Boundary problems for the one-dimensional kinetic equation with the collisional frequence proportional to the module velocity of molecules

TL;DR

This paper derives analytical solutions for temperature jump and weak evaporation problems in rarefied gases, considering a kinetic equation with velocity-dependent collision frequency, and provides numerical and graphical analyses.

Contribution

It introduces new analytical solutions for boundary problems in kinetic theory with velocity-dependent collision frequency, including temperature and concentration jumps.

Findings

Quantified temperature and concentration jumps.

Constructed distributions of concentration, velocity, and temperature.

Performed numerical calculations and graphical analysis.

Abstract

For the one-dimensional linear kinetic equations with collisional frequency of the molecules, proportional to the module velocity of molecules, analytical solutions of problems about temperature jump and weak evaporation (condensation) in rarefied gas are received. Quantities of temperature and concentration jumps are found. Distributions of concentration, mass velocity and temperature are constructed. Necessary numerical calculations and graphic researches are done.