Electromagnetic natural convection flow in a vertical microchannel with Joule heating: exact solution

Abstract

This article explores the combined role of Joule heating and transversely applied magnetic field on natural convection flow in a vertical microchannel with asymmetric wall heating. The governing momentum and energy equations are obtained and transformed to their corresponding dimensionless form using suitable dimensionless parameters. Exact solutions are obtained for the coupled momentum and energy equations and presented graphical to understand the role of governing dimensionless parameters. During the course of numerical and graphical simulations, the results indicate that the presence of Joule heating and electromagnetic field lead to enhancement of fluid velocity, temperature, skin-friction and Nusselt number in the microchannel. In addition, the heat transfer can be improved when heat is been transported from the walls of the microchannel to the fluid and for purely asymmetric wall heating compared to the case when heat is transfer from the fluid to the wall.