Compared to the regular (monodisperse) porous medium (MDPM) with one porosity scale, the bidisperse porous medium (BDPM) has two porosity scales, which may enhance the heat transfer capability. This work investigates the forced convective heat transport through a circular pipe filled with a BDPM. The two-velocity two-temperature model is utilized to describe the flow and temperature fields for both the fracture phase (macropores) and the porous phase (the matrix with micropores). The bidispersion effect is taken into account by altering the permeability of the porous phase in the medium. Analytical solutions of the velocities and temperatures for both phases are derived under the constant wall heat flux boundary condition. The local Nusselt number and heat transfer performance (HTP) are also developed to investigate how the bidispersivity affects the thermal characteristics over a wide range of parameter space.

References

1.
Satyamurty
,
V. V.
, and
Bhargavi
,
D.
,
2010
, “
Forced Convection in Thermally Developing Region of a Channel Partially Filled With a Porous Material and Optimal Porous Fraction
,”
Int. J. Therm. Sci.
,
49
(
2
), pp.
319
332
.
2.
Nield
,
D. A.
,
Kuznetsov
,
A. V.
, and
Xiong
,
M.
,
2002
, “
Effects of Local Thermal Non-Equilibrium on the Thermally Developing Forced Convection in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
45
(
25
), pp.
4949
4955
.
3.
Yang
,
K.
, and
Vafai
,
K.
,
2011
, “
Analysis of Heat Flux Bifurcation Inside Porous Media Incorporating Inertial and Dispersion Effects-An Exact Solution
,”
Int. J. Heat Mass Transfer
,
54
(
25
), pp.
5286
5297
.
4.
Chen
,
G. M.
, and
Tso
,
C. P.
,
2012
, “
Field Synergy Principle Analysis on Convective Heat Transfer in Porous Medium With Uniform Heat Generation for Thermally Developing Flow
,”
Int. J. Heat Mass Transfer
,
55
(
15–16
), pp.
4139
4147
.
5.
Ouyang
,
X. L.
,
Vafai
,
K.
, and
Jiang
,
P. X.
,
2013
, “
Analysis of Thermally Developing Flow in Porous Media Under Local Thermal Non-Equilibrium Conditions
,”
Int. J. Heat Mass Transfer
,
67
(
12
), pp.
768
775
.
6.
Wang
,
K. Y.
,
Tavakkoli
,
F.
,
Wang
,
S. J.
, and
Vafai
,
K.
,
2015
, “
Forced Convection Gaseous Slip Flow in a Porous Circular Microtube: An Exact Solution
,”
Int. J. Therm. Sci.
,
97
, pp.
152
162
.
7.
Wang
,
K. Y.
,
Tavakkoli
,
F.
, and
Vafai
,
K.
,
2015
, “
Analysis of Gaseous Slip Flow in a Porous Micro-Annulus Under Local Thermal Non-Equilibrium Condition—An Exact Solution
,”
Int. J. Heat Mass Transfer
,
89
(
5
), pp.
1331
1341
.
8.
Wang
,
K. Y.
,
Tavakkoli
,
F.
,
Wang
,
S. J.
, and
Vafai
,
K.
,
2015
, “
Analysis and Analytical Characterization of Bioheat Transfer During Radiofrequency Ablation
,”
J. Biomech.
,
48
(
6
), pp.
930
940
.
9.
Chen
,
Z. Q.
,
Cheng
,
P.
, and
Hsu
,
C. T.
,
2000
, “
A Theoretical and Experimental Study on Stagnant Thermal Conductivity of Bi-Dispersed Porous Media
,”
Int. Commun. Heat Mass Transfer
,
27
(
5
), pp.
601
610
.
10.
Chen
,
Z. Q.
,
Cheng
,
P.
, and
Zhao
,
T. S.
,
2000
, “
An Experimental Study of Two Phase Flow and Boiling Heat Transfer in Bi-Dispersed Porous Channels
,”
Int. Commun. Heat Mass Transfer
,
27
(
3
), pp.
