DIRECT (CLASSICAL) METHOD OF CALCULATION OF THE TEMPERATURE FIELD IN A HOLLOW MULTILAYER CYLINDER

Abstract

A structural scheme of construction of a solution to a mixed problem for the heat-conduction equation in the case of a hollow multilayer cylinder under the conditions of ideal thermal contact between the layers is proposed and substantiated. The presence of connective heat exchange with the environment is assumed, i.e., boundary conditions of the third kind are observed. Coefficients of the heat-conduction equation are considered to be piecewise-continuous as far as the space coordinate is concerned. The scheme is based on the: reduction method, concept of quasi derivatives, modcern theory of systems of linear differential equations, Fourier method, and modified method of eigenfunctions. A numerical example of calculation of the temperature field in an actual hollow four-layer pipeline under external-fire conditions is given.