RESEARCH OF THE TEMPERATURE FIELD IN THE SYSTEM OF MULTILAYER CYLINDRICAL SOLID BODIES UNDER FIRE CONDITIONS

Abstract

Introduction. The current urgent task is to find the temperature field distribution in cylindrical structures such as "solid cylinder inside a multilayer cylindrical shell". A characteristic feature of such structures is different mechanical and thermophysical characteristics of the layers combination, which makes them more perfect. However, this approach causes significant difficulties in developing analytical methods for their study. Therefore, new research methods development for multilayer, in particular, cylindrical structures is an urgent task today.
Purpose. Direct method is used to study the heat transfer processes in the system "one-piece cylinder inside a multilayer cylindrical shell".
Methods. To solve the initial parallel, the auxiliary problem of determining the distribution of a nonstationary temperature field in a multilayer hollow cylindrical structure with a "removed" cylinder of a sufficiently small radius is set. The solution of the auxiliary problem is realized by applying the method of reduction using the concept of quasi-derivatives. The Fourier scheme
is used by using a modified method of eigenfunctions.
Results. To find the solution to the problem, we used the idea of a boundary transition by directing the radius of the removed
cylinder to zero. It is established that in this approach, all eigenfunctions of the corresponding problem have no singularities at
zero, which means that the solutions of the original problem are limited in the whole structure. To illustrate the proposed method,
a model example of finding the temperature field distribution in a four-layer column of circular cross-section (tubular concrete
column) under the influence of the standard temperature of the fire. The results of the calculations are presented in the form of a
three-dimensional graph of temperature changes depending on time and spatial coordinates.
Conclusions. A direct method was used to solve the initial problem, using the idea of a boundary transition for the first time.
In the general formulation (the function of changing the temperature of the environment is considered arbitrary, no restrictions
are imposed on the thickness of the shell and the number of layers) such a problem is solved for the first time.
The structure of the obtained explicit exact formulas allows creating an algorithm for calculating the temperature field in
the form of automated programs, where it is enough to enter the initial data. Note that such algorithms include: a) calculating the
roots of the characteristic equation; b) multiplication of a finite number of known matrices; c) calculation of definite integrals; d)
summation of the required number of members of the series to obtain a given accuracy of the calculation.