MIXED CONVECTION FLOW IN A VERTICAL POROUS CHANNEL WITH BOUNDARY CONDITIONS OF THE THIRD KIND WITH HEAT SOURCE/SINK

Abstract

A numerical study of mixed convection in a vertical channel filled with a porous medium, including the effects of inertia forces, is studied by taking into account the effects of viscous and Darcy dissipations with heat source or sink. The flow is modeled using the Brinkman Forchheimer-extended Darcy equations. The plate exchanges heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. The governing equations are solved using Runge-Kutta fourth-order method with shooting technique for extended Darcy model and analytically using the perturbation series method for the Darcy model. The velocity and temperature fields are obtained for various porous parameters, inertia effect, and perturbation parameters for equal and unequal Biot numbers and are shown graphically. It is also found that both analytical and numerical solutions agree to a great extent with the small values of the perturbation parameter in the absence of inertial forces.