Journal of Theoretical
and Applied Mechanics

11, 4, pp. 417-442, Warsaw 1973

Stacjonarne oddziaływanie układu dwu nieskończenie małych dowolnie zorientowanych elementów, poruszającego się w ośrodku swobodno-molekularnym z dowolną prędkością

Stanisław Kosowski
In the paper is solved the problem of drag and heat exchange for a system of two infinitesimal, arbitrarily oriented surface elements in a free-molecular flow. Reflection of the gas from the surface is described by a Maxwell model with anisotropic diffusive part. Since the model contains, as particular cases, a number of models being in common use, such as the diffusion model, Maxwell's, Nocilla's and the anisotropic diffusion models, the solution creates the possibility of investigating of the interaction of bodies moving in a free-molecular medium from the point of view of model of gas reflection from the surface. The solution also enables us to investigate the interaction from the point of view of velocity of the system and orientation of its elements. As far finite dimension bodies are considered, the simplest case of two spheres placed in the medium can not be solved analytically to yield an accurate result, even in the case of the simplest, diffusion model of gas reflection; the problem of interaction in a general form is, however, not suitable for numerical analysis. The drag and heat exchange for infinitely small bodies may be solved analytically in an accurate manner: the solutions are expressed in terms of special functions (error function and the function of parabolic cylinder).