Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions

Abstract

Mixed convection flow and heat transfer in a vertical channel filled with composite porous medium using Robin boundary conditions is analyzed. The flow is modeled using the Darcy-Lapwood-Brinkman model. The viscous and Darcy dissipation terms are included in energy equation. The plate exchanges heat with an external fluid. Both the conditions of equal and different reference temperature of the external fluid are considered. The governing equations are coupled and non-linear because of inclusion of dissipation terms and buoyancy forces. The equations are solved using perturbation method valid for small values of perturbation parameter. However, the restriction on the perturbation parameter is relaxed by finding the solutions of governing equations by using Differential Transform Method. The effects of various parameters such as mixed convection parameter, porous parameter, viscosity ratio, width ratio, conductivity ratio and the Biot numbers on the flow are discussed. The percentage of error between perturbation method and differential transformation method increases as the perturbation parameter increases for both equal and unequal Biot numbers.