For the first time, in the quasi-stationary Stokes approximation at low Reynolds and Peclet numbers, a theory has been constructed that takes into account the effect of convective heat transfer on the photophoresis of a heated large spherical aerosol particle using the method of matched asymptotic expansions. When solving gasdynamics equations, the power-law form of the dependences of the molecular transfer coefficients (viscosity, thermal conductivity) and density of the gaseous medium on temperature is taken into account.

An approximate solution of a boundary value problem for the convective heat transfer equation is obtained by the method of matched asymptotic expansions for small Péclet and Reynolds numbers. When solving the stationary system of gasdynamic heat transfer equations including the system of Navier–Stokes equations linearized in the velocity, the convective heat transfer equation, and the Poisson equation, it is assumed that the temperature dependences of the viscosity, thermal conductivity, and density of a gaseous medium are power-law.

This paper describes a theoretical study of the steady motion of a large solid nonvolatile aerosol spherical particle, which contains thermal sources within itself, in a concentration gradient of binary gas mixture components. It is assumed that an average particle surface temperature significantly differs from the temperature of the binary gas mixture surrounding it. Equations of gas dynamics are solved taking into account the power-law dependence of the molecular transfer coefficients (viscosity, thermal conductivity, and diffusion) and the density of the gaseous medium on temperature. Under boundary conditions, diffusion and thermal slip are taken into account. Numerical estimates show that the diffusion and photophoretic forces and velocity substantially depend on the average particle surface temperature.

AbstractA theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

This paper presents the theoretical description of steady motion of a moderately large spherical aerosol particle in the external temperature gradient field in the Stokes approximation with Reynolds and Peclet numbers much smaller than unity. It is assumed that the average temperature of the particle surface significantly differs from the temperature of its gaseous environment. Gas dynamics equations are solved with account for the power dependence of molecule transport coefficients (viscosity and thermal conductivity) and the density of the gaseous environment on temperature. Boundary conditions are written in the linear approximation based on the Knudsen number. It is shown that the thermophoretic force and velocity substantially depend on the Knudsen number and the average temperature of the particle surface.

A theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

Assuming that the fluid viscosity is an exponential-power function of temperature, a boundary value problem for the Navier–Stokes equations linearized with respect to velocity is solved and the uniqueness of the solution is proved. The problem of a nonuniformly heated spherical solid particle settling in fluid is considered as an application.

In the Stokes approximation at small Reynolds and Peclet numbers, we obtain a solution to the boundary-value problem of flow around of particles of spherical shape for stationary system of equations of a viscous non-isothermal fluid comprising a linearized by speed Navier–Stokes equation system and the equation of heat transfer given an exponential-power law of dependence of viscosity of fluid on temperature.

АннотацияВ работе получены выражения для скорости термофореза твердой двухслойной умеренно крупной длинной цилиндрической аэрозольной частицы, позволяющие оценивать ее величину с учѐтом в граничных условиях всех поверхностных газокинетических эффектов линейных по числу Кнудсена, постоянного коэффициента теплопроводности ядра и зависящего от радиальной координаты переменного коэффициента теплопроводности оболочки.Рассматриваемая частица расположена перпендикулярно к градиенту температуры газа.Проведенный анализ показал, что увеличение (уменьшение) коэффициента теплопроводности ядра и среднего

We obtain an analytical solution of a boundary value problem for a viscous incompressible nonisothermal fluid assuming an exponential–power law dependence of the fluid viscosity on temperature. A uniqueness theorem for the Navier–Stokes equation linearized with respect to the velocity is proved. We obtain expressions for the mass velocity components and pressure. The solution of the boundary value problem is sought in the form of an expansion in Legendre polynomials.

The stationary motion of a large spherical aerosol particle in the external field of a temperature gradient in zero gravity is theoretically described using the Stokes approximation and the assumption that the average temperature of the particle surface differs considerably from the temperature of the surrounding gaseous medium. The gas dynamics equations are solved taking into account the power-law temperature dependence of the molecular transport coefficients (viscosity, thermal conductivity) and the density of the gaseous medium. Numerical estimates show that the dependence of the thermophoretic force and velocity on the average temperature of the particle surface is nonlinear.

The steady-state diffuse vaporization (sublimation) of a stationary coarse nonspherical particle has been simulated mathematically in the situation when the ambient temperature changes considerably. The formulas found make it possible to estimate the rate of change of the temperature and the particle mass with regard to the particle surface shape, thermal diffusion, and temperature variations in the transfer coefficients. The analysis performed indicated that the rate of particle vaporization (sublimation) can depend strongly on the shape of the particle surface. Thermal diffusion can also pronouncedly affect the particle vaporization rate.

For the problem on a plane-parallel gas flow with velocity U∞ past a fixed uniformly heated spherical particle, we obtain a solution of the Navier–Stokes equations linearized with respect to velocity in the spherical coordinate system with regard to the power-law dependence of the molecular transport coefficients (viscosity and thermal conductivity) and the gas medium density on the temperature. The uniqueness of this solution is proved.