Transactions A, 1999: 30 : 1971 79. [ 31 ] Perkins, Richard A. Measurement of the Thermal Properties of Electrically Conducting Fluids using Coated Transient Hot Wires, Presented at the 12 th Symposium on Energy Engineering Sciences, Dept of Energy, CONF 9404137, 1994 : 90 97. [ 3 2 ] Yu, We nhua Hull, John R and Choi. Stephen U. S., Stable and Highly Conductive Nanofluids Experimental and Theoretical Studies, The 6th ASME JSME Thermal Engineering Conference, Hawaii Islands, Hawaii., 2 003. [ 3 3 ] Jwo, C. S Teng T. P., Hung C. J., and Guo Y. T Research and Development Device for Thermal Conductivity of Nanofluids, Journal of Physics, Conference Series 13 : 55 58 [ 3 4 ] Ma, Jack Jeinhao M.S. Thesis: Thermal Conductivity of Fluids Conta ining Suspensions of Nanometer Sized Particles, Massachusetts Institute of Technology, 2006.

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58 BIOGRAPHICAL SKETCH Samaun Nili was born in 1987 in Miami Florida and moved overseas at the age 7 due to his father s professions. He complet ed his elementary as w ell as high school educations in Tehran Iran. Since Samaun had technical and mathematical oriented mind he chose mathematics and physics as his major in pre university studies His achievements from elementary through pre university were outstanding. He took a national university entry examination and he got the eligibility to take any engineering major in the top ten universities in Tehran but he chose m echanical engineering as his major. Samaun completed his undergraduate studies in 2009 with an excel lent performance from Azad University in Tehran Iran. Then he decided to move back to Florida for continuation of his higher educations in m echanical engineering. Samaun was admitted and started his first semester at Florida Atlantic University (FAU) in s pring of 2011 as a graduate student, majoring in m echanical e ngineering. During this time he realized that the Department of Mechanical and Aerospace E ngineering at the University of Florida (UF) wo uld serve his purpose the best therefore, he applied and was accepted into the Departm ent of M e chanical and Aerospace E ngineering in UF for fall of 2011 and completed his requirement for his M S degree in spring term of 2013 at the UF Samaun thinks there is much more to learn in the field of m echanical e ngineering and for that reason he is trying to enter to PhD program preferably at the University of Florida which he is anxiously waiting to receive his admission.