scholarly journals Numerical identification of the thermal conductivity tensor and the heat capacity per unit volume of an anisotropic material

2019 ◽  
Vol 20 (6) ◽  
pp. 603
Author(s):  
Kossi Atchonouglo ◽  
Jean-Christophe Dupré ◽  
Arnaud Germaneau ◽  
Claude Vallée
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Method ◽  
Heat Capacity ◽  
Unit Volume ◽  
Time Integration ◽  
Volume Measurement ◽  
Conductivity Tensor ◽  
Inverse Approach ◽  
Thermal Conductivity Tensor ◽  
Principal Axes

In this paper, an inverse approach based on gradient conjugate method for thermal conductivity tensor and heat capacity per unit volume measurement is summarized. A suitable analysis is done for the mesh in finite element method and for the time steps for the time integration. For a composite material, it is shown the importance to identify the thermal conductivity tensor components in the principal axes.

scholarly journals The Solution of the Inverse Problem of Identifying the Thermal Conductivity Tensor in Anisotropic Materials

2021 ◽  
Vol 24 (3) ◽  
pp. 6-13
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Thermal Conductivity ◽  
Root Mean Square ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Orientation Angle ◽  
Conductivity Tensor ◽  
Mean Square ◽  
Two Dimensional ◽  
Thermal Conductivity Tensor ◽  
Principal Axes

On the basis of A. N. Tikhonov's regularization theory, a technique has been developed for solving inverse heat conduction problems of identifying the thermal conductivity tensor in a two-dimensional domain. Such problems are replaced by problems of identifying the principal heat conductivity coefficients and the orientation angle of the principal axes, with the principal coefficients being approximated by Schoenberg’s cubic splines. As a result, the problem is reduced to determining the unknown coefficients in these approximations and the orientation angle of the principal axes. With known boundary and initial conditions, the temperature in the domain will depend only on these coefficients and the orientation angle. If one expresses it by the Taylor formula for two terms of series and substitutes it into the Tikhonov functional, then the determination of the increments of the coefficients and the increment of the orientation angle can be reduced to solving a system of linear equations with respect to these increments. By choosing a certain regularization parameter as well as some functions for the principal thermal conductivity coefficients and the orientation angle as an initial approximation, one can implement an iterative process for determining these coefficients. After obtaining the vectors of the coefficients and the angle of orientation as a result of the converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to choose the regularization parameter in such a way that this discrepancy is within the root-mean-square discrepancy of the measurement error. When checking the efficiency of using the proposed method, a number of two-dimensional test problems for bodies with known thermal conductivity tensors were solved. The influence of random measurement errors on the error in the identification of the thermal conductivity tensor was analyzed.

Thermal conductivity tensor of NbO2

2019 ◽  
Vol 137 ◽  
pp. 263-267 ◽  
Author(s):  
Hai Jun Cho ◽  
Gowoon Kim ◽  
Takaki Onozato ◽  
Hyoungjeen Jeen ◽  
Hiromichi Ohta
Keyword(s):  
Thermal Conductivity ◽  
Conductivity Tensor ◽  
Thermal Conductivity Tensor

Determination of the thermal conductivity tensor of the n = 7 Aurivillius phase Sr4Bi4Ti7O24

2012 ◽  
Vol 101 (2) ◽  
pp. 021904 ◽  
Author(s):  
M. A. Zurbuchen ◽  
D. G. Cahill ◽  
J. Schubert ◽  
Y. Jia ◽  
D. G. Schlom
Keyword(s):  
Thermal Conductivity ◽  
Conductivity Tensor ◽  
Aurivillius Phase ◽  
Thermal Conductivity Tensor
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