Steady two-dimensional natural convection taking place in a rectangular cavity, partially filled with an isotropic porous material, has been investigated numerically using an ADI method. It is assumed that one of the vertical walls of the cavity has a ramped temperature distribution. The vorticity-stream function formulation has been used to solve the set of nonlinear partial differential equations governing the flows in the clear region and the adjoining porous region. The effects of Darcy number and Rayleigh number have been discussed in detail.
Alazmi, B., Vafai, K., 2001. Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int. J. Heat Mass Transf., 44, 1735-1749.
Beavers, G.S., Joseph, D.D., 1967. Boundary conditions at a naturally permeable wall. J. Fluid Mech., 30, 197-207.
Beckermann, C., Viskanta, R., Ramadhyani, S., 1988. Natural convection in vertical enclosures containing simultaneously fluid and porous layers. J. Fluid Mech., 186, 257-284.
Bhatt, B.S., Sacheti, N.C., 1994. Flow past a porous spherical shell using the Brinkman model. J. Physics D, 27, 37-41.
Callahan, G.D., Marner, W.J., 1976. Transient free convection with mass transfer on an isothermal vertical plate. Int. J. Heat Mass Transf., 19, 165-174.
Chandran, P., Sacheti, N.C., Singh, A.K., 2001. Exact solution for the convective flow of fluids of different Prandtl numbers near an infinite vertical plate in a rotating system. Int. J. Appl. Mech. Engng, 6, 573-590.
Chandran, P., Sacheti, N. C., Singh, A. K., 2005. Natural convection near a vertical plate with ramped wall temperature. Heat Mass Transf., 41, 459-464.
Chandrasekhara, B.C., Vortmeyer, D., 1979. Flow model for velocity distribution in fixed porous beds under isothermal conditions. Thermo. Fluid Dyn., 12, 105-111.
Collins, R.E., 1961. Flow of Fluids through Porous Materials. Reinhold, New York.
Hayday, A.A., Bowlus, D.A., McGraw, R.A., 1967. Free convection from a vertical plate with step discontinuities in surface temperature. ASME J. Heat Transf., 89, 244-250.
Hill, A.A., Straughan, B., 2009a. Global stability for thermal convection in a fluid overlying a highly porous material. Proc. R. Soc. London A, 465, 207-217.
Hill, A.A., Straughan, B., 2009b. Poiseuille flow in a fluid overlying a highly porous material. Adv. Water Resour., 32, 1609-1614.
Kao, T.T., 1975. Laminar free convective heat transfer response along a vertical flat plate with step jump in surface temperature. Lett. Heat Mass Transf., 2, 419-428.
Kuznetzov, A.V., 1996. Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium. Appl. Sci. Res., 56, 53-67.
Lee, S., Yovanovich, M.M., 1991. Laminar natural convection from a vertical plate with a step change in wall temperature. ASME J. Heat Transf., 113, 501-504.
Lefebvre, L.P., Banhart, J., Dunand, D.C., 2008. Porous metals and metallic foams: Current status and recent developments. Adv. Engng. Mater., 10, 775-787.
Magyari, E., Keller, B., 2003. Buoyancy sustained by viscous dissipation. Transp. Porous Media, 53, 105-115.
Mallinson, G., De Vahl Davis, G., 1973. The method of false transient for the solution of coupled elliptic equations. J. Comput. Phys., 12, 435-461.
Neale, G., Nader, W., 1974. Practical significance of Brinkman's extension of Darcy's law: coupled parallel flows within a channel and a bounding porous medium. Canad. J. Chem. Engng., 52, 475-478.
Nield, D.A., 1977. Onset of convection in a fluid layer overlying a layer of porous medium. J. Fluid Mech., 81, 513-522.
Nield, D.A., Bejan, A., 2006. Convection in Porous Media. 3rd Ed. Springer Verlag, Berlin.
Nishimura, T., Takumi, T., Shiraishi, M., Kawamura, Y., Ozoe, H., 1986. Numerical analysis of natural convection in a rectangular enclosure horizontally divided into fluid and porous regions. Int. J. Heat Mass Transf., 29, 889-898.
Palm, E., Weber, J. E., Kvernvold, O., 1972. On steady convection in a porous medium. J. Fluid Mech., 54, 153-161.
Paul, T., Jha, B.K., Singh, A.K., 1996. Transient free convection flow in a vertical channel with constant temperature and constant heat flux on walls. Heat Mass Transf., 32, 61-63.
Sacheti, N.C., Bhatt, B.S., 1988. Stokes and Rayleigh layers in presence of naturally permeable boundaries. In: Cheremisinoff, P.N., Cheremisinoff, N.P., Cheng S.L. (Eds.): Civil Engineering Practice. Technomic, Basel, pp. 659-695.
Scheidegger, A.E., 1974. The Physics of Flow through Porous Media. Univ. Toronto Press, Toronto.
Singh, A.K., Singh, J., 1983. Mass transfer effects on the flow past an accelerated vertical plate with constant heat flux. Astrophys. Space Sci., 97, 57-61.
Singh, A.K., Thorpe, G.R., 1995. Natural convection in a confined fluid overlying a porous layer - A comparison study of different models. Indian J. Pure Appl. Math., 26, 81-95.
Singh, A.K., Leonardi, E., Thorpe, G.R., 1993. Threedimensional natural convection in a confined fluid overlying a porous bed. ASME J. Heat Transf., 115, 631-638.
Singh, A.K., Paul, T., Thorpe, G.R., 2000. Natural convection in a non-rectangular porous enclosure. Forsch. Ingenieurwesen, 65, 301-308.
Singh, A.K., Sacheti, N.C., Chandran, P., 2006. Stratification effects on transient Stokes flow in the presence of a permeable boundary. Forsch. Ingenieurwesen, 70, 67-73.
Singh, A.K., Sacheti, N.C., Chandran, P., 2008. Developing flow near a semi-infinite vertical wall with ramped temperature. Int. J. Appl. Math. Stat., 13, 34-45.
Singh, A.K., Sacheti, N.C., Chandran, P., 2009. Flow of an incompressible fluid in a cubical cavity with a free fluid - porous medium interface. Indian J. Indus. Appl. Math., 2, 61-71.
Straughan, B., 2002. Effect of property variation and modelling on convection in a fluid overlying a porous layer. Int. J. Numer. Anal. Meth. Geomech., 26, 75-97.
Vafai, K., Tien, C.L., 1981. Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transf., 24, 195-203.
Valencia-López, J.J., Ochoa-Tapia, J.A., 2001. A study of buoyancy-driven flow in a confined fluid overlying a porous layer. Int. J. Heat Mass Transf., 44, 4725-4736.
Zhao, C.Y., Lu, T.J., Hodson, H.P., 2004. Thermal radiation in ultralight metal foams with open cells. Int. J. Heat Mass Transf., 47, 2927-2939.