Green element numerical solution of generalized Couette flow with heat transfer

Abstract

This paper provides a Green element  method (GEM) numerical  analysis of the effects of  a uniform transverse magnetic field on fluid flow. The Green element method is a robust numerical scheme that evolved essentially from the singular integral  theory of the boundary element method (BEM) with the unique variety of numerically implementing the theory  by  the finite element procedure. One of the advantages inherent in this approach is that the coefficient matrix from the discrete  equations of the assembled element equations is banded and amenable to numerical  solution. For the purposes of this study,   the fluid is incompressible, and electrically conducting, and  flows between two parallel plates, one of which is moving with a uniform speed  while the other is stationary. The depth of the channel is taken to be much smaller than the width and the channel is considered to be  very long in the horizontal direction. As a result,  the flow is  assumed to be fully developed and  driven by a pressure gradient in a uniform magnetic field. Numerical solutions obtained with GEM closely match analytical results. In order to validate the physics and numerics of the problem formulation,  comprehensive  parametric studies are carried out to show the effects on flow  and electromagnetic fields of Hartmann number, pressure gradient, current distributions, and temperature .