Heat transfer between a small sphere and a dilute gas; the influence of the kinetic boundary layer

The transfer of heat between an object not too large compared to a mean free path and a gas surrounding it is influenced considerably by the structure of the kinetic boundary layer around the object. We calculate this effect for a spherical object in a dilute gas by applying a recently developed variant of the moment method to solve the stationary linearized Boltzmann equation for the gas surrounding the sphere, From the solution we determine the temperature jump coefficient, which occurs in the boundary condition to be used for the heat conduction equation at the surface of the sphere. We study the dependence of this quantity on the radius and on the thermal accomodation coefficient. We find that typical boundary layer effects become less important as the accomodation coefficient decreases, and propose a simple approximate formula, which describes the results for large spheres to within about half a percent.