Mixed convection flow of an electrically conducting fluid in a vertical channel with boundary conditions of the third kind

Abstract

In this study, the effects of viscous and Ohmic dissipation in steady, laminar, mixed, convection heat transfer for an electrically conducting fluid flowing through a vertical channel is investigated in both aiding and opposing buoyancy situations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed using a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. In the examined cases of velocity and temperature fields, the Nusselt numbers at both the walls and the average velocity are explored. It is found that the velocity profiles for an open circuit (E > 0 or E < 0) lie in between the short circuit (E = 0). The graphical results illustrating the effects of various parameters on the flow as well as the average velocity and Nusselt numbers are presented for open and short circuits. In the absence of electric field load parameter and Hartmann number, the results agree with Zanchini (Int. J. Heat Mass Transfer, 41, 3949 (1998)). Further, the analytical and numerical solutions agree very well for small values of the perturbation parameter.

Heat transfer characteristics of magnetohydrodynamic two fluid oscillatory flow in an inclined channel with saturated porous medium

“…Nikodijevic et al 13 investigated the MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field. Umavathi et al 14 reported on the characteristics of the flow and heat transfer of the fluid-saturated porous medium in a double passage channel. Hasnain et al 15 studied the MHD convection flow of two immiscible liquids in an inclined channel.…”