Mathematical simulation of heat transfer in an elliptic channel under the action of a pressure gradient

A method for calculating the heat flux through the cross section of an elliptic channel in the presence of a pressure gradient that is normal to the symmetry axis of the channel has been suggested. As a basic equation that describes the process kinetics, the Williams equation is taken, and the model of diffuse reflection sets boundary conditions at the channel wall. The deviation of the state of the gas from equilibrium is assumed to be small. The dependence of the heat flux through the cross section of the channel on the Knudsen number has been derived. The heat fluxes in the limiting cases of free-molecular and hydrodynamic regimes have been compared.