Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium

摘要

The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We 1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.