Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P2.60 - Experimental Setup to Investigate Gas Solid Heat Transfer in a Riser
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00497
 Material Information
Title: P2.60 - Experimental Setup to Investigate Gas Solid Heat Transfer in a Riser Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Saffaraval, F.
Siamie, A.
Mokhtarifar, N.
Saffar-Avval, M.
Razfar, M.R.
Mansoori, Z.
Imani, Y.
Abolgasemi, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: two-phase heat transfer
gas-solid flow
Nusselt number
Thermal effectiveness
 Notes
Abstract: An experimental study has been carried out on gas solid flowing in a tube at vertical position, the tube boundary condition is adiabatic condition, and the gas and solid particles are at different temperatures. Sand and hot air are used as solid and gas medium. The experimental rig enables to investigate the heat transfer between the gas and particles in which the effects of different parameters such as solid feed rate and air velocity on air-solid Nusselt number, thermal effectiveness of air and solid are studied. The particles diameter is 253 μm in a bed of 12 and 18.5 m/s gas velocities. Nusselt number is shown to be decreased with solids feed rate at lower solids feed rates typical of dilute/fast-fluidization regime, while it can be increased at higher solids feed rates. Thermal effectiveness of air was found to increase with solids feed rate and decrease with air velocity. Thermal effectiveness of solids was found to decrease with solids feed rate.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00497
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: P260-Saffaraval-ICMF2010.pdf

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1 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Experimental Setup to Investigate Gas Solid Heat Transfer in a Riser


F. Saffaraval, A. Siamie, N. Mokhtarifar, M. Saffar-Avval*, M.R. Razfar, Z. Mansoori, Y. Imani,
M. Abolgasemi

Mechanical Engineering Department, Amirkabir University of Technology,
Tehran, 15875-4413, Iran
mavval(aut.ac.ir



Keywords: Two-phase heat transfer, Gas-solid flow, Nusselt number, Thermal effectiveness


Abstract

An experimental study has been carried out on gas solid flowing in a tube at vertical position, the tube boundary condition is
adiabatic condition, and the gas and solid particles are at different temperatures. Sand and hot air are used as solid and gas
medium. The experimental rig enables to investigate the heat transfer between the gas and particles in which the effects of
different parameters such as solid feed rate and air velocity on air-solid Nusselt number, thermal effectiveness of air and solid are
studied. The particles diameter is 253 gtm in a bed of 12 and 18.5 m/s gas velocities. Nusselt number is shown to be decreased
with solids feed rate at lower solids feed rates typical of dilute/fast-fluidization regime, while it can be increased at higher solids
feed rates. Thermal effectiveness of air was found to increase with solids feed rate and decrease with air velocity. Thermal
effectiveness of solids was found to decrease with solids feed rate.


1. Introduction

Gas solid flow has found wide application in process industry
such as chemical, pharmaceutical, material, transportation
and process industries. Gas solid interaction is widely used to
transfer sufficient heat from gas to particles. This process
provides a method for drying of solid material in food
industry, pharmaceutical products, and chemical industry,
another application of gas solid heat transfer is found in heat
recovery from exhaust gas to preheat solid particles as raw
materials in process industries.
Extensive researches have been reported in the literatures
about gas solid flow fields and heat transfer. In spite of a
large number of research works on gas-solid flow field, less
attention has been paid to heat transfer in gas-solid flow.
Three main modes of heat transfer, bed-to-surface,
inter-particle and gas-to-particle heat transfer arise in
gas-solid flows. Many studies have been made on bed
to-surface heat transfer. Heat transfer in wall bounded
gas-solid flows with heat flux on the wall, considering
wall-bed and the gas-particle heat transfer were reported by
many authors (Jepson et al. [1], L. Farber and C. A. Depew et
al. [2] and others).
Particle-to-particle heat transfer can be the result from three
main mechanisms, heat transfer by radiation, heat conduction
through the contact points between the particles, and finally
heat exchange through the gas layer separating the particles.
The first mechanism is only significant at high temperatures.
The second one occurs when moving particles collide and
heat is conducted through the impact area, which is
negligible.
Most researches have theoretical, and few ones have
experimental approach. Mansoori et al. (2000) [3] showed
that the particle interactions and collisions could markedly


