Natural Convection Inside a Bidisperse Porous Medium Enclosure

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks $(N2)$⁠, macropore volume fraction $(ϕE)$⁠, and internal Darcy number $(DaI)$ for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both $DaI$ and $DaE$⁠. At low Ra values, Nu is strongly affected by both $DaI$ and $ϕE$⁠. When $N2$ is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of $Raϕ$⁠, $DaE$⁠, $DaI$⁠, and $N2$⁠. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, $RaϕDaE$⁠.