MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER THROUGH A CIRCULAR TUBE FILLED WITH HOMOGENEOUS AND HETEROGENEOUS POROUS MEDIUM

Abstract

In this paper, we study the laminar steady flow of incompressible viscous magnetohydrodynamic (MHD) fluid inside a circular tube filled with homogeneous/heterogeneous porous medium. A transverse uniform/nonuniform magnetic field is applied, along with a uniform heat flux boundary condition. The Brinkman equation is used to model the flow through the saturated porous medium. Exact solutions of velocity and temperature fields, friction factor, and Nusselt number (<i>Nu</i>) in terms of the shape parameter (σ) and Hartmann number (<i>M</i>) are presented. In the limit of the zero shape parameter and the absence of magnetic field, the Brinkman model results converge to the Hagen-Poiseuille flow solution of circular pipe flow. In the opposite limit of the infinite shape parameter and the absence of magnetic field, the solutions approach the Darcy model results. In terms of the hydro-thermal characteristics of the flow, the Poiseuille flow results and the Darcy model results are shown to serve as the lower and upper bounds, respectively. A significant increase in the heat transfer in heterogeneous porous medium with the nonuniform magnetic field (highest <i>Nu</i> = 12) compared to homogeneous porous medium with uniform magnetic field is identified (highest <i>Nu</i> = 8). We also validate the results of homogeneous and heterogeneous porous medium with uniform/nonuniform magnetic field using numerical solutions.