An effective porosity concept has been introduced to account for the effects of tortuosity and thermal dispersion on the individual effective thermal conductivities of the solid and fluid phases in a fluid-saturated porous medium. Using this effective porosity concept, a thermal nonequilibrium model has been proposed to attack locally thermal nonequilibrium problems associated with convection within a fluid-saturated porous medium. Exact solutions are obtained, assuming a plug flow, for the two cases of thermally fully developed convective flows through a channel, namely, the case of isothermal hot and cold walls and the case of constant heat flux walls. These exact solutions for the cases of metal foam and air combination reveal that the local thermal equilibrium assumption may hold for the case of isothermal hot and cold walls, but may fail for the case of constant heat flux walls.
References
1.
Nakayama
, A.
, Kuwahara
, F.
, Sugiyama
, M.
, and Xu
, G.
, 2001, “A Two-Energy Equation Model for Conduction and Convection in Porous Media
,” Int. J. Heat Mass Transfer
, 44
(22
), pp. 4375
–4379
. 2.
Yang
, C.
, Liu
, W.
, and Nakayama
, A.
, 2009, “Forced Convective Heat Transfer Enhancement in a Tube With its Core Partially Filled With a Porous Medium
,” Open Transp. Phenom. J.
, 1
, pp. 1
–6
. 3.
Rees
, D. A. S.
, and Pop
, I.
, 2000, “Vertical Free Convective Boundary Layer, Flow in a Porous Medium Using a Thermal Nonequilibrium Model
,” J. Porous Media
, 1
, pp. 31
–44
.4.
Kuwahara
, F.
, Shirota
, M.
, and Nakayama
, A.
, 2001, “A Numerical Study of Interfacial Convective Heat Transfer Coefficient in Two-Energy Equation Model for Convection in Porous Media
,” Int. J. Heat Mass Transfer
, 44
, pp. 1153
–1159
. 5.
Quintard
, M.
, 1998, “Modelling local non- equilibrium heat transfer in porous media
,” Proceeding 11th International Heat Transfer Conference
, 1
, pp. 279
–285
.6.
Quintard
, M.
, and Whitaker
, S.
, 1993, “One and Two Equation Models for Transient Diffusion Processes in Two-Phase Systems
,” Adv. Heat Transfer
, 23
, pp. 369
–465
. 7.
Quintard
, M.
, and Whitaker
, S.
, 1995, “Local Thermal Equilibrium for Transient Heat Conduction: Theory and Comparison With Numerical Experiments
,” Int. J. Heat Mass Transfer
, 38
, pp. 2779
–2796
. 8.
Minkowycz
, W. J.
, Haji-Sheikh
, A.
, and Vafai
, K.
, 1999, “On Departure From Local Thermal Equilibrium in Porous Media Due to a Rapidly Changing Heat Source: The Sparrow Number
,” Int. J. Heat Mass Transfer
, 42
, pp. 3373
–3385
. 9.
Kim
, S. J.
, and Jang
, S. P.
, 2002, “Effects of the Darcy Number, the Prandtl Number, and the Reynolds Number on Local Thermal Non-Equilibrium
,” Int. J. Heat Mass Transfer
, 45
, pp. 3885
–3896
. 10.
Kiwan
, S.
, and Al-Nimr
, M. A.
, 2002, “Examination of the Thermal Equilibrium Assumption in Periodic Forced Convection in a Porous Channel
,” J. Porous Media
, 5
, pp. 35
–40
.11.
Al-Nimr
, M. A.
, and Abu-Hijleh
, B.
, 2002, “Validation of Thermal Equilibrium Assumption in Transient Forced Convection Flow in Porous Channel
,” Transp. Porous Media
, 49
, pp. 127
–138
. 12.
Abu-Hijleh
, B. A.
, Al-Nimr
, M. A.
, and Hader
, M. A.
, 2002, “Thermal Equilibrium in Transient Forced Convection Flow in Porous Channel
,” Transp. Porous Media
, 49
, pp. 127
–138
. 13.
Khashan
, S.
, Al-Amiri
, A. M.
, and Al-Nimr
, M. A.
, 2005, “Assessment of the Local Thermal Non-Equilibrium Condition in Developing Forced Convection Flows Through Fluid-Saturated Porous Tubes
,” Appl. Therm. Eng.
, 25
, pp. 1429
–1445
. 14.
Khashan
, S.
, and Al-Nimr
, M. A.
, 2005, “Validation of the Local Thermal Equilibrium Assumption in Forced Convection of Non-Newtonian Fluids Through Porous Channels
,” Transp. Porous Media
, 61
, pp. 291
–305
. 15.
Haddad
, O. M.
, Al-Nimr
, M. A.
, and Al-Khateeb
, A. N.
, 2004, “Validation of the Local Thermal Equilibrium Assumption in Natural Convection From a Vertical Plate Embedded in Porous Medium: Non-Darcian Model
,” Int. J. Heat Mass Transfer
, 47
, pp. 2037
–2042
. 16.
