Thermal Radiation Effect on Fully Developed Natural Convection Flow in a Vertical Micro-Channel

Abstract

The effect of thermal radiation on steady fully developed natural convection flow in a vertical micro-channel is presented in this article. Effects of velocity slip and temperature jump conditions are taken into account due to their counter effects on both the volume flow rate and the rate of heat transfer. Due to the presence of thermal radiation, the momentum and energy equations are coupled system of ordinary differential equations. Governing coupled nonlinear equations are solved analytically by employing the perturbation analysis method to obtain an expression for fluid temperature, fluid velocity, rate of heat transfer and skin friction on the microchannel walls. The effect of various parameters controlling the physical situation such as thermal radiation, temperature difference, Knudsen number, and fluid wall interaction are discussed with the aid of line graphs and Tables. Results indicate that both velocity and temperature enhanced with the increase of the thermal radiation parameter.

Keywords: Thermal radiation, Natural convection, Micro-channel, Velocity slip, Temperature jump