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This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.
Rooda Eelkman J, Van Beckum FPH. Heat transfer during the cooling process of exponential heat generating produce, Lebensm. Wiss. Technol. 1978;2:209– 214.
Hwang IT. Finite amplitude thermal convection in porous media with heat source and variable viscosity PhD thesis, University of Minnesota; 1971.
Buretta R. Thermal convection in a fluid filled porous layer with uniform internal heat source PhD dissertation, University of Minnesota; 1972.
Sun WJ. Convective instability in superposed porous and free layers. PhD Thesis, University of Minnesota; 1973.
Gabor JD, Sowa ES, Baker L, Cassulo JC. Studies and experiments on heat removal from fuel debris in sodium. Proc. Fast Reactor Safety Mtg., Beverly Hills, California, April 2 – 4, Conf. – 740401 – P2:823 – 844 U.S. atomic energy commission; 1974.
Gasser RD, Kazimi MS. Onset of convection in a porous medium with internal heat generation. J. Heat Transfer. 1976;98:49–54.
Hardee HC, Nilson RH. Natural convection in porous media with heat generation. Nuclear Science and Engineering. 1977; 63:119–132.
Bergholz RF. Natural convection of a heat generation fluid in a closed cavity. J. Heat Transfer. 1980;102:242–247.
Gill AE. The boundary-layer Regime for convection in a rectangular cavity. J. Fluid Mech. 1966;25:515–536.
Emara AA, Kulacki FA. A numerical investigation of thermal convection in a heat-generating fluid layer. ASME Paper No. 79 – HT – 103.
Beukema KJ, Bruin S, Schenk J. Three-dimensional natural convection in a confined porous medium with internal heat generation. Int. J. Heat Mass Transfer. 1983;26(3):451–458.
Haajizadeh M, Ozguc AF, Tien CL. Natural convection in a vertical porous enclosure with internal heat generation Int. J. Heat Mass Transfer. 1984;27(10):1893–1902.
Acharya S, Goldstein RJ. Natural convection in an externally heated vertical or inclined square box containing internal energy source. ASME J. Heat Transfer. 1985;107:855–866.
Prasad V. Thermal convection in a regular cavity filled with a heat generation, Darcy porous medium. J. Heat Transfer. 1987; 109:697-703.
Churbanov AG, Vabishchevich PN, Chudanov VV, Strizhov VF. A numerical study on natural convection of a heat generating fluid in rectangular enclosure. Int. J. Heat Mass Transfer. 1994;37(18): 2969–2984.
Kim Gi Bin, Hyun Jae Min. Buoyant convection of a power law fluid in an enclosure filled with heat generating porous media. Numerical Heat Transfer, Part A. 2004;45:569–582.
Degan G, Vasseur P. Natural convection in a vertical slot filled with an anisotropic porous medium with oblique principal axes. Numerical Heat Transfer, Part A. 1996;30:397–412.
Bear J. Dynamic of fluid in porous media. American Elsevier Publishing Company, New York; 1972.
Kantorovich LV, Krylov VI. Approximate methods of higher analysis. Noordhoff, the Netherlands. 1958;304–327.