influence the particle thermal fluctuation intensity. In a four
way interaction Eulerian-Lagrangian model, Mansoori et al.
(2002) [4] computed the inter-particle contact heat transfer in
turbulent gas-solid flow using a deterministic kinetic model.
It is shown that inter-particle collision amplifies the effect of
solid phase to decrease temperature intensity near the wall
and increase it near the pipe center line region. Boulet et al.
[5] have suggested the same Eulerian-Lagrangian model to
predict the heat transfer in a vertical pipe wall and a turbulent
gas-solid suspension. More details about gas-solid
theoretical approach are given in several references [6, 7, and
8].
Experimental works in literature as mentioned before, are not
numerous. Some of them such as Y. Tsuji et al. (1984) [9]
have been experimentally investigated flow field and related
specification of gas solid flow in vertical riser. C. Crowe et al.
(1998) [10] proposed heat transfer coefficient for single
particle in gas flow. Recent study on gas solid heat transfer is
to determine gas solid heat transfer on wall in vertical tube
done by Mansoori et al. (21.i 14 [11].The only limitation in
this experimental set up is loading ratio. K. S. Rajan et al.
(2008) [12] have conducted an experimental study on
vertical pneumatic conveying, in this experimental scheme,
particles were introduced to riser by means of air flow rate,
therefore particles flow rate is dependent of air flow rate, and
they could not independently investigate the effect of
particles mass flow rates on heat transfer.
In this study, an experimental set up is designed so that the
riser as the test section can be adjusted from vertical to
horizontal positions. Solid particle feeder has the possibility
to feed more particles to provide higher solid mass fraction.
Also solids feed rate can be regulated independent of air flow
rate. Hence the experimental set up provides vast ability to
study the gas-solid heat transfer.








2. Nomenclature


D Diameter (m)
A Heat transfer area (m2)
m Mass (kg)
mh Mass flow rate (kg/s)
z Load ratio
V Velocity (m/s)
T Temperature (C)
T Temperature of solid particle before feeder (C)
P
Tbf Temperature of air in the riser before feeder (C)
C Specific heat (J/kg K)
K Thermal conductivity (W/m k)
U Heat transfer coefficient (W/ m2 K)
Nu Nusselt number
S Thermal effectiveness
Greek letters
P Density (kg/ m3)
AT Temperature difference (C)
ATin Log-mean temperature difference (C)
At Time difference (s)
Subscripts
g Gas
P Particle


3. Experimental Facility

3-1. Test apparatus


The experimental apparatus used in the
illustrate" 4-U4 1


present study is


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

5000.0 centimeter length. This bed consists of 5 pipes of 1
meter which are attached with flanges. A feeder is placed to
feed the solid particles to the air flow, solid mass flow rate is
regulated by means of a helical screw RPM. An inverter and
an electrical motor is used to control the screw RPM. The
hot air is supplied by an indirect gas fired heater then an
electrical heater is used to tune the hot air temperature, all
parts are insulated to maintain an adiabatic wall condition.
The end of the pipe is connected to a cyclone in order to
recover the solids in a receiver tank. Control valves are
installed to control air flow rate.
Pt-100 high precision temperature sensors and velocity pitot
tube gauge are connected to a data logger and then to a
control unit to save the data which are transmitted to a
computer to be analyzed. Pt-100 temperature measuring
accuracy is about 0.25-0.4 C in the range of -200 to +600 C
and its dynamic response time is 20 seconds. Thus, the
uncertainty in measuring temperature of 100 C would be
0.35%. The air velocity is measured by a well calibrated pitot
tube with 35 cm length and 7 mm diameter. This pitot tube is
connected to data logger and the measuring system is
designed to automatically calculate density on the basis of
the measured values of temperature and humidity. The
uncertainty in measuring gas velocity is about 0.3% when the
gas velocity is indicated as 15 m/s.
The centerline gas velocity is measured by putting the pitot
tube in the pure gas streamline direction and the pitot tube
length is justified so that the pitot tube opening would be in
the pipe centerline. The reported gas velocity is the pure gas
velocity measured in a point with enough distance before the
particle feeding point. The particles are spherical sand with
diameters of 253 ipm. The gas temperature is measured at the


6--


4



I~f


4-5


II R B f
1-Fan 2-Gas Heater 3-Electrical Heater 4-Particles Feeder 5-Rizer
Structure 6-Rizer (bed) 7-Cyclone
Figure 1: Experimental apparatus.


