Nonlinear thermal conductivity in gases

Abstract

The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. A.J. Janavičius proposed nonlinear equation which describes more exactly the diffusion of impurities in Si crystals in many interesting practical applications. The heat transfer in gases is also based on 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 can be considered using similar nonlinear thermal diffusivity equation. The approximate analytical solution of this nonlinear equation can be used for the experimental analysis of thermal conductivity coefficients using temperature profiles dependence on different temperatures and pressures in gases.

Nonlinear Thermodiffusion in Gases at Moderate Temperatures

“…A similar task and approach have been considered for nonlinear diffusion [2], [13], [14] in gases. In this case, the definition of diffusion coefficients, which depend on average values of frequencies of molecule collisions in the frontier region of diffusion profiles, has been introduced.…”

“…In the previous papers, we have discussed the nonlinear diffusion of impurities in semiconductors [1], [2], nonlinear thermodiffusion in gasses [3] and heat transfer in metals by electrons [4] using mathematical methods of similarity variables [1] for nonlinear equations. The obtained results are important for engineering applications.…”

“…can be rewritten in a more convenient form (4) which mathematically coincides with nonlinear diffusion equation [1]. The numerical calculations provided in [2] give dependence ) , ( t x n as a straight line in the region is possible only if it exists in the points x . This requirement is equivalent to the approval that thermodiffusion must occur with finite velocity.…”

“…This requirement is equivalent to the approval that thermodiffusion must occur with finite velocity. It is very important for definition of thermal conductivity [3] and diffusion coefficients [1], [2].…”