Abstract: Steady non-Darcian natural convection in a square cavity filled with a heat-generating porous medium is studied numerically by adopting the local thermal non-equilibrium model.The vertical walls maintain constant temperature T₀ while the horizontal walls are considered to be adiabatic.The flow field is modeled by using the Brinkman-Darcy-Forchheimer model.Comprehensive numerical solutions are obtained in the wide range of two main dimensionless parameters,i.e.the effective fluid-to-solid thermal conductivity ratio,0.001≤γ≤1.0,and the dimensionless volumetric heat transfer coefficient,1.0≤H≤1000.The effects of γ and H on the flow and heat transfer characteristics are analyzed.It is found that the local thermal non-equilibrium model should be adopted at the low values of γ and H for predicting the flow and heat transfer characteristics exactly.