Air is blown by a fan and after passing through the heater,
enters a vertical bed of 5 centimeter internal diameter and


measuring points specified in Fig. 2. The first measuring
point is 7 cm upper the solid particles entrance section. As


2i









shown in Fig. 2, in two first section levels after the particles
feeder three temperature sensors are located at r, r
and r which r denotes to radial of bed.

3-2. Experiment procedure

To study the effect of particle presence in the gas, the
experiments have been done to measured the gas
temperatures at different levels of bed as shown in Fig. 2,
then it is possible to obtain solid temperatures at different
sections of bed and finally gas solid heat transfer coefficient
is calculated. So in first step, the particles at ambient
temperature are fed in a hot gas flow, inlet hot air temperature
is adjustable between 110 C to 180 C, this experiments are
repeated using different mass loading ratio and hot air
velocity.


t



5 cm


Thermocouples positions
at A-A section


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


3-3. Experimental analysis

Mass loading ratios were defined as the ratio of particles
mass flow rate to gas flow rate z = n p/i g Here th and
izg are particle and gas mass flow rates, respectively.
Considering a computational cell as shown in Fig. 3, particles
and gas enter cell-n at the temperatures of T T by mass
flow rates of m ihg and leaving it at the temperature of
T +1 T +1 At cell exit, particles temperature can be
achieved by a simple energy balance Eq. 1.


Tpn+1 Tn+1
P g
T Tg


n



TPn Tgn


0




Hot air


6.5 cm

7 cm Particles
Motor


Figure 2: Schematic diagram of the bed.

Temperatures were maintained constant throughout the bed
for 15 min before each test. The repeatability test is examined
and the uncertainty of repeated experiments is under 5%.
Almost 5 minutes were allowed between runs. Of course, the
actual duration of running times were dependent on the air
velocity, solid rate and obtained loading ratios.
Table 1 shows the range of variables and Table 2 shows the
relevant properties of the solid investigated.

Table 1
Physical properties of the particles
S. No Property Value
1 Density 1500 kg/m3
2 Specific heat 800 J/kg K
3 Thermal conductivity 0.80 W/m K

Table2
Range of variable investigated
S. No Variable Value
1 Particle size 253 gtm
2 Air velocity 12, 18.5 m/s
3 Solid feed rate 9, 15, 18, 22, 25 g/s


Figure 3: Schematic diagram of nth-computational cell.

n gC pg (T[ -T +n+1) nPC P (Tp -Tn+l) = (1)

Since the particle concentration is low and gas velocities are
high, it is assumed that the particles are uniformly dispersed
at the measuring points. It can be assumed that the particles
velocity nearly equals the air velocity. Hence solids holdup
can be calculated from equations 2 and 3. The first
measuring point is 7 cm upper of the particles entrance
section.


AZ =V At


Ap = np At


Assuming particles to be spherical, heat transfer area (A, ) is
the surface area of the particles in the duct at any instant
related to the holdup (AM ), density (p,) and size of the
particles (D, ), as


6Ai p
A = (4)
ppDp
Air-solid heat transfer coefficient was calculated as follows.


mgcpgT -T )= UA ATLn


A --- .-






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Here ATL, is the logarithmic mean temperature difference
and is defined as


A n AT1 -AT"-
ATln = A7
ln(aTI" /AT2


U
E


where, AT,", ATf are gas and particle temperature differences
at inlet and outlet, respectively.


0


AT1" =T -Tn T


AT n =T n2+ _Tpn+
2g P


Figure 4: Variations of air temperature with time.


Hence air-solid Nusselt number can be achieved by Eq. 9.


(9) 60.00


Thermal effectiveness of a phase is generally defined as the
ratio of temperature change of that phase to the maximum
possible temperature change for that phase. Therefore,
thermal effectiveness of air at different height of the fluidized
bed is defined as follows.


