Алгоритм решения обобщенной задачи нестационарной теплопроводности в телах простой геометрической формы

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В.Н. Елисеев, В.А. Товстоног, Т.В. Боровкова
126 ISSN 0236-3941. Вестник МГТУ им. Н.Э. Баумана. Сер. Машиностроение. 2017. № 1
Просьба ссылаться на эту статью следующим образом:
Елисеев В.Н., Товстоног В.А., Боровкова Т.В. Алгоритм решения обобщенной задачи
нестационарной теплопроводности в телах простой геометрической формы // Вестник
МГТУ им. Н.Э. Баумана. Сер. Машиностроение. 2017. № 1. С. 112–128.
DOI: 10.18698/0236-3941-2017-1-112-128
SOLUTON ALGORTHIM OF GENERALIZED NON-STATIONARY
HEAT CONDUCTION PROBLEM IN THE BODIES OF SIMPLE
GEOMETRIC SHAPES
V.N. Eliseev
V.A. Tovstonog
T.V. Borovkova
Bauman Moscow State Technical University, Moscow, Russian Federation
Abstract Keywords
The study proposes a single algorithm for solving the one-
dimensional non-stationary heat conduction problems in
the bodies of simple geometric shapes with internal energy
sources of different nature. The bodies under consideration
may have the shape of a plate, a rod (rib), a solid or hollow
cylinder and a sphere. The basis of the problem solution is a
generalized formulation of the heterogeneous differential
equation of non-stationary heat conduction in partial
derivatives for the bodies of the specified form and the
method of integral transformations in finite bounds. The
procedure for solving a specific boundary-value problem
involves the presence of a mathematical model, but does
not require integration of the differential equation of heat
conduction. We give an example of determining the tem-
perature field in a plate with unevenly distributed heat
sources and different conditions of heat transfer at the
boundary surfaces. It is relevant to use the solutions of this
type, particularly, for testing the complex programs calcu-
lating the temperature field of thermal-loaded design ele-
ments, as well as for the analysis of the thermal regime in
the early stages of design and substantiation of the eligible
assumptions
Temperature field, generalized
heat conduction problem, bodies
of a simple shape, solution algorithm
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