Abstract
The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source. In the previous papers A. J. Janavičius proposed the nonlinear diffusion equation which provided a more exact description of impurities diffusion by fast moving vacancies generated by X-rays in Si crystals. This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. Heat transfer in gas must be compatible with the Maxwell distribution function. Heat transfer in gas described by using nonlinear thermodiffusion equation with heat transfer coefficients directly proportional to temperature . The solution of the thermodiffusion equation in gas was obtained by using similarity variables. The equation is solved by separating the linear part of the equation that coincides with Fick's second law. The obtained results coincide with Ya.B. Zeldovich’s previously published solutions of nonlinear equations by changing the respective coefficients.
Highlights
The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source
This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions
Heat transfer in gas described by using nonlinear thermodiffusion equation with heat transfer coefficients directly proportional to temperature T
Summary
The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source. Janavičius proposed the nonlinear diffusion equation which provided a more exact description of impurities diffusion by fast moving vacancies generated by X-rays in Si crystals This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. Heat transfer can be described by using a modified theory of nonlinear diffusion in solids [1] In this case the frequency of the jumps of diffusing molecules [2] depends upon the coordinates and changing molecules concentration n and temperature T according law of ideal gas defining pressure p nkT. The constant pressure p n(r,t)kT (r,t) nS (r,t)kTS (r,t) at slow impurities transmission in gas with decreasing temperature T (r,t) is compensated by increasing the concentration n(r,t) of impurities in gases with heating from the spherical source of temperature TS
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