Reconstruction of variable thermophysical properties of a rectangular region

Authors

  • Nesterov S.A. Southern Mathematical Institute, a branch of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russian Federation ORCID iD 0000-0003-3780-5104

UDC

563.24

EDN

NBFMDW

DOI:

10.31429/vestnik-21-4-45-54

Abstract

The article studies a two-dimensional coefficient inverse problem of heat conductivity based on reconstruction of variable thermophysical properties of a rectangular region. Zero temperature is specified on the lower side of the functionally gradient rectangle, the lateral sides are thermally insulated, and an unsteady heat flux acts on the upper side. The temperature specified on the upper boundary of the rectangular region for some moments of time serves as additional information. The solution of the direct problem in a weak formulation is implemented in the finite element package FreeFem++. The influence of the thermal conductivity coefficient and specific heat capacity on the temperature of the upper face is investigated. A projection-iteration scheme for solving the inverse problem is proposed. Thermophysical characteristics at each stage of the iteration process are presented as an expansion in a system of polynomials. The expansion coefficients are determined by solving a system of algebraic equations obtained by discretizing the Fredholm integral equation of the first kind. Tikhonov's method is used to regularize the ill-conditioned algebraic system of equations. The results of separate reconstruction of the coefficient of thermal conductivity and specific heat capacity of a rectangle for monotone functions are presented.

Keywords:

Fredholm integral equation of the first kind, identification, rectangular domain, coefficient of thermal conductivity, specific heat capacity, coefficient inverse problem, finite element package FreeFem , iterative-projection approach.

Funding information

The study did not have sponsorship.

Author info

  • Sergey A. Nesterov

    д-р физ.-мат. наук, ведущий научный сотрудник отдела дифференциальных уравнений Южного математического института - филиала ВНЦ РАН

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Issue

Vol. 21 (2024) No. 4

Pages

45-54

Section

Mechanics

Dates

Submitted

October 14, 2024

Accepted

November 27, 2024

Published

December 20, 2024

How to Cite

[1]
Nesterov, S.A., Reconstruction of variable thermophysical properties of a rectangular region. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2024, т. 21, № 4, pp. 45–54. DOI: 10.31429/vestnik-21-4-45-54

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Copyright (c) 2024 Нестеров С.А.

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