Tbf -T
Sg= (10)
Tbf -T

'n = 1, 2, 3, and 4' which represent the axial location of
temperature sensor (thermocouple/K type) at distances of
0.07, 0.135, 0.285 and 0.435 m from the particles feeder.
Also thermal effectiveness of solid is given by

T -T
S p (11)
Tbf -T


4. Results and Discussion

4-1. Variations of air and particles temperature with time

Figs. 4 and 5 show the variations of air temperature and the
particles temperature in the axial location of temperature
sensor (thermocouple/K type) at distance of 0.07 m from the
particles feeder versus time at different load ratios for 253
micro meter particle sizes and at the air velocity of 18.5 m/s
respectively. It can be observed from Figs. 4 and 5 that the
gas temperature decreases while the particles temperature
increases with time until their temperature reaches a constant
value called steady state temperature. Also, the gas
temperature decreases while the particles temperature
increases with increase in load ratio. From the equation at
constant air velocity, increasing load ratio increases the
solids holdup. Hence according to the Eq. 4 the heat transfer
area between the particles and the air increases with load
ratio.


50.00
40.00
30.00
20.00
10.00
0.00


Jr -


-a-L.R=0.352
--L.R=0.413
---L.R=0.5
-*-L.R=0.568


0 100 200 300 400


Time(s)

Figure 5: Variations of particles temperature with time.

At higher load ratio and constant air velocity, the heat
capacity of solid (product of solids feed rate and specific heat
capacity) is also high leading to a relatively small increase in
particles temperature. This causes increase in local driving
force. Hence the increase in heat transfer area and driving
force leads to the higher air-solid heat transfer rate due to
increase in solids feed rate (increase in load ratio at constant
air velocity). However, heat transfer rate increases with the
load ratio leading to an increase in the ratio of air-solid heat
transfer rate to the heat capacity of solid. Therefore from Eq.
1 for a fixed particles size at constant air velocity the
particles temperature increases with increase in load ratio.
Also a combination of higher heat transfer rate and constant
heat capacity of air (product of mass flow rate of air and
specific heat capacity) leads to decrease in air temperature
with load ratio. Hence for a fixed particles size at constant air
velocity the air temperature decreases with increase in the
load ratio.

4-2. Effect of load ratio on the air-particle Nusselt
number

Fig. 6 shows the effect of load ratio on the air-particle Nusselt
number for 253 micro meter particles at the air velocity of
18.5 m/s. It can be seen from Fig. 6, that the air-solid Nusselt
number decreases with solids feed rate at low solids feed
rates, while it increases with solids feed rate at higher solids
feed rates. This can be explained as follows:
From Eq. 9 it can be seen that the air-particle Nusselt number
is directly proportional to the product of air-solid heat
transfer coefficient and particle diameter inversely


---L.R=0.352
--L.R=0.413
---L.R=0.5
--1-L.R=0.568


0 100 200 300 400
Time(s)


n (UpAp)n D
Nu tea- Ap x
stec 4 A xp Kg









proportional to air heat conductivity. Since the particle size is
fixed and air heat conductivity is almost constant, it is
assumed that the air-particle Nusselt number is merely
changed with air-solid heat transfer coefficient. Gas-particle
heat transfer coefficient decreases with solids feed rate at
lower solids feed rates typical of dilute/fast-fluidization
regime.[13] Gas-particle heat transfer coefficient increases
with solids feed rate at higher solids feed rates.[13] Hence in
the range of load ratio corresponding to dilute-phase and
fast-fluidization regimes, air-particle Nusselt number
decreases with load ratio and also the air-particle Nusselt
number increases with load ratio in the dense-phase regime.

500
400 --------* -


GJ
30C

200
10C


Figure
numb'

4-3. S

The fl


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

obvious that most of the air-solid heat transfer and mass
interaction in fluidized beds is done at acceleration region
after the particles feeder where particles are rapidly
accelerated from initial low velocity. Hence a big change in
air and particles temperature or a rapid increase in thermal
effectiveness of air is observed in the lower portion of the
duct.
It can also be seen from Fig. 7 that the thermal effectiveness
of air increases with solids feed rate. It is explained earlier
that for a fixed particle size and at constant air velocity, heat
transfer between air and particles increases with increase in
solids feed rate. It causes the rapid change in temperature of
air and an increase in thermal effectiveness of air. Hence
thermal effectiveness of air increases with solids feed rate.

