Properties of Viscous and Joulean Dissipation on Fully Developed Natural Convection in a Vertical Micro-channel in Existence of Lorentz Forces

Abstract

Magnetohydrodynamic natural convection flow in a vertical parallel plate micro-channel in presence of viscous and Joulean dissipation is theoretically examined by using a perturbation series method. The effects of velocity slip and temperature jump conditions were taken into consideration. Due to the presence of viscous and Joulean dissipation effects, the momentum and energy equations are coupled system of ordinary differential equations. Roles of Hartmann number, Knudsen number, fluid - wall interaction parameter and
dissipation parameter on the flow formation as well as rate of heat transfer are presented. The results revealed that increase in Hartmann number reduced the influence of viscous as well as Joulean dissipation on the velocity, temperature, skin friction and rate of heat transfer. Effect of Hartmann number, rarefaction parameter, fluid wall interaction parameter as well as buoyancy parameter on temperature and velocity is significantly pronounced in the case of symmetric heating.