Mixed convection of a permeable fluid in a vertical channel with boundary conditions of a third kind

Abstract

Numerical investigation of a steady mixed convective flow through a fluid-saturated porous media in a vertical channel with boundary conditions of the third kind including the effects of viscous dissipation and Darcy dissipation has been studied. The plates exchange heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed by a perturbation series method valid for small values of perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge-Kutta method of four slopes as an integration scheme and the Newton-Raphson method as a correction scheme. The problem is analyzed for different values of mixed convection parameters, porous parameter for equal and unequal Biot numbers, keeping the wall temperatures symmetric or asymmetric. The graphical results illustrating the effects of various parameters on the flow as well as average velocity and Nusselt numbers are presented. Further the analytical and numerical solutions agree very well for small values of the perturbation parameter. © 2012 Wiley Periodicals, Inc.