Natural convection in a vertical porous enclosure with internal heat generation

Abstract

A theoretical study is performed on steady natural convection inside a rectangular porous enclosure with uniform internal heat generation and cooling from the side walls. For low Rayleigh numbers, the problem is tackled by regular expansion in the Rayleigh number and the resulting Poisson equations are sequentially solved by the modified Galerkin method. For large Rayleigh numbers, the boundary layer equations valid near the vertical walls along with the core region equations are examined using the Gill linearization method. The analytical predictions agree well with the numerical solutions based on the power-law difference representation of the full governing equations.