Numerical study of flow and heat transfer in a porous T-shaped pipe under mixed convection

Heat transfer improvement in heat exchangers is important for enhancing energy efficiency and reducing system size in engineering applications. Although the flow and thermal conditions in porous media remain insufficiently investigated, extensive studies have focused on mixed convection and the impact of T-shaped geometries. This study aims to examine the combined effects of T-shaped geometry and porous media on mixed convection heat transfer. The governing equations were nondimensionalized and reformulated in curvilinear coordinates using a vorticity-stream function technique, and numerically solved via the finite difference method in MATLAB. Simulations were conducted over a broad range of parameters, including Reynolds number (400≤Re≤900), Prandtl number (0.71≤Pr≤3), Richardson number (0.1≤Ri≤10), Darcy number (10−3≤Da≤10−1), and porosity (ϵ=0.75). With increasing Reynolds number, the results show a significant improvement in heat transfer, with the average Nusselt number increasing by approximately 36% at the bottom wall and by 55% along the side walls due to stronger convective effects. Additionally, rising the Darcy number from 10−3 to 10−1 reduces heat transfer at the bottom wall by about 24%, while enhancing it along the side walls by 34%, highlighting the influence of permeability on the flow structure and thermal gradients.