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

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.

Analytical solution of problem about moderately strong evaporation (condensation) for one-dimensional kinetic equation

“…For comparison we will present coefficients of jump of temperature and jump of concentration found by means of the one-dimensional kinetic equations with constant frequency of collisions [12] ε T = −0.4443(2U ), ε n = −0.8958(2U ).…”

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

“…Let us notice, that the continuous spectrum of the characteristic equation, answering to the initial equation (1.2), represents the empty set (see [2] and [4]). This fact speaks that the equation (1.2) does not contain convection derivative.…”

“…For comparison we will bring coefficients of temperature and concentration jumps found by means of the one-dimensional kinetic equations with constant frequency of collisions [4] ε T = 1.3068g T − 0.4443(2U ),…”

“…In work [4] the generalized problem of Smolukhovsky has been solved for special case of affine dependence of collisional frequency on the module of velocity of molecules. Namely, the case, when collisional frequency is constant has been considered.…”