Aproksymacja nieustalonego pola temperatury w ciałach walcowych i kulistych

The paper presents a method for the choice of the approximate temperature distribution in the bodies of cylindrical and spherical geometry. The method is appropriate for solving any problem governed by diffusion-type equation with the aid of the methods using the concept of thermal boundary layer. Particular cases considered in this paper include the transient temperature distributions in a hollow cylinder 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's and Pohle's methods are 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 [7] cannot be improved to produce better results with parabolic temperature distribution in a cylindrical body.