Mathematical modeling of heat transfer process in a rectangular channel in the problem of Poiseuille flow

We propose an analytical solution of problem of heat transfer in a long channel with a rectangular cross section. A rarefied gas flow trough cross section is studied on the basis of Williams kinetic equation in the whole range of the Knudsen number varying from the free molecular regime to the hydrodynamic one. A wide range of the aspect ratio is considered. The heat flow is calculated as a function of a constant pressure gradient supported in the channel.