4-3-2. Effect of air velocity on thermal effectiveness
profile of air


Fig. 8 shows the effect of air velocity on thermal
effectiveness of air for heat transfer to 253 size particles at
nearly same solids feed rate of 22gr/s. It can be observed
from Fig. 8 that the thermal effectiveness of air at all
0.3 0.35 0.4 0.45 0.5 0.55 0.6
locations decreases while increasing air velocity at constant
Load Ratio solids feed rate for a given particle size. This can be
explained as follows: For a given particle size and at constant
e 6: Effect of load ratio on the air-particle Nusselt air velocity, with increase in air velocity, mass flow rate of air
er. in the duct increases. Hence the heat capacity of air (product
of mass flow rate of air and specific heat capacity) increases.
studies on the thermal effectiveness of air This leads to slow change in temperature of air and a
decrease in thermal effectiveness of air. Hence the thermal
uidized bed set un in this study can be used as a heat effectiveness of air decreases with increase in air velocity.


exchanger. Knowledge of axial air temperature profiles will
provide information on the useful height of the fluidized bed
heat exchanger. Air temperature profiles in the duct are
expressed as the profiles of thermal effectiveness of air [12].

4-3-1. Effect of particles feed on thermal effectiveness

Fig. 7 shows the variations of thermal effectiveness of air
with height of the riser from the particles feeder at different
solids feed rates for 253 micro meter particle sizes at the air
velocity of 18.5 m/s.


9-* gr/s
-15 gr/s
-18 gr/s
-0-22 gr/s
---25 gr/s


0 0.1 0.2 0.3 0.4 0.5
Height From feeder (m)


Figure 7: Effect of solid feed rate on thermal effectiveness
profile of air.

It can be seen from Fig. 7 that the thermal effectiveness of air
increases rapidly between first section of duct at 0.07 m
height from the particles feeder and third section of the duct
at 0.285 m height from the particles feeder. After third
section, the thermal effectiveness of air increases lowly. It is


0.3
" 0.25
r 0.2


: 0.1
0.05
i o


--18.5 m/s
-12 m/s


0 0.1 0.2 0.3 0.4 0.5
Height From feeder (m)


Figure 8: Effect of air velocity on thermal effectiveness of
air.

4-4. Studies on the thermal effectiveness of solid

Form Eqs, 1 and 11 the thermal effectiveness of solid can be
assumed as the ratio of air-solid heat transfer rate to the
product of solids feed rate and its specific heat capacity.
Hence, it can be studied as the ratio of the heat transfer rate
per unit heat capacity of solid.
In this study the thermal effectiveness of solid is calculated
by Eq. 11 for 'n = 4' which represents the section of duct at
distance of 0.435 m from the particles feeder.

4-4-1. Effect of solids feed rate on thermal effectiveness
of solid

Fig. 9 shows the effect of solids feed rate on thermal
effectiveness of solid for particle size of 253 micro meter at









an air velocity of 18,5m/s.
0.5s


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

regime. Although, thermal effectiveness of air increases
with solids feed rate, thermal effectiveness of solid decreases
regarding to it. Thermal effectiveness of air decreases with
increase in air velocity.


References


0.01 0.015


0.02 0.025


[1] G. Jepson, A. Poll, W. Smith, Heat Transfer From Gas to
Wall in a Gas/ Solid Transport Line. Trans. Instn. Chem. Eng.,
0.03 41 (1963) 207.


Feed Rate (kg/s)

Figure 9: Effect of solids feed rate on thermal effectiveness
of solid.

It can be seen from Fig. 9 that the thermal effectiveness of
solid decreases with increase in solids feed rate. It was
discussed earlier that increase in solids feed rate results in
increase in heat transfer rate and heat transfer area. However,
an increase in the heat capacity of solid leads to a decrease in
the ratio of air-solid heat transfer rate to the heat capacity of
the solid. Hence for a fixed particle size and air velocity, an
increase in solids feed rate results in decrease the thermal
effectiveness of solid.

