Non-Darcy and localized heating effects on Benard convection in porous enclosure

Bénard convection in a porous medium using the non-Darcy model with localized heating is studied numerically in the present paper. The Forchheimer-Brinkman-extended Darcy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the heater size (0.2 ≤ H ≤ 1), the Rayleigh number (10² ≤ Ra ≤ 10⁵), the porosity of the porous medium (0.4 ≤ ε ≤ 0.99), the Darcy number (10^-5 ≤ Da ≤ 10^-2), and the thermal conductivity ratio of solid matrix to fluid (1 ≤ k_s/k _f ≤ 10). The Prandtl number is fixed at Pr = 1. It is found that an extremum heat transfer rate occurs about H = 0.8 for any value of the porosity and any porous material considered.