Boundary problems for one-dimensional kinetic equation with constant collision frequency

TL;DR

This paper derives analytical solutions for temperature jump and evaporation problems in a one-dimensional kinetic equation with BGK collision integral and constant collision frequency, providing explicit distributions of concentration, velocity, and temperature.

Contribution

It presents the first analytical solutions to boundary problems for a 1D kinetic equation with BGK collision integral and constant collision frequency.

Findings

Explicit distributions of concentration, velocity, and temperature are obtained.

Solutions describe temperature jump and evaporation phenomena.

Analytical methods are developed for this class of kinetic equations.

Abstract

For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and constant frequency of collisions of molecules. Distribution of concentration, mass speed and temperature is received.