Thermal non-equilibrium in porous medium is a prevailing condition when discrepancy of temperature exists between the two phases. The solution of a thermal non-equilibrium model requires that the two heat transport equations corresponding to fluid and solid phases, can be solved separately, which, in turn, provides the information of temperature variations of fluid as well as solid phases of the porous domain. A new method is proposed in the current article to solve the energy equations of the thermal non-equilibrium condition in a porous square cavity. The proposed method is able to predict the thermal equilibrium as well as thermal non-equilibrium accurately. The proposed method is used to investigate the heat transfer through the porous cavity subjected to two different boundary conditions with a heating strip being placed inside the porous cavity. It was found that the new method predicted the heat and fluid flow behavior accurately for the previously mentioned case studies. It is noted that the heat transfer is higher when the heating strip is placed toward the cold surface. The Nusselt number at the bottom of the strip toward the right side is almost 10 times higher than that of the left side of the strip.
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