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

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 compone...

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Bibliographic Details
Published in:Applicable analysis 2017-11, Vol.96 (15), p.2604-2618
Main Authors: Hussein, M. S., Kinash, N., Lesnic, D., Ivanchov, M.
Format: Article
Language:English
Subjects:
65M30
Conductors
Destructive testing
Fixed points (mathematics)
Heat conductivity
heat equation
Heat flux
Heat transfer
inverse problem
Mathematical analysis
Nondestructive testing
Orthotropic heat conductor
Parameter identification
regularization
Schauder fixpoint theorem
Thermal conductivity
Thermodynamic properties
Time dependence
Volterra integral equations
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2016.1232401