An integral method for the boundary layer of MHD non-Newtonian power-law fluid in the entrance region of channels

Abstract

This paper presents the analytical solutions to laminar flow of MHD Newtonian and non-Newtonian power-law fluids in the entrance region of channels. The boundary layer growth and velocity profile of developing flow in a two-dimensional channel, under the influence of a uniform magnetic field, are investigated. The direction of the magnetic field is assumed perpendicular to the flow. For each case, a novel and useful non-dimensional correlation for computing the magnetic entrance length is proposed, using the integral equations method. In addition, the effect of different parameters on the magnetic entrance length, boundary layer thickness and thus core velocity and pressure loss are studied. It was found that with the increase of the Hartmann number, the entrance length declined. Furthermore, the entrance length decreases while the power-law index and magnetic interaction parameter increase. As well as, the results have shown that the augmentation of the magnetic interaction parameter leads to greater pressure drop in comparison with the hydrodynamic flow.