293
302
.
11.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2004
, “
Forced Convection in a Bi-Disperse Porous Medium Channel: A Conjugate Problem
,”
Int. J. Heat Mass Transfer
,
47
(
24
), pp.
5375
5380
.
12.
Petersen
,
E. E.
,
1991
, “
Adsorption in Bidisperse-Pore Systems
,”
AICHE J.
,
37
(
5
), pp.
671
678
.
13.
Semenic
,
T.
,
Lin
,
Y. Y.
,
Catton
,
I.
, and
Sarraf
,
D. B.
,
2008
, “
Use of Biporous Wicks to Remove High Heat Fluxes
,”
Appl. Therm. Eng.
,
28
(
4
), pp.
278
283
.
14.
Qu
,
Y.
,
Zhou
,
K.
,
Zhang
,
K. F.
, and
Tian
,
Y.
,
2016
, “
Effects of Multiple Sintering Parameters on the Thermal Performance of Bi-Porous Nickel Wicks in Loop Heat Pipes
,”
Int. J. Heat Mass Transfer
,
99
, pp.
638
646
.
15.
Hooman
,
K.
, and
Maas
,
U.
,
2014
, “
Theoretical Analysis of Coal Stockpile Self-Heating
,”
Fire Saf. J.
,
67
(
7
), pp.
107
112
.
16.
Nield
,
D.
, and
Kuznetsov
,
A. V.
,
2005
, “
A Two-Velocity Two-Temperature Model for a Bi-Dispersed Porous Medium: Forced Convection in a Channel
,”
Transport Porous Med.
,
59
(
3
), pp.
325
339
.
17.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2006
, “
Thermally Developing Forced Convection in a Bidisperse Porous Medium
,”
J. Porous Media
,
9
(
5
), pp.
393
402
.
18.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Asymmetric Case
,”
Int. J. Heat Mass Transfer.
,
53
(
23
), pp.
5167
5175
.
19.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2011
, “
Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Symmetric Case
,”
ASME J. Heat Transfer
,
133
(
7
), p.
072601
.
20.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2011
, “
Laminar Forced Convection in a Heat Generating Bi-Disperse Porous Medium Channel
,”
Int. J. Heat Mass Transfer
,
54
(
1
), pp.
636
644
.
21.
Narasimhan
,
A.
,
Reddy
,
B. V. K.
, and
Dutta
,
P.
,
2012
, “
Thermal Management Using the Bi-Disperse Porous Medium Approach
,”
Int. J. Heat Mass Transfer
,
55
(
4
), pp.
538
546
.
22.
Ajay
,
K. P. V.
,
Giranchandran
,
A. C.
, and
Kamath
,
P. M.
,
2013
, “
A Numerical Investigation to Improve Heat Transfer Using Bi-Disperse Porous Heat Sink
,”
Int. J. Technol. Eng. Sci.
,
1
(
5
), pp.
445
453
.http://www.ijtes.com/upload/IJTES%20-%20Paper%20ajay.kumarpv007%40gmail.com%20-%208.pdf
23.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2006
, “
The Onset of Convection in a Bidisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
49
(
17
), pp.
3068
3074
.
24.
Straughan
,
B.
,
2009
, “
On the Nield-Kuznetsov Theory for Convection in Bidispersive Porous Media
,”
Transport Porous Med.
,
77
(
2
), pp.
159
168
.
25.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2008
, “
Natural Convection About a Vertical Plate Embedded in a Bidisperse Porous Medium
,”
Int. J. Heat Mass Transfer
,
51
(
7–8
), pp.
1658
1664
.
26.
Rees
,
D. A. S.
,
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2008
, “
Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium
,”
ASME J. Heat Transfer
,
130
(
9
), p. 092601.
27.
Revnic
,
C.
,
Grosan
,
T.
,
Pop
,
I.
