Homotopy analysis method for boundary layer flow and heat transfer over a permeable flat plate in a Darcian porous medium with radiation effects

The aim of this article is to extend recent work of Dayyan et al. [24] in the case of radiative plate. We also introduced another parameter namely Darcy number which characterizes the porous medium. The governing equations (for boundary layer flow and heat transfer over permeable plate in Darcy porous medium) are transformed into a system of nonlinear ordinary differential equations using similarity transformations available in the literature. Approximate analytical solutions for the dimensionless velocity, temperature, friction factor and heat transfer rates are obtained using homotopy analysis method (HAM). Convergence of the HAM solution is discussed in detail. The effects of important controlling parameters on the dimensionless velocity, temperature, friction factor and heat transfer rates are analyzed graphically. It is shown that the friction factor increases with Darcy number, whereas the heat transfer rate decreases with the radiation-conduction parameter and increases with Darcy number. (C) 2014 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.