Heat transfer process in an elliptical channel

Abstract

This paper addresses the problem of heat transport in an elliptical channel in the presence of a temperature gradient parallel to its axis. The Williams equation is used as the basic equation describing the kinetics of the process and a model of diffusive reflection is used as the boundary conditions on the channel wall. The deviation of the gas condition from the equilibrium is assumed to be small. In order to find a linear correction to the local equilibrium function of distribution, a boundary problem consisting of a linear homogeneous partial differential equation of the first order with a homogeneous boundary condition has been built. The solution of the built boundary value problem has been found by the method of characteristics. The value of the heat flow through the cross section of the channel is found by using numerical procedures implemented by the computer algebra Maple 17 system. The results were compared with the analogous results found in the open press.