Optimum slip flow based on the minimization of entropy generation in parallel plate microchannels

The effects of 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 thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid–wall interfaces. After the analytic solutions for the velocity and temperature fields in the fluid and walls of microchannel are obtained, the entropy generation rate is discussed in detail and investigated considering slip flow and convective effects, simultaneously. The results show that the global entropy generation rate is minimized for certain suitable combination of the geometrical and physical parameters of the system. It is possible to find an optimum slip velocity which leads to a minimum global entropy generation rate. The Nusselt number is also calculated and explored for different conditions. An optimum value of the slip length that maximizes the heat transfer is derived.