Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem

Abstract

In this article, the determination of the time-dependent heat transfer coefficient, involving nonlinear boundary conditions of the third kind in the one-dimensional transient heat conduction from a non-standard boundary measurement is investigated. For this inverse, nonlinear, ill-posed problem, the existence and uniqueness of the solution are proved. Numerical results are obtained, using the boundary element method, and discussed.

Keywords:

• boundary element method
• heat conduction
• heat transfer coefficient
• inverse problem

Acknowledgements

Slodička was supported by the BOF/GOA-project No. 01G00607 of Ghent University and the grant number 3G008206 of the Fund for Scientific Research–Flanders.