Heat transfer process in an elliptic channel

Consider the problem of heat transfer in the elliptic channel with its axis parallel to the temperature gradient. As the basic equation, that describes the kinetics of the process, the Williams kinetic equation, and as a boundary condition on the wall of the channel — a model of diffuse reflection are used. The deviation from the equilibrium state of the gas is assumed small. In order to find a linear correction to the local equilibrium distribution function the problem is reduced to solving a linear homogeneous differential equation of the first order. It’s solution is constructed using the method of characteristics. An analytical method for calculating the heat flux of rarefied gas through a cross section in the elliptic channel by the using a simple numerical procedures, which are realized in the system of computer algebra of Maple 17, is presented. A comparison with analogical results presented in the open data is done.