Effect of viscous heating on heat transfer performance in microchannel slip flow region

Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions and one wall as adiabatic and the other wall at constant heat flux input are studied. The solution method is verified for the cases where micro-scale effects are neglected. The effects of viscous heating on the temperature profiles and on the heat transfer performance are analyzed in detail. It is concluded that the effect of viscous heating, like an internal energy source, heats the fluid along the flow direction and severely distorts the temperature profiles. The effects of key parameters, such as the Brinkman and Knudsen numbers, on the Nusselt number, which expresses the heat transfer performance are investigated.