Thermal force on a spherical particle with an outer shell in a slightly rarefied gas

Abstract

A spherical solid particle with an outer shell in an infinite expanse of a slightly rarefied gas at rest with a uniform temperature gradient is considered. The flow induced around the particle and the force acting on it (thermal force) are investigated on the basis of the asymptotic theory for a slightly rarefied gas. The velocity of steady motion of the particle which is left free in the gas is also obtained. All the results (velocity and temperature of the gas, thermal force, etc.) except the temperature field inside the particle coincide with the corresponding results for a homogeneous sphere with an appropriate thermal conductivity (virtual thermal conductivity), which is determined by the thermal conductivities of the shell and the core and the thickness of the shell. The concept of the virtual thermal conductivity is generalized to a nonuniform sphere whose thermal conductivity is a function of the radial position.