DETERMINATION OF NON-STATIONARY TEMPERATURE FIELD IN THE SYSTEM OF TWO SPHERICAL SHELL

Abstract

The main classification indicator, in terms of fire safety, is the degree of fire resistance of the house. Depending on this indicator normalize its surface, the area of development and distance to other buildings and structures. The de-gree of fire resistance of the house is determined by the limit of fire resistance of its building structures and the limit of the fire spread by these structures. Therefore, the value of the fire resistance limit of building constructions, which con-sists of a house, significantly affect its architectural solution and the parameters of construction in general. On this ba-sis, taking into account the approaches to ensuring normalized fire resistance limits of the design and the features of their behavior under high-temperature (fire) influence is very relevant.Most research on building constructions. The proposed work is devoted to the application of the direct method to the study of heat transfer processes in the system of two embedded spherical bodies – a ball in a sphere. It is assumed that there is an ideal thermal contact between the balls, and the law of temperature change on the outer surface is an arbitrary function of time, and evenly distributed over the surface of the ball. Consequently, isotherms inside this construction are concentric fields, that is, the problem is symmetric and is solved for the first time in such a statement. To solve such a problem, in parallel, the auxil-iary problem of determining the distribution of a non-stationary temperature field in a two-layer hollow spherical structure with a "extracted" sphere of sufficiently small radius is raised. In this case the symmetry condition of the original problem is replaced by the condition of the second kind on the inner surface of this construction. The implementation of the solution of the auxiliary problem is carried out by applying a reduction method using the concept of quasiderivatives. In the future, the Fourier scheme is used with the use of the modified eigenfunctions method. To find the solution of the original problem, the idea of the boundary transition is used by passing the radius of the withdrawn bullet to zero. It is established that in this approach all the eigenfunctions of the corresponding problem on the eigenvalues have no singularities at zero, which means that the solutions of the original problem are constrained throughout the design. The solution of this problem at zero temperature on the outer surface coincides with those known in the literature. To illustrate the proposed method, a model example of finding the temperature field distribution in a system of two spherical bodies with different thermophysical properties of materials is solved. The results of the calcu-lations are presented in the form of a table and a three-dimensional graph of temperature change, depending on the time and spatial coordinates. The generalization of the results obtained in the event of any finite number of nested balls is a purely technical problem, and not a fundamental one. Note that while changing the boundary condition of the first kind to any other boundary condition (for example, the third kind) does not affect the scheme of solving similar tasks. Since the general scheme of studying the distribution of temperature fields in multi-layered structures with an arbitrary number of layers in the presence of internal sources of heat is studied in detail, the setting and solving of such problems for the system of nested balls does not cause any difficulty.