Three-dimensional non-Darcy free convective heat transfer flow in a bidisperse porous medium within a cubical cavity

Abstract

Heat transport in porous media, especially in a bidisperse porous matrix, has recently received considerable attention due to its diverse real-life applications in applied science and engineering. In the current study, we employ the Darcy-Brinkman-Forchheimer model and three temperature equations incorporating the local thermal nonequilibrium conditions among the fluid and the porous matrix to examine the three-dimensional free convective heat transfer flow in a bidisperse permeable matrix inside a cubical cavity. The Galerkin weighted residual finite element method simulates the model's non-dimensional governing equations. We examine the effects of the significant model parameters on the flow and heat domains considering (104 ≤ Raf ≤ 106), (103 ≤ Rap ≤ 106), (10−3 ≤ Daf ≤ 10−1), (10−4 ≤ Dap ≤ 10−2),(0.7 ≤ ϕ ≤ 0.9) and (0.4 ≤ ε ≤ 0.7). It is found that the average Nusselt number in the macrophase, microphase, and solid matrix increased with the increase of the macro porosity for about 7.18%, 7.06%, and 9.86%, respectively, when it rises from 0.7 to 0.9. Furthermore, increasing the micro-porosity enhances the rate of heat transfer. As the Raleigh number advances, there is a noticeable increase in heat transfer in both the macrophase and the microphase.

Keywords

• Free convection
• Bidisperse permeable matrix
• Cubical cavity
• Non-Darcy flow
• Local thermal non-equilibrium