Numerical simulation for MHD Williamson fluid utilizing modified Darcy’s law

Abstract

Objective of present investigation is to study peristaltic flow of MHD Williamson fluid in a planar symmetric channel. An incompressible fluid occupies the porous medium in a channel. Unlike the traditional approach, the modified Darcy’s law of Williamson fluid is utilized in the modeling. Numerous attempts for this aspect in non-Newtonian fluids have been made just by employing classical Darcy’s law of viscous fluid which is not correct. Heat and mass transfer equations are studied in the presence of Soret and Dufour effects. The walls of channel are flexible. In addition effects of slip are not ignored. The relevant problem formulation has been made and then simplified under long wavelength and low Reynolds number consideration. The effects of different embedded parameters on velocity, temperature, concentration and heat transfer rate are plotted numerically. Velocity, temperature and heat transfer rate are seen increasing when porosity parameter is enhanced. A decreasing effect of both Soret and Dufour numbers is observed for concentration profile. Keywords: Peristalsis, Modified Darcy’s law, Soret and Dufour effects, Hartman number, Slip conditions, Compliant walls, Numerical solutions