, and
Ingham
,
D. B.
,
2009
, “
Free Convection in a Square Cavity Filled With a Bidisperse Porous Medium
,”
Int. J. Therm. Sci.
,
48
(
10
), pp.
1876
1883
.
28.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2010
, “
Natural Convection Inside a Bidisperse Porous Medium Enclosure
,”
ASME J. Heat Transfer
,
132
(
1
), p.
012502
.
29.
Narasimhan
,
A.
, and
Reddy
,
B. V. K.
,
2011
, “
Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure
,”
ASME J. Heat Transfer
,
133
(
4
), p.
042601
.
30.
Cekmer
,
O.
,
Mobedi
,
M.
,
Ozerdem
,
B.
, and
Pop
,
I.
,
2012
, “
Fully Developed Forced Convection in a Parallel Plate Channel With a Centered Porous Layer
,”
Transport Porous Med.
,
93
(
93
), pp.
179
201
.
31.
Mahmoudi
,
Y.
,
Karimi
,
N.
, and
Mazaheri
,
K.
,
2014
, “
Analytical Investigation of Heat Transfer Enhancement in a Channel Partially Filled With a Porous Material Under Local Thermal Non-Equilibrium Condition: Effects of Different Thermal Boundary Conditions at the Porous-Fluid Interface
,”
Int. J. Heat Mass Transfer
,
70
, pp.
875
891
.
32.
Wang
,
B.
,
Hong
,
Y.
,
Hou
,
X.
,
Xu
,
Z.
,
Wang
,
P.
,
Fang
,
X.
, and
Ruan
,
X.
,
2015
, “
Numerical Configuration Design and Investigation of Heat Transfer Enhancement in Pipes Filled With Gradient Porous Materials
,”
Energy Convers. Manage.
,
105
, pp.
206
215
.
33.
Wang
,
K. Y.
,
Vafai
,
K.
, and
Wang
,
D. Z.
,
2016
, “
Analytical Characterization of Gaseous Slip Flow and Heat Transport Through a Parallel-Plate Microchannel With a Centered Porous Substrate
,”
Int. J. Numer. Method Heat Fluid Flow
,
26
(
3/4
), pp.
854
878
.
34.
Dehghan
,
M.
,
Valipour
,
M. S.
, and
Saedodin
,
S.
,
2016
, “
Microchannels Enhanced by Porous Materials: Heat Transfer Enhancement or Pressure Drop Increment?
Energy Convers. Manage.
,
110
, pp.
22
32
.
35.
Magyari
,
E.
,
2013
, “
Normal Mode Analysis of the High Speed Channel Flow in a Bidisperse Porous Medium
,”
Transport Porous Med.
,
97
(
3
), pp.
345
352
.
36.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2013
, “
A Note on Modeling High Speed Flow in a Bidisperse Porous Medium
,”
Transport Porous Med.
,
96
(
3
), pp.
495
499
.
37.
Cheng
,
C. Y.
,
2013
, “
Natural Convection Heat Transfer From an Inclined Wavy Plate in a Bidisperse Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
43
, pp.
69
74
.
38.
Amiri
,
A.
,
Vafai
,
K.
, and
Kuzay
,
T. M.
,
1995
, “
Effects of Boundary Conditions on Non-Darcian Heat Transfer Through Porous Media and Experimental Comparisons
,”
Numer. Heat Transfer Appl.
,
27
(
6
), pp.
651
664
.
39.
Wang
,
K. Y.
,
Wang
,
D. Z.
, and
Li
,
P. C.
,
2015
, “
Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium
,”
Appl. Math. Mech.
,
36
(
5
), pp.
494
504
(in Chinese).
40.
Dukhan
,
N.
,
Al-Rammahi
,
M. A.
, and
Suleiman
,
A. S.
,
2013
, “
Fluid Temperature Measurements Inside Metal Foam and Comparison to Brinkman-Darcy Flow Convection Analysis
,”
Int. J. Heat Mass Transfer
,
67
(
4
), pp.
877
884
.
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