A numerical study has been made to analyze the effects of anisotropic permeability and thermal diffusivity on natural convection in a heat generating porous medium contained in a vertical cylindrical enclosure with isothermal wall and the top and bottom perfectly insulated surfaces. The results show that the anisotropies influence the flow field and heat transfer rate significantly. The non-dimensional maximum cavity temperature increases with increase in permeability ratio. For aspect ratio greater than or equal to two, the nondimensional maximum cavity temperature increases with an increase in the thermal diffusivity ratio. For aspect ratio equal to unity, there exists a critical value of thermal diffusivity ratio at which the maximum cavity temperature is a minimum. This critical value increases with an increase in the value of anisotropic permeability ratio. Based on a parametric study correlations for maximum cavity temperature and average Nusselt number are presented.

Issue Section:
Technical Notes
Keywords:
thermal diffusivity, natural convection, confined flow, flow through porous media, numerical analysis, permeability
Topics:
Anisotropy, Flow (Dynamics), Heat, Natural convection, Permeability, Porous materials, Temperature, Thermal diffusivity, Heat transfer
1.
Haajizadeh
,
M.
,
Ozgue
,
A. F.
, and
Tien
,
C. L.
,
1984
, “
Natural Convection in a Vertical Porous Enclosure With Internal Heat Generation
,”
Int. J. Heat Mass Transf.
,
27
, pp.
1893
–
1902
.
2.
Prasad
,
V.
,
1987
, “
Thermal Convection in a Rectangular Cavity Filled With a Heat Generating, Darcy Porous Medium
,”
ASME J. Heat Transfer
,
109
, pp.
697
–
703
.
3.
Stewart
,
W. E.
, Jr., and
Dona
,
C. L. G.
,
1988
, “
Free Convection in a Heat Generating Porous Medium in a Finite Vertical Cylinder
,”
ASME J. Heat Transfer
,
110
, pp.
517
–
520
.
4.
Prasad
,
V.
, and
Chui
,
A.
,
1989
, “
Natural Convection in a Cylindrical Porous Enclosure With Internal Heat Generation
,”
ASME J. Heat Transfer
,
111
, pp.
916
–
925
.
5.
Rao
,
Y. F.
, and
Wang
,
B. X.
,
1991
, “
Natural Convection in Vertical Porous Enclosures With Internal Heat Generation
,”
Int. J. Heat Mass Transf.
,
34
, pp.
247
–
252
.
6.
Royer
,
J. J.
, and
Flores
,
L.
,
1994
, “
Two-Dimensional Natural Convection in an Anisotropic and Heterogeneous Porous Medium With Internal Heat Generation
,”
Int. J. Heat Mass Transf.
,
37
, pp.
1387
–
1399
.
7.
Parthiban
,
C.
, and
Patil
,
P. R.
,
1997
, “
Thermal Instability in an Anisotropic Porous Medium With Internal Heat Source and Inclined Temperature Gradient
,”
Int. Commun. Heat Mass Transfer
,
24
, pp.
1049
–
1058
.
8.
Gosman, A. D., Pun, W. M., Runchal, A. K., Spalding, D. B., and Wolfshtein, M., 1969, Heat and Mass Transfer in Recirculating Flows, Academic Press, London.
9.
Neale
,
G.
,
1977
, “
Degrees of Anisotropy for Fluid Flow and Diffusion Through Anisotropic Porous Media
,”
AIChE J.
,
23
, pp.
56
–
62
.
10.
Chang
,
W. J.
, and
Lin
,
H. C.
,
1994
, “
Natural Convection in a Finite Wall Rectangular Cavity Filled With an Anisotropic Porous Medium
,”
Int. J. Heat Mass Transf.
,
37
, pp.
303
–
312
.
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 by ASME
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