Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

Abstract

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation, the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method (GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.