Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

Abstract

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterized by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the time-dependent thermal conductivity components of an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification.

Keywords:

• Orthotropic heat conductor
• heat equation
• inverse problem
• thermal conductivity
• regularization

AMS Subject Classifications:

• 65M30
• 65M32
• 80A23

Acknowledgements

M.S. Hussein would like to thank the Ministry of Higher Education and Scientific Research for their financial support in this research. He would also like to thank the hospitality of Leeds University.

Notes

No potential conflict of interest was reported by the authors.