Optimal heating protocols in finite-length flat microchannels : the effect of rarefaction, streamwise conduction and viscous dissipation

Abstract

We present an analytical solution of the convectionconduction problem, in laminar flow conditions in finite-length flat microchannels including slip/no-slip flows, effects of rarefaction, streamwise conduction and viscous dissipation, for prescribed wall heat flux boundary conditions. The solution proposed is valid for low-intermediate Peclet values Pe ≤ 1/a, a being the microchannel aspect ratio height/length. The analytical solution is compared with numerical solutions obtained by means of finite-elements method (FEM Comsol 3.5 ) in a wide range of Pe and a values and for different wall heat flux profiles. Optimal heating protocols in the presence and in the absence of viscous dissipation are presented.