Natural convection in a non-Darcy anisotropic porous cavity with a finite heat source at the bottom wall

Abstract

The problem of natural convection with heat source located at the bottom surface of a cavity containing anisotropic porous medium is analyzed numerically by a generalized non-Darcy approach. Initially for a Darcy–Rayleigh number of Ra m = 1000 the computations are carried out both in non-Darcy ( Ra = 10 5 ; Da = 10 − 2 ) and Darcy ( Ra = 10 9 ; Da = 10 − 6 ) regimes by varying the anisotropic properties of the porous medium. The properties considered for the study are permeability ratio ( K ∗ ), inclination of the principal axes ( θ) and ratio of Forchheimer constants ( F ∗ ). Results are presented in terms of Isotherms, streamlines, maximum temperature and average Nusselt number to understand the flow physics. It is observed that the anisotropic properties have significant influence on the flow behavior and heat transfer. Further correlations for average Nusselt number and maximum temperature at the heat source surface for wide range of parameters ( 10 7 ⩽ Ra ⩽ 10 8 , 10 − 5 ⩽ Da ⩽ 10 − 3 , 0.2 ⩽ w ⩽ 0.8 , 0 ° ⩽ θ ⩽ 90 ° , 0.1 ⩽ K ∗ ⩽ 10 and 1 ⩽ F ∗ ⩽ 100 ) in non-Darcy regime are presented.