Flow and heat transfer analysis of magnetohydrodynamic (MHD) second-grade fluid in a channel with a porous wall

Abstract

Steady flow of a magnetohydrodynamic (MHD) second-grade fluid in a parallel channel is considered. One of the heated walls is cooled by coolant injection through the other porous wall. This work builds on the analysis of Parida et al. (Meccanica, 46(5):1093–1102, 2011) who, based on the regular perturbation method for a small viscoelastic parameter, solved the similarity transform equations and thereby analyzed the flow of MHD second-grade fluid and heat transfer on the plate. In this work, we show that it is possible to solve the self-similar equations analytically using Homotopy Analysis Method (HAM) for a range of viscoelastic parameter values. We illustrate the analytical solution of the problem, and the results for flow fields with skin friction and rate of heat transfer are discussed for various flow parameter values. The finding reveals the dependency of the rate of heat transfer variations on a wide range of viscoelastic parameter values. The HAM solution and the solution obtained by regular perturbation method agree well for small viscoelastic parameter values.