Transient conjugate heat transfer in a circular microchannel involving rarefaction, viscous dissipation and axial conduction effects

Transient conjugate heat transfer of a hydrodynamically developed and thermally developing laminar flow in a circular microchannel is investigated considering the effects of rarefaction, viscous dissipation and axial conduction. The problem is solved numerically by a finite difference method based on Patankar's (1980) control volume approach. Momentum and energy equations are solved with the boundary conditions of the first degree velocity slip and temperature jump. The problem depends on four parameters. These are the Peclet number (Pe), the Knudsen number (Kn), the Brinkman number (Br) and the wall thickness ratio (d′). The results obtained showed that heat transfer characteristics are significantly affected by these parameters and that in micro channel flows, the fluid's rarefaction effects, viscous dissipation and axial conduction should not be ignored.