Flow of Two-Immiscible Fluids in Porous and Nonporous Channels

Abstract

This study considers steady, laminar flow of two viscous, incompressible, electrically-conducting and heat-generating or absorbing immiscible fluids in an infinitely-long, impermeable parallel-plate channel filled with a uniform porous medium. A magnetic field of uniform strength is applied normal to the flow direction. The channel walls are assumed to be electrically nonconducting and are maintained at two different temperatures. When present, the porous medium is assumed to act as an electrical insulator and that it is in local thermal equilibrium with the fluid. The transport properties of both fluids are assumed to be constant. This study is expected to be useful in understanding the influence of the presence of slag layers on the flow and heat transfer aspects of coal-fired Magnetohydrodynamic (MHD) generators when the porous medium is absent and the effects of thermal buoyancy and a magnetic field on enhanced oil recovery and filtration systems where the porous medium is present. The problem is formulated by employing the balance laws of mass, linear momentum, and energy for both phases. Continuous conditions for the velocity and temperature as well as the shear stress and heat flux of both phases at the interface are employed. The resulting governing ordinary differential equations are solved numerically subject to the boundary and interface conditions for the velocity and temperature distributions of both fluids in the channel. Analytical solutions for a special case of the problem where the porous medium is absent or only its inertia effect is neglected are obtained. Comparisons with previously reported velocity profiles are performed and excellent agreements are obtained. A parametric study illustrating the influence of the physical parameters involved in the problem is conducted and the results are presented graphically and discussed. [S0098-2202(00)02101-5]