### Основы решения нелинейных нестационарных задач теплопроводности многослойных стенок

В. Г. Демченко, Б. Х. Драганов

#### Анотація

FUNDAMENTALS SOLVING NONLINEAR NONSTATIONARY PROBLEMS THE HEAT MULTILAYER WALL

V. G. Demchenko, B. H. Draganov

Taking into account the actual values of thermophysical characteristics of materials as a function of temperature leads to the need to solve non-linear first-order non-stationary problems of heat transfer through a single-layered and multilayered wall of external fences of buildings. In this case, it is necessary to take into account the influence of the dependence of the thermophysical characteristics of materials on their temperature on heat transfer through the outer enclosing structures of buildings.

The aim of the study is to develop a method for solving nonlinear nonstationary thermal conductivity problems of a multilayer wall.

Among integral, the most convenient is the method of finite integral transformations, since it makes it possible to move from images to originals much easier than in cases of other integral transformations. The method of finite integral transformations leads to a nonhomogeneous boundary value problem of heat conduction in the image region in the case of single-walled walls to an ordinary differential equation of the first order, and in the case of multilayer walls to the (n - 1) dimensional vector system (2n + 1) of Volterra integral equations of the second kind, the solution Which are known. This is the manifestation of the new side of the method of finite integral transformations.

The above method was used to solve a nonlinear nonstationary heat conduction problem for a multilayer wall.

Effective methods were proposed for reducing non-stationary heat transfer problems through multilayer walls, taking into account the dependence of thermal characteristics on temperature to vector integral equations, and then to a system of algebraic equations. Problems of non-stationary heat transfer through single-layered and multi-layered enclosures with ideal and non-ideal thermal contacts between layers were set and solved for the conditions of sharp temperature difference between the external and internal air.

The above theoretical studies allow us to explain the physical processes taking place in lightweight structures in summer and winter conditions. Thus, it is possible to indicate ways and means to improve the efficiency of the heat supply of a particular facility.

PDF

#### Посилання

Grinberg, G. A. (1948). Izbrannyye voprosy matematicheskoy teorii elektricheskikh i magnitnykh yavleniy [Selected questions of the mathematical theory of electrical and magnetic phenomena] – Moskow: Izd –vo AN SSSR, 254.

Lykov, A. V. (1967). Teoriya teploprovodnosti [Theory of heat conduction]. Moskow: Vysshaya shkola, 599.

Lykov, A. V. (1970). Nekotoryye analiticheskiye metody resheniya zadach nestatsionarnoy teploprovodnosti [Some analytical methods for solving non-stationary heat conduction problems]. Izd- vo AN SSSR, 5, 109-150.

Tabunshchikov, Y.A. (1975). Teploustoychivost’ i trebuyemoye soprotivleniye teploperedachi [Heat resistance and required heat transfer resistance]. Tr. NII stroit. Fiziki,10, 52-59.

Draganov, B. Kh., Chernykh, L. F., Fert, A. R.(1991). Metodika raschëta teplovogo rezhima naruzhnykh ograzhdayushchikh konstruktsiy sel’skokhozyaystvennykh zdaniy [Method for calculating the thermal conditions of external enclosing structures of agricultural buildings]. Kysv: Izd-vo USKHA, 126.

Chernykh, L. F. (1972). K voprosu nestatsionarnoy teploperedachi cherez naruzhnyye ograzhdayushchiye konstruktsii pri peremennykh teplofizicheskikh kharakteristikakh [To the problem of non-stationary heat transfer through external enclosing structures under variable thermophysical characteristics]. Kyiv: Budivel’nik,.18-191.

Farenyuk, R. G. (1969). Otsenka i povysheniye teplofizicheskiy kachestv i nadezhnosti po teplozashchite ograzhdayushchikh konstruktsiy zdaniy [Evaluation and improvement of thermal and physical properties and reliability of thermal protection of building envelopes.]. Moskow, 136.

Fokin, K. F. (1973). Stroitel’naya teplotekhnika ograzhdayushchikh chastey zdaniy [Building heat engineering of enclosing parts of buildings]. Moskow: Stroyizdat, 287.

Van Deyk , M. (1967). Metody vozmeshcheniy v mekhanike zhidkostey [Methods of compensation in the mechanics of liquids ]. Moskow: Mir, 311.

Koul, Dzh. (1972). Metod vozmushcheniy v prikladnoy matematike [The perturbation method in applied mathematics ]. Moskow: Mir, 274.

Krylov, A. N. (1954). Lektsii o priblizhënnykh vychisleniyakh [Lectures on approximate calculations]. Moskow: Gostekhizdat, 400.

Mitropol’skiy, Y. A., Moisenkov, B. I.(1968). Lektsii po primeneniyu asimptomaticheskikh metodov k resheniyu uravneniy v chastnykh proizvodnykh [Lectures on the application of asymptotic methods to the solution of partial differential equations ]. Kyiv: Naukova dumka, 414.

#### Метрики статей

Завантаження метрик ...