Radiation-conduction heat transfer in a thin semitransparent cylinder in the light-guide approximation

Abstract

The calculation of the temperature and radiation intensity in a region at the boundary of which multiple reflection and refraction of light is possible is, in general, a complex and little-investiga ted probh~m in the theory of complex heat transfer. It is therefore natural that we should wish to consider models which, without losing sight of the main features of the phenomena and remaining of practical value, enable one to reduce the mathematical difficulties to reasonable limits. The traditional problem of radiant heat transfer is a problem of a plane layer in which the temperature and radiation intensity vary only over its thickness [1, 2]. Another type of problem arises when investigating heat transfer in thin regions when the mean temperature variation occurs along the region, while transverse to the region the temperature can be regarded as practically constant. Such a "one-dimensional " approach has been known for a long time in the theory of heat conduction. However, in the theory of radiation-conduc tion heat transfer it has only recently been developed, although the problem in this formulation is not only of theoretical but also of considerable practical interest, for example, when extracting semitransparent crystals from a melt using the Czochralski or Stepanov method. In this paper we consider heat transfer in a thin circular cylinder surrounded by a cylindrical screen with an axisymmetrical temperature distribution. The gap between the screen and the cylinder is evacuated or filled with a gas having a low absorption. It is assumed that the following relations are satisfied: