Thermal Modeling of Forced Convection in a Parallel-Plate Channel Partially Filled With Metallic Foams

Abstract

Fully developed forced convective heat transfer in a parallel-plate channel partially filled with highly porous, open-celled metallic foam is analytically investigated. The Navier–Stokes equation for the hollow region is connected with the Brinkman–Darcy equation in the foam region by the flow coupling conditions at the porous–fluid interface. The energy equation for the hollow region and the two energy equations of solid and fluid for the foam region are linked by the heat transfer coupling conditions. The normalized closed-form analytical solutions for velocity and temperature are also obtained to predict the flow and temperature fields. The explicit expression for Nusselt number is also obtained through integration. A parametric study is conducted to investigate the influence of different factors on the flow resistance and heat transfer performance. The analytical solution can provide useful information for related heat transfer enhancement with metallic foams and establish a benchmark for similar work.