Nonlinear Thermodiffusion in Gases at Moderate Temperatures

Abstract

Abstract The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the diffusion processes, which occur with a finite velocity. In the previous papers, A. J. Janavičius proposed the nonlinear diffusion equation with the diffusion coefficient directly proportional to the concentration of impurities. This equation provides a more exact description of the profiles of impurities in Si crystals. The heat transfer in gases carries a greater average kinetic energy based on nonlinear diffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. In this case, the heat transfer in gases can be described by using nonlinear thermodiffusion equation with heat transfer and thermodiffusion coefficients directly proportional to temperature T. The obtained approximate analytical solutions are successfully applied in defining temperature profiles and heat transfer coefficients in gases as well as providing opportunities for practical applications. It has been concluded that heat spreading in gases depends on temperature differences and pressure in gases.