HEAT TRANSFER THROUGH A POROUS SATURATED CHANNEL WITH PERMEABLE WALLS USING TWO-EQUATION ENERGY MODEL

In this work, fluid flow and heat transfer of a viscous and incompressible fluid through a porous medium imbedded inside a channel with permeable walls are investigated using Darcy-Brinkman equations and two-equation energy model. The governing equations of flow and energy are reduced to a system of ordinary differential equations using appropriate similarity solutions. The obtained nonlinear differential equations are solved using the homotopy analysis method (HAM). As a cross check for the presented models and HAM results, a numerical solution is presented based on the finite volume method and a good agreement is observed. Finally, the effects of key parameters are considered on dimensionless velocity profiles, solid and fluid temperature distributions, as well as Nusselt number under the thermal nonequilibrium condition.

Darcy–Brinkman equations, thermal nonequilibrium condition, permeable walls, homotopy analysis method