Homotopy perturbation and numerical solutions for MHD flow of PTT fluid through a channel embedded in a porous medium

Abstract

An analysis is made of the steady one dimensional flow and heat transfer of an incompressible viscoelastic electrically conducting fluid (PTT model) in a channel embedded in a saturated porous medium. The pressure driven flow is subjected to a transverse magnetic field of constant magnetic induction (field strength). The heat transfer accounts for the viscous dissipation. The governing equation (a non-linear ordinary differential equation) is solved analytically (Homotopy Perturbation Method) and numerically (Runge-Kutta method with shooting technique) providing the consistency of the result. The role of Deborah number substantiates both Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces affects rheological property of the flow model considered. Temperature distribution in the boundary layer is shown when the channel surfaces are held at constant temperatures. A novel result of the analysis is that the contribution of viscous dissipation is found to be negligible as the variation of temperature is almost linear across the flow field in the present PTT fluid model indicating preservation of thermal energy loss.