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Method of complex determination of the dependence of the thermophysical characteristics of metal on temperature by solving the inverse problem of thermal conductivity

A.K. Sokolov, V.P. Zhukov, N.N. Smirnov, N.N. Yarunina

Vestnik IGEU, 2024 issue 6, pp. 23—30

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Abstract in English: 

Background. The temperature fields of materials used in thermal power engineering affect the intensity of heat transfer, the quality of safety assessment of equipment and technical and economic indicators of installations. The accuracy of calculating temperature fields in materials depends significantly on the reliability of the values of the thermophysical characteristics (TC) of materials: thermal diffusivity a, m2/s, thermal conductivity coefficient l, W/(m×K), and heat capacity c, J/(m3×K). Methods to determine thermophysical characteristics are constantly being improved to reduce the labor intensity of a thermophysical experiment, simplify the procedures of solving the inverse problem of heat conductivity for complex determination of several thermophysical characteristics. In this regard, the development and study of more effective methods remain relevant.

Materials and methods. The thermophysical characteristics of materials are determined by solving the inverse problem of thermal conductivity using analytical, numerical, or numerical-analytical methods of the temperature field obtained as a result of a physical experiment.

Results. The authors have proposed a numerical and analytical method. Based on the results of one experiment, it allows us to determine the dependence of the metal TC: l, c and a on the temperature. The calculation of thermophysical characteristics is performed considering the surface temperatures of an unlimited plate Т(R,ti), T(x=0,ti) with a thickness of 2R, symmetrically heated by constant heat fluxes q, W/m2. Thermophysical characteristics are determined by simple algebraic formulas derived from the heat balance equations for each time interval Dti+1 = ti+1 − ti. A numerical experiment is conducted to assess the complexity and error of the method. The temperatures Т(R,ti) and T(x=0,ti) of the plate R = 0,02 m have been calculated by the finite difference method at q = 60000 W/m2 for 30 time points 0 ≤ t ≤ 2250 s. The initial dependencies l(T) and a(T) are described by polygonal lines. The relative errors of l(Tm) have not exceeded 1 %, and the errors of a(Tm,int) and c(Tm,int) have exceeded 2 % only in the area of changing the sign of the first-order derivatives of the functions a(Tm,int) and c(Tm,int).

Conclusions. The proposed method allows us to calculate the dependence of TC on temperature using simple algebraic formulas based on the results of one experiment

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Key words in Russian: 
обратная задача теплопроводности, температуропроводность, коэффициент теплопроводности, теплоемкость, квазистационарный режим, численный эксперимент
Key words in English: 
inverse problem of thermal conductivity, thermal conductivity, coefficient of thermal conductivity, heat capacity, quasi-stationary mode, numerical experiment
The DOI index: 
10.17588/2072-2672.2024.6.023-030
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