Identification of nonlinear heat transfer laws from boundary observations

Abstract

We consider the problem of identifying a nonlinear heat transfer law at the boundary, or of the temperature-dependent heat transfer coefficient in a parabolic equation from boundary observations. As a practical example, this model applies to the heat transfer coefficient that describes the intensity of heat exchange between a hot wire and the cooling water in which it is placed. We reformulate the inverse problem as a variational one which aims to minimize a misfit functional and prove that it has a solution. We provide a gradient formula for the misfit functional and then use some iterative methods for solving the variational problem. Thorough investigations are made with respect to several initial guesses and amounts of noise in the input data. Numerical results show that the methods are robust, stable and accurate.

Keywords:

• inverse problem
• nonlinear boundary condition
• heat transfer law

AMS Subject Classifications:

• 35R25
• 35R30
• 65M30
• 65M32

Acknowledgements

 

Notes

This research was partially supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme and by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.02-2014.54].