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

Abstract

An 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 are considered. Due to the presence of thermal radi
ation, the momentum and energy equations are a coupled system of ordinary differen
tial equations. The effect of various parameters controlling the physical situation such as 
thermal radiation, temperature difference, Knudsen number, and fluid wall interaction is 
discussed with the aid of line graphs and tables. The results of the analyses indicated that 
the rate of heat transfer on the permeable microchannel 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 the suction/injection parameter. For both asymmetric heating situations(ξ = −
0, 1), an increase in suction velocity (negative value 
of S) results in an increase in volume flow rate (
Qx ).