Analysis of effects of Thermal Non-Equilibrium and Non-Darcy Flow on Natural Convection in a Square Porous Enclosure Provided with a Heated L Shape Plate

Abstract

This work involves a study on the convective heat transfer over a two perpendicular plates embedded inside a square porous cavity using non-Darcian flow and Local Thermal Non-Equilibrium (LTNE) assumptions. The problem has been assumed to be steady and two-dimensional coordinates. For non-Darcy flow, the effects of inertia and boundary layer have been included. Finite volume method has been used to discretize and solve the governing equations. The results show that the total average Nusselt number (NuT) is a strong function of modified Rayleigh number (Ra*) and inertia parameter (Fs/Pr*). For a fixed Fs/Pr*, the fluid Nusselt number (Nuf) has been found higher than the solid Nusselt number (Nus). The results also demonstrated that the thermal conductivity ratio (Kr) has a significant impact on all average Nusselt numbers compared to the scaled heat transfer coefficient (H). However, H has a considerable influence on the intensity of LTNE region in comparison to Kr, especially for their lower values. The size and the power of LTNE region are increased with increasing in Ra* and decreasing in Fs/Pr*. For higher Kr and H, the medium inside cavity be close to the thermal equilibrium condition. The results show that the effect of Kr on all Nu is comprehensive, whereas the effect of H is limited to Nus and hence, the behaviour of NuT is similar to the behaviour of Nuf. As Kr is increased, NuT becomes very close to Nuf. Finally, the obtained results have been summarised by developing a correlation of NuT which can be used in engineering design.