Temperature-dependent viscosity effect in buoyancy driven flow of a gas or a liquid in an enclosure filled with a porous medium is studied numerically based on the general model of momentum transfer in a porous medium. The exponential form of viscosity-temperature relation is applied to examine three cases of viscosity-temperature relation: constant, decreasing, and increasing. Application of arithmetic and harmonic mean values of the viscosity is also investigated for their ability to represent the Nusselt number versus the effective Rayleigh number. Heat lines are illustrated for a more comprehensive investigation of the problem.
1.
Narasimhan
, A.
, and Lage
, J. L.
, 2005, “Variable Viscosity Forced Convection in Porous Medium Channels
,” Handbook of Porous Media
, K.
Vafai
, ed., Taylor & Francis
, New York
, pp. 195
–233
.2.
Nield
, D. A.
, and Bejan
, A.
, 2006, Convection in Porous Media
, Springer-Verlag
, New York
.3.
Nield
, D. A.
, 1994, “Estimation of an Effective Rayleigh Number for Convection in a Vertically Inhomogeneous Porous-Medium or Clear Fluid
,” Int. J. Heat Fluid Flow
0142-727X, 15
, pp. 337
–340
.4.
Nield
, D. A.
, 1996, “The Effect of Temperature-Dependent Viscosity on the Onset of Convection in a Saturated Porous Medium
,” ASME Trans. J. Heat Transfer
0022-1481, 118
, pp. 803
–805
.5.
Chu
, T. Y.
, and Hickox
, C. E.
, 1990, “Thermal-Convection With Large Viscosity Variation in an Enclosure With Localized Heating
,” ASME Trans. J. Heat Transfer
0022-1481, 112
, pp. 388
–395
.6.
Siebers
, D. L.
, Moffatt
, R. F.
, and Schwind
, R. G.
, 1985, “Experimental, Variable Properties Natural-Convection From a Large, Vertical, Flat Surface
,” ASME Trans. J. Heat Transfer
0022-1481, 107
, pp. 124
–132
.7.
Vafai
, K.
, and Tien
, C. L.
, 1981, “Boundary and Inertia Effects on Flow and Heat-Transfer in Porous-Media
,” Int. J. Heat Mass Transfer
0017-9310, 24
, pp. 195
–203
.8.
Hsu
, C. T.
, and Cheng
, P.
, 1990, “Thermal Dispersion in a Porous-Medium
,” Int. J. Heat Mass Transfer
0017-9310, 33
, pp. 1587
–1597
.9.
Guo
, Z. L.
, and Zhao
, T. S.
, 2005, “Lattice Boltzmann Simulation of Natural Convection With Temperature-Dependent Viscosity in a Porous Cavity
,” Prog. Comput. Fluid Dyn.
1468-4349, 5
, pp. 110
–117
.10.
Prasad
, V.
, and Kulacki
, F. A.
, 1984, “Natural-Convection in a Rectangular Porous Cavity With Constant Heat-Flux on One Vertical Wall
,” ASME Trans. J. Heat Transfer
0022-1481, 106
, pp. 152
–157
.11.
Merrikh
, A. A.
, and Mohamad
, A. A.
, 2002, “Non-Darcy Effects in Buoyancy Driven Flows in an Enclosure Filled With Vertically Layered Porous Media
,” Int. J. Heat Mass Transfer
0017-9310, 45
, pp. 4305
–4313
.12.
Antohe
, B. V.
, and Lage
, J. L.
, 1997, “The Prandtl Number Effect on the Optimum Heating Frequency of an Enclosure Filled With Fluid or With a Saturated Porous Medium
,” Int. J. Heat Mass Transfer
0017-9310, 40
, pp. 1313
–1323
.13.
Harms
, T. M.
, Jog
, M. A.
, and Manglik
, R. M.
, 1998, “Effects of Temperature-Dependent Viscosity Variations and Boundary Conditions on Fully Developed Laminar Forced Convection in a Semicircular Duct
,” ASME Trans. J. Heat Transfer
0022-1481, 120
, pp. 600
–605
.14.
Kakaç
, S.
, 1987, “The Effect of Temperature-Dependent Fluid Properties on Convective Heat Transfer
,” Handbook of Single-Phase Convective Heat Transfer
, S.
Kakaç
, R. K.
Shah
, and W.
Aung
, eds., Wiley
, New York
.15.
Bejan
, A.
, 2004, Convection Heat Transfer
, Wiley
, Hoboken, NJ
.16.
Nield
, D. A.
, Porneala
, D. C.
, and Lage
, J. L.
, 1999, “A Theoretical Study, With Experimental Verification, of the Temperature-Dependent Viscosity Effect on the Forced Convection Through a Porous Medium Channel
,” ASME Trans. J. Heat Transfer
0022-1481, 121
, pp. 500
–503
.17.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2003, “Effects of Temperature-Dependent Viscosity in Forced Convection in a Porous Medium: Layered-Medium Analysis
,” J. Porous Media
1091-028X, 6
, pp. 213
–222
.18.
Hooman
, K.
, 2006 “Entropy-Energy Analysis of Forced Convection in a Porous-Saturated Circular Tube Considering Temperature-Dependent Viscosity Effects
,” Int. J. Exergy
1742-8297, 3
, pp. 436
–451
.19.
Hooman
, K.
, and Gurgenci
, H.
, 2007, “Effects of Temperature-Dependent Viscosity Variation on Entropy Generation, Heat, and Fluid Flow Through a Porous-Saturated Duct of Rectangular Cross-Section
,” Appl. Math. Mech.
0253-4827, 28
, pp. 69
–78
.20.
Lauriat
, G.
, and Prasad
, V.
, 1987, “Natural-Convection in a Vertical Porous Cavity—A Numerical Study for Brinkman-Extended Darcy Formulation
,” ASME Trans. J. Heat Transfer
0022-1481, 109
, pp. 688
–696
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