Analytical solution of Stokes’ second problem on the behavior of rarefied gas over an oscillating surface

Abstract

Stokes' second problem on the behavior of rarefied gas occupying a half-space is analytically solved. The plane bounding the half-space executes harmonic oscillations. The kinetic equation with the model collision integral in the form of a τ-model is used and the case of diffuse reflection of gas molecules from the wall is considered. The distribution function of gas molecules is constructed and the mass velocity of the gas in the half-space, together with its value directly at the wall, is determined. The drag force acting from the gas on the boundary executing oscillatory motion in its plane is obtained. Moreover, the energy dissipation rate per unit area of the oscillating plate bounding the gas is determined.

The second Stokes problem with specular–diffusive boundary conditions

“…Уравнение (3.4) -интегральное уравнение Фредгольма второго рода. Укажем на связь между функцией L(k) и дисперсионной функцией λ(z) [17]- [19]. Представим функцию L(k) в виде:…”

Analytical solution of the second Stokes problem for rarefied gas with Cercignani boundary conditions

“…В наших работах [9]- [11] для второй задачи Стокса отыскиваются собственные функции и соответствующие собственные значения, отвечающие как дискретному, так и непрерывному спектрам. Исследована структура дискретного и непрерывного спектров.…”

Temperature jump in second Stokes' problem by nonlinear analysis

“…In our works [11] and [12] the second Stokes' problem analytically for rarefied gas is solved. The model Boltzmann' kinetic equation with integral of collisions type BGK thus was used.…”

“…The model Boltzmann' kinetic equation with integral of collisions type BGK thus was used. In [11] the problem with diffusion boundary conditions was solved. It is shown, that results of works [8] and [10] are rather close with the results received from the analytical decision [11].…”

“…In [11] the problem with diffusion boundary conditions was solved. It is shown, that results of works [8] and [10] are rather close with the results received from the analytical decision [11]. Results from [11] on a case of boundary Cercignani' conditions in [12] have been generalized.…”