The effect of gaseous slip on microscale heat transfer: an extended Graetz problem

On the basis of Langmuir's theory of adsorption of gases on solids, the effect of temperature jump on microscale heat transfer is investigated. A mathematical model, extended from the classical Graetz problem, is developed to analyze convective heat transfer in a microtube in various slip-flow regimes. The surface slip corrections are made by employing the Langmuir model, as well as the conventional Maxwell model. The effects of axial heat conduction are also investigated by extending the finite integral transform technique to the slip-flow case. We show that the Langmuir model always predicts a reduction in heat transfer with increasing rarefaction, as does the Maxwell model, except when the energy accommodation coefficient is relatively much smaller than that for momentum accommodation. This implies that, for most physical applications, the Reynolds analogy between heat transfer and momentum transfer is preserved in slip-flow regimes with low Mach numbers.