Hsu
, C. T.
, 2000, “Heat Conduction in Porous Media
,” Handbook of Porous Media
, K.
Vafai
, ed., Marcel Dekker
, New York
, pp. 170
–200
.17.
Hsu
, C. T.
, Cheng
, P.
, and Wong
, K. W.
, 1995, “A Lumped Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media
,” ASME Trans. J. Heat Transfer
, 117
, pp. 264
–269
. 18.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010, “Effect of Local Thermal Non-Equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid
,” Transp. Porous Media
, 83
, pp. 425
–436
. 19.
Kuznetsov
, A. V.
, 1996, “A Perturbation Solution for a Nonthermal Equilibrium Fluid Flow Through a Three-Dimensional Sensible Heat Storage Packed Bed
,” J. Heat Transfer
, 118
, pp. 508
–510
. 20.
Kuznetsov
, A. V.
, 1997, “A Perturbation Solution for Heating a Rectangular Sensible Heat Storage Packed Bed With a Constant Temperature at the Walls
,” Int. J. Heat Mass Transfer
, 40
, pp. 1001
–1006
. 21.
Yang
, C.
, Ando
, K.
, and Nakayama
, A.
, 2011, “A Local Thermal Non-Equilibrium Analysis of Fully Developed Forced Convective Flow in a Tube Filled With a Porous Medium
,” Transp. Porous Media
, (in press).22.
Cheng
, P.
, 1978, “Heat Transfer in Geothermal Systems
,” Adv. Heat Transfer
, 14
, pp. 1
–105
. 23.
Nakayama
, A.
, 1995, PC-aided Numerical Heat Transfer and Convective Flow
, CRC
, Boca Raton, FL
, pp. 49
–50
, 103–115.24.
Nakayama
, A.
, Kuwahara
, F.
, and Kodama
, Y.
, 2006, “An Equation for Thermal Dispersion Flux Transport and Its Mathematical Modelling for Heat and Fluid Flow in a Porous Medium
,” J. Fluid Mech.
, 563
, pp. 81
–96
. 25.
Yang
, C.
, and Nakayama
, A.
, 2010, “A Synthesis of Tortuosity and Dispersion in Effective Thermal Conductivity of Porous Media
,” Int. J. Heat Mass Transfer
, 53
(15–16
), pp. 3222
–3230
. 26.
Paek
, J. W.
, Kang
, B. H.
, Kim
, S. Y.
, and Hyun
, J. M.
, 2000, “Effective Thermal Conductivity and Permeability of Aluminium Foam Materials
,” Int. J. Thermophys.
, 21
(2
), pp. 453
–464
. 27.
Dul’nev
, G. N.
, 1965, “Heat Transfer Through Solid Disperse Systems
,” J. Eng. Phys. Thermophys.
, 9
, pp. 275
–279
.28.
Krishnan
, S.
, Murthy
, J. Y.
, and Garimella
, S. V.
, 2006, “Direct Simulation of Transport in Open-Cell Metal Foam
,” J. Heat Transfer
, 128
, pp. 793
–799
. 29.
Lemlich
, R.
, 1978, “A Theory for the Limiting Conductivity of Polyhedral Foam at Low Density
,” J. Colloid Interface Sci.
, 64
, pp. 107
–110
. 30.
Calmidi
, V. V.
, and Mahajan
, R. L.
, 1999, “The Effective Thermal Conductivity of High Porosity Fibrous Metal Foams
,” ASME Trans. J. Heat Transfer
, 121
, pp. 466
–471
. 31.
Calmidi
, V. V.
, and Mahajan
, R. L.
, 2000, “Forced Convection in High Porosity Metal Foams
,” ASME Trans. J. Heat Transfer
, 122
, pp. 557
–565
. 32.
Bhattacharya
, A.
, Calmidi
, V. V.
, and Mahajan
, R. L.
, 2002, “Thermophysical Properties of High Porosity Metal Foams
,” Int. J. Heat Mass Transfer
, 45
, pp. 1017
–1031
. 33.
Singh
, R.
, and Kasana
, H. S.
, 2004, “Computational Aspects of Effective Thermal Conductivity of Highly Porous Metal Foams
,” Appl. Therm. Eng.
, 24
, pp. 1841
–1849
. 34.
Dukhan
, N.
, Picon-Feliciano
, R.
, and Alvarez-Hernandez
, A. R.
, 2006, “Heat Transfer Analysis in Metal Foams With Low-Conductivity Fluids
,” J. Heat Transfer
, 128
, pp. 784
–792
. 35.
Nakayama
, A.
, Kuwahara
, F.
, Umemoto
, T.
, and Hayashi
, T.
, 2002, “Heat and Fluid Flow Within an Anisotropic Porous Medium
,” ASME Trans. J. Heat Transfer
, 124
, pp. 746
–753
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