ISSN 0862-5468 (Print), ISSN 1804-5847 (online) 

Ceramics-Silikáty 31, (4) 323 - 332 (1987)


RIEŠENIE STACIONÁRNEHO PRESTUPU TEPLA CEZ ROVINNÚ A VALCOVÚ STENU ITERAČNOU METÓDOU

SOLUTION OF STATIONARY HEAT TRANSFER THROUGH PLANAR AND CYLINDRICAL WALLS WITH THE USE OF THE ITERATION METHOD


 
Zábavník Viktor 1
 
1 Ústav výpočtovej techniky pri Vysokej škole technickej, ul. Boženy Němcovej, 040 00 Košice
1 Institute of Computer Technology at the Technical University, ul. Boženy Němcovej, 040 00 Košice

Riešenie stacionárneho prestupu tepla cez zloženú rovinnú, resp. valcovú stenu pre prípad, lineárnej teplotnej závislosti tepelnej vodivosti vedie pri výpočte teplôt na stykoch vrstiev k riešeniu sústavy nelineárnych rovnic. Použitím iteračného prístupu je možné značne zjednodušiť riešenie uvedeného problému. Pri výpočte teplot na stykoch vrstiev v smere od jedného povrchu steny k druhému riešime kvadratické rovnice, pričom hodnoty neznámych veličín je potrebné na začiatku iterácie predpokladať. Iteračný proces sa opakuje do dosiahnutia súladu medzi predpokladmi a hraničnými podmienkami. Algoritmus stanovenia teplotného profilu zostáva rovnaký pre rozdielne hraničné podmienky. Doba realizácie riešenia neprekročí 10 s na počítači SM 3.

The stationary heat transfer through a sandwich wall is a current problem being solved in practice with the use of simplifying assumptions (e.g. λ = const.). For a linear dependence of thermal conductivity, the problem of determining the temperature profile for some combinations of boundary conditions leads to the solution of a system of non-linear equations. The solution of the problem can be considerably simplified by using the iteration approach. In this way, quadratic equations have to be solved to determine the temperature profile. In the course of the iteration process, the temperature profile is determined for the assumed values of unknown quantities, and is concluded only on attainment of agreement between those and the initial boundary conditions. Thus a single algorithm is obtained for various combinations of the boundary conditions. The program suggested has a modular structure which allows it to be simply and conveniently adjusted to new requirements, which are mostly new boundary conditions; moreover, the program can be utilized within the framework of a wider simulation system. The program has been written in the FORTRAN IV language and implemented on the SM 3 computer.


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