Heat Transfer in the Rarefied Gases (I)

Abstract

Fundamentally, the properties of rarefied gases must be deduced from the Maxwell-Boltzmann equation. We will treat the problem of steady one-dimensional heat transfer between two parallel plates in the rarefied gases. H. Grad expressed the distribution function of the gas molecules in the Hermite polynomials. This method, however, cannot satisfy the boundary conditions that the distribution function is discontinuous between incidental molecules and reflecting ones. Then we will divide the distribution function for incidental molecules and for reflecting ones separately, which have different coefficients. Using these distribution functions, we get four equations of the moments of distribution function and three equations can be obtained from the Maxell-Boltzmann equation. From these seven equations we can solve the temperature distribution between two parallel plates in the rarefied gases as the function of the distance from the wall. And we get the relation between wall temperature and heat flux vector.