Direct method of research of the temperature field in the system of multilayer spherical shell

Abstract

The article is devoted to the application of the direct method to the research of heat transfer processes in the system – bullet inside multilayered spherical shell. To solve the initial problem in parallel, we put an auxiliary problem on the determination of the distribution of a unsteady temperature field in a multilayer spherical solid with a «deleted» bullet of sufficiently small radius. Implementation of the solution of the auxiliary problem is carried out by applying the reduction method using the concept of quasi derivatives. In the future, is used the Fourier scheme with the use of the modified eigenfunctions method. To find the solution of the original problem used the idea of the marginal transition by direction of the radius of the deleted bullet to zero. It is established that in this approach all the eigenfunctions of the corresponding problem with the eigenvalues have no singularities at zero, which means that the solutions of the original problem are limited in the whole construction.