Combined effects of uniform heat flux boundary conditions and hydrodynamic slip on entropy generation in a microchannel

Abstract

The effects of wall heat flux boundary conditions, wall to fluid thermal conductivity ratio and slip flow on heat transfer and entropy generation by considering the conjugate heat transfer problem in microchannels are studied, analytically. The heat transfer equations in the fluid and the finite thickness walls of the microchannel are solved analytically using uniform heat flux boundary conditions at the outer surfaces of the walls with appropriate continuity of temperature and heat flux at the fluid-wall interfaces. Exact analytic solutions for the velocity and temperature fields in the fluid and walls of microchannel are utilized to compute the entropy generation rate. The latter is integrated in the whole region of analysis so that the finite dimensions of the device are considered to get the global entropy generation rate. Finally, this quantity is discussed in detail and investigated considering combined effects of wall and hydrodynamic slip. Findings reveal that it is possible to find optimum values of heat flux across the walls of microchannel where the global entropy generation reaches a minimum. Special attention has been given to the effect of the wall heat flux on optimal values of other parameters. The optimum values of both the slip length and wall to fluid thermal conductivity ratio, where the entropy generation is minimum, decrease with the wall heat flux. Also, optimum values of Peclet number with minimal entropy are found for certain suitable combination of geometrical and physical parameters of the system.