Boundary heat flow calculation in heat conduction problem with piecewise constant coefficient

Khodalitskii D.N., Mokin A.Yu., Savenkova N.P.

Lomonosov Moscow State University

The article considers a nonstationary heat conduction equation with a variable coefficient of thermal conductivity and boundary conditions of a mixed type. By the method of separation of variables, the solution of the problem in the form of a functional series is obtained.

A study was carried out on the selection of the number of harmonics of the functional series necessary to determine the magnitude of the flow at the point x = 0 with a given accuracy.

The results of calculations are demonstrated by illustrative examples that have a specific physical interpretation.

This task simulates the process of heat exchange with the environment through composite thermal insulation of thickness L. In this case, the point x = 0 corresponds to the inner surface of the thermal insulation, and the point x = L corresponds to the outer surface. The quality of thermal insulation is determined by the value of the heat flow at the point x = 0. Therefore, the results of the research are of great practical importance in modeling the heat exchange process in an industrial electrolysis bath, the walls of which have multilayer thermal insulation.


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