Natural convection in a heat generating hydrodynamically and thermally anisotropic non-Darcy porous medium

Natural convection in a two-dimensional square cavity containing hydrodynamically and thermally anisotropic porous medium with internal heat generation is analyzed numerically by generalized non-Darcy approach. The properties considered for the study are permeability ratio (K∗), inclination of the principal axes (θ), ratio of Forchheimer constants (F∗) and thermal conductivity ratio (k∗). Results are presented in terms of isotherms, streamlines and maximum temperature in the cavity to understand the flow physics. It is observed that the anisotropic properties have significant influence on the flow behaviour and heat transfer. A correlation for maximum temperature in the cavity for a wide range of parameters (107 ⩽ Ra ⩽ 108, 10−6 ⩽ Da ⩽ 10−3, 0° ⩽ θ ⩽ 90°, 1 ⩽ F∗ ⩽ 100, 0.1 ⩽ K∗ ⩽ 10 and 0.1 ⩽ k∗ ⩽ 10) is developed.