Conjugate local thermal nonequilibrium and non-Darcy flow inside porous enclosure: Analysis of localized heating and cooling arrangements

This study covers a simulation on conjugate free convective in a porous enclosure containing a side wall thickness and partially heated and cooled from sides under the considerations of local thermal nonequilibrium (LTNE) and non-Darcy flow. Interest has been focused on how the side wall thickness and the locations of cooled and heated parts affect the effectiveness of the Nusselt number (Nu). Three different cases of localized heating and cooling locations have been implemented for the following ranges: scaled heat transfer coefficient ($0.1\le H\le 100$), wall to fluid thermal conductivity ratio ($0.1{\le R}_k\le 100$), modified Rayleigh number ($200\le \mathit{Ra}*\le 1000$), wall width ($0.1\le \stackrel{?}{Z}\le 0.5$), inertial parameter (${10}^{?4}{\le F}_s/P_r^{*}\le {10}^{?2}$), and thermal conductivity ratio ($0.1\le K_r\le 100$). Outcomes show that $\stackrel{?}{Z}$ and the locations of cooled and heated parts have remarkable impacts on all the Nusselt numbers. The intensity of LTNE region considerably relies on $\mathit{Ra}*$, $K_r$ and $H$. The total average Nu_T is highly dependent on $R_k$, $\mathit{Ra}*$, $\stackrel{?}{Z}$, $F_s/P_r^{*}$, and $K_r$ as compared to H. The increase in $\stackrel{?}{Z}$ leads to change of the convective mechanism to conductive mode. The rise in $R_k$ guides to increase Nu, where $R_k$ can control the flow strength. The actions of $F_s/P_r^{*}$ on Nu_f is more evident than Nu_s. For low H and K_r, the size of LTNE zone is considerably affected by H as compared to K_r although K_r has a high influence on Nu. For high K_r and H, the LTNE zone has closely vanished. Findings display that the Case 2 provided the highest Nu for all tested parameters except the case of $K_r=0.1$. Finally, it is evident that for the problems that employed solid conduction wall with localized heating and cooling sections, Case 2 is recommended for future use in the applications that implement a porous medium and depend on free convection.