Approximation of an Unsteady Temperature Field in Cylindrical and Spherical Bodies.

This paper presents a method for choosing the approximate temperature distribution in bodies of cylindrical and spherical geometry. The method is appropriate for solving any problems governed by a diffusion-type equation with the aid of methods using the concept of a thermal boundary layer. Particular cases considered in this paper include the transient temperature distributions in a hollow cyliner in the case of heat being transferred at a constant rate to the inner wall surface, while the outer wall surface is insulated against heat losses. It is found that, for problems involving polar or spherical symmetry, Lardner and Pohle's method is inappropriate, because the solution does not tend to the proper form of the steady-state solution in the limit for large time (in the second phase of heat penetration). It is shown that Vujanovic's variational method cannot be improved to produce better results with a parabolic temperature distribution in a cylindrical body.