Stationary heat exchange in a system of two spheres in uniform rectilinear motion through a free-molecule medium

The present paper is concerned with a particular problem of stationary interaction of a system of two spheres moving in a free-molecule medium. This is a problem of heat exchange at equal temperatures of the spheres. It is demonstrated that the solution of the continuity equations (impermeability of the wall), which constitute a set of Fredholm integral equations of the second kind can be avoided in this case, in which the heat exchange can be expressed by energy fluxes and numbers of incident particles coming only from the ambient medium and not from the other sphere, which is the general case. The expression for heat exchange is obtained in an effective manner in the case of hypersonic motion. As an auxiliary problem the problem of screening of a sphere by the other sphere is solved in detail. The quintuple quadratures of interaction representing heat exchange are expressed in terms of elementary functions.