4-4-2. Effect of air velocity on thermal effectiveness of
solid

Fig. 10 shows the effect of air velocity on thermal
effectiveness of 253 micro meter size particles as a function
of solids feed rate. It can be observed from Fig. 10, that the
thermal effectiveness of solid decreases while the air velocity
increases. In this range of air velocity and particle size, an
increase in air velocity leads to a decrease in heat transfer
area. Hence air-solid heat transfer decreases with air velocity
from 12 to 18.5 m/s for this particle size. Hence thermal
effectiveness of solid also decreases with air velocity in this
range.


[2] L. Farbar, C.A. Depew, Heat transfer effects to gas-solid
mixtures using solid spherical particles of uniform size,
Indust. Eng. Chem. Fundament. 2 (1963) 130-135.

[3] Z. Mansoori, M. Saffar-Awal, H. Basirat-Tabrizi, The
effect of particle-particle interaction on heat transfer in a
horizontal turbulent gas-solid channel flow, in: The
ISHMT/ASME Heat andMass Transfer Conf., India, 2000,
379-384.

[4] Z. Mansoori, M. Saffar-Awal, H. Basirat-Tabrizi, G.
Ahmadi, Thermo mechanical modeling of turbulent heat
transfer in gas-solid flows including particle collisions, Int. J.
Heat Fluid Flow 23 (2002) 792-806.

[5] P. Boulet, S. Moissette, R. Andreux, B. Oesterle', Test of
an Eulerian-Lagrangian simulation of wall heat transfer in a
gas-solid pipe flow, Int. J. Heat Fluid Flow 21 (2000)
381-387.

[6] M. Saffar-Awal, H. Basirat Tabrizi, Z. Mansoori, P.
Ramezani, Gas-solid turbulent flow and heat transfer with
collision effect in a vertical pipe, International Journal of
Thermal Sciences 46 (2007) 67-75.


[7] S. Matsumoto, D.C.T. Pei,
pneumatic drying of grains
International Journal of Heat
(1984) 843-849.


A mathematical analysis of
- I. Constant drying rate,
and Mass Transfer 27 (6)


-.-18.5 m/s
-- 12 m/s


0 0.02 0.04 0.06 0.08
Feed Rate (kg/s)

Figure 10: Effect of air velocity on thermal effectiveness of
solid.


5. Conclusions

Air-solid heat transfer rate in vertical fluidized bed heat
exchanger increases with respect to solids feed rate. In the
range of load ratio corresponding to dilute-phase and
fast-fluidization regimes, increase in load ratio leads to
decrease air-particle Nusselt number. However air-particle
Nusselt number increases with load ratio in dense-phase


[8] T. Yokomine, A. Shimizu, Prediction of turbulence
modulation by using j-e model for gas-solid flow, in:
Advances in Multiphase flow 1995, Elsevier Science B.V.,
1995,p. 191.

[9] Y. Tsuji, Y. Morikawa, H. Shiomi, LDV measurements
of an air-solid two-phase flow in a vertical pipe, J. Fluid
Mech. 139 (1984) 417-434.

[10] C.T. Crowe, M. Sommerfeld, Y. Tsuji, Multiphase
Flows with Droplets and Particles, CRC Press, Boca Raton,
1998.

[11] Z. Mansoori, M. Saffar-Awal, H. Basirat Tabrizi, G.
Ahmadi, Experimental study of turbulent gas-solid heat
transfer at different particles temperature, Experimental
Thermal and Fluid Science 28 (21 '41) 655-665.

[12] K.S. Rajan, S.N. Srivastava, B. Pitchumani, K.
Dhasandhan, Experimental study of thermal effectiveness in
pneumatic conveying heat exchanger, Applied Thermal
Engineering 28 (2008) 1932-1941






7 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


[13] K.S. Rajan, K. Dhasandhan, S.N. Srivastava, B.
Pitchumani, Studies on gas-solid heat transfer during
pneumatic conveying, International Journal of Heat and
Mass Transfer 51 (2008) 2801-2813




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