Steady-state conjugate natural convection in a fluid-saturated porous cavity

The current numerical investigation addresses the wall heat conduction effect on the natural-convection heat transfer within a two-dimensional cavity, which is filled with a fluid-saturated porous medium. The problem configuration consists of two insulated horizontal walls of finite thickness and two vertical walls which are maintained at constant but different temperatures. The generalized model of the momentum equation, which is also known as the Forchheimer-Brinkman-extended Darcy model, is used in representing the fluid motion inside the porous cavity. The local thermal equilibrium condition is assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The steady-state solution is sought from the undergoing investigation. The momentum and energy transport processes within the porous cavity is examined through depicting the streamlines and isotherms for different domains of a selected dimensionless groups. These dimensionless groups and their respective domains are as follows: W = 0.0075 s(-) 0.2, K_r = 1 s(-) 10, k_s / k_f = 0.1 s(-) 100, Ra = 10⁴ s(-) 10⁶, Da = 10^{- 5} s(-) 10^{- 1}, ε = 0.25 s(-) 0.95 and AR = 0.25 s(-) 2. The significance of varying these parameters on the predicated average Nusselt number is highlighted and discussed. Finally, the investigation is concluded by presenting the sensitivity of the interface temperature upon varying the above dimensionless groups.