On Laminar Magnetoconvection Flow in a Vertical Channel in the Presence of Heat Generation and Heat Absorption

Abstract

The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel and asymmetric wall heating conditions in the presence of electrical conductivity effect is considered through proper choice of dimensionless variables. The governing with symmetric equations are developed and three types of thermal boundary conditions are presented. These boundary conditions are isothermal-isothermal, isoflux-isothermal, and isothermal-isoflux for the left-right walls of the channel respectively. The velocity field and the temperature field are obtained by perturbation series method which employs a perturbation parameter proportional to the Brinkman number. In addition, closed form expressions for reversal flow conditions at both the left-right channel walls are derived. Selected set of graphical results illustrating the effects of the various parameters involved in the problem including magnetic dissipation, heat generation or absorption, and the electrical conductivity on the velocity and temperature profiles as well as flow reversal situation are presented. The solutions obtained are also compared with that of results obtained by finite difference method. Copyright © 2013 by ASME.