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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 (), wall to fluid thermal conductivity ratio (), modified Rayleigh number (), wall width (), inertial parameter (), and thermal conductivity ratio (). Outcomes show that and the locations of cooled and heated parts have remarkable impacts on all the Nusselt numbers. The intensity of LTNE region considerably relies on , and . The total average NuT is highly dependent on , , , , and as compared to H. The increase in leads to change of the convective mechanism to conductive mode. The rise in guides to increase Nu, where can control the flow strength. The actions of on Nuf is more evident than Nus. For low H and Kr, the size of LTNE zone is considerably affected by H as compared to Kr although Kr has a high influence on Nu. For high Kr 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 . 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.

The effect of modified Rayleigh number, positions and lengths of two perpendicular heated surfaces on natural convection heat transfer was studied numerically, where the two surfaces are embedded in square cavity filled with saturated porous medium. All walls of the cavity are kept at constant temperature. Indirect numerical method was used to solve the governing equations, which are: the nondimensional Darcy flow equation as well as the non-dimensional energy equation, which were solved numerically by finite difference method using Gauss-Seidel iteration coupled with (Successive Under Relaxation) technique. This study covered a wide range of modified Rayleigh number range (100-1000), nine positions and the ratios of length of vertical surface to the horizontal (0. 5,1, 2). It was found that the positions of two heated surfaces have small effect on the heat transfer rate, but any increase in the length of two surfaces leads to an increase in average Nusselt number, but an increase in the length of vertical surface leads to more increase in the average Nusselt number.