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Mathematical Modelling and Exact Solution of Fully Developed Natural Convection Flow in a Vertical Permeable Micro-Channel in the Existence of Thermal Radiation

Analytical solution to the steady natural convection flow in a vertical permeable micro-channel in the existence of thermal radiation is presented. Specifically, the effects of velocity slip and temperature jump is considered. Due to the presence of thermal radiation, the momentum and energy equations are coupled system of ordinary differential equations. 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. The results of the analyses indicated that the rate of heat transfer on the permeable micro-channel walls can be enhanced with the increase in the temperature difference parameter. Furthermore, the skin friction on the cold wall could be reduced with the increase in suction/injection parameter. For both asymmetric heating situations, increase in suction velocity (negative value of S) results to increase volume flow rate.