Mixed Convection in a Vertical Channel with Discrete Heat Sources Using a Porous Matrix

Abstract

In this work, we present the mixed convection air-cooling of two identical heat sources mounted in a vertical channel by using a porous matrix. The flow field is governed by the Navier–Stokes equation in the fluid region, the Darcy–Brinkman–Forchheimer equation in the porous region, and the thermal field by the energy equation. The effects of the Richardson number, Darcy number, thermal conductivity, and thickness of the porous matrix on the flow and heat transfer were studied. Results show that a better cooling is obtained for the channel completely filled with a porous material, except the components, with the Richardson number (Ri = Gr/Re² = 0.25), where Gr = 10⁴ is the Grashof number and Re = 200 is the Reynolds number, and for all Darcy numbers (10⁻⁵ ≤ Da ≤ 10⁻³). It was also seen that for Gr/Re² = 20, where the buoyancy effect is stronger, the average Nusselt number with porous matrix is higher than without porous matrix for all Richardson numbers (Ri = 0.25, 1, 10, and 20). As a result, we can economize the energy of the fan. Finally, the insertion of the porous matrix with high thermal conductivity ameliorates the cooling of the heat sources.

The authors gratefully acknowledge the financial support of this work (Phd Thesis) provided by the Algerian Ministry of High Education and Scientific Research. The authors also take this opportunity to express sincere respect to the reviewers for their comments.

Notes

Num1 and Num2 are the average Nusselt numbers for the first and second component, respectively. Num is the average Nusselt number for both components, and Θ_max is the maximum dimensionless temperature.