Modeling mixing convection analysis of discrete partially filled porous channel for optimum design

Mixing convection flow inside a convergent horizontal channel partially filled with porous material and a clear channel are investigated numerically in the present study. Four discrete heat sources with uniform heat flux have been applied on the bottom surface of the channel. Three different channel exit heights are studied (He = 1, 0.5 and 0.25). The thermal and flow-field analysis inside the channel is investigated for different wide range of Reynolds number (50 ⩽ Re ⩽ 300), Darcy number (10−2 ⩽ Da ⩽ 10−6), Richardson number (0 ⩽ Ri ⩽ 100) and Prandtl number (0.7 ⩽ Pr ⩽ 10). The present study carried out the effect of the channel exit height, Richardson number, Reynolds number, Darcy number and Prandtl number on the flow-field, the Nusselt number and the overall heat transfer performance. The Brinkman–Forchheimer–extended Darcy model is used to solve the governing equations of the fluid in the porous medium. The results reveal that the boundary layer thickness and flow velocity increase at high Richardson number for both porous and clear channels. The overall Nusselt number increases significantly for further increase in Darcy number, particularly for Ri > 10. The smallest channel exit height (He = 0.25) provides a high Nusselt number and low overall heat transfer performances. Furthermore, Richardson number has a small significant effect on overall Nusselt number and heat transfer performance at low Prandtl number.