The aim of the present paper is to study the steady state natural convection in a square porous enclosure using a thermal non-equilibrium model for the heat transfer between the fluid and the solid phases. The analysis assumes that the porous medium is homogeneous and isotropic. The present study also assumes the non-Darcy model of natural convection in porous media. It is assumed that the heat generation is only in solid phase. Two dimensional steady convection in a cavity bounded by isothermal walls at constant temperatures has been studied numerically by adopting a two-temperature model of microscopic heat transfer. Such a model, which allows the fluid and solid phases not to be in local thermal equilibrium, is found to modify the flow behaviour and heat transfer rates. Knowledge of this behaviour is very important for the design of the many engineering applications. Copyright (C) 2003 John Wiley Sons, Ltd.