Fluid heat transfer characteristics with viscous heating in the slip flow region

An analytical solution for steady laminar fully developed convective heat transfer between parallel plates in the slip flow region with non-symmetric constant-heat-flux boundary condition, which can cover most practical microflow boundary conditions, is given, based on the superposition principle. The velocity slip and temperature jump at the wall, which are the characteristics in the slip flow region, and the viscous heating effect are considered in the calculation. The solution method is verified for the cases of constant-heat-flux boundary condition and for one wall taken as adiabatic and the other wall with constant-heat-flux boundary condition, where microscale effects are neglected (Knudsen number Kn=0, Brinkman number Br=0). The effects of the Brinkman number, non-symmetric heat flux and Knudsen number on the Nusselt number, which expresses the heat transfer performance are analyzed systematically. It is found that the closer the heat flux at the two walls is, namely the closer the symmetric ratio q* to 1, the higher the observed heat transfer performance for the microchannels.