# Identification of the Thermal Conductivity Coefficient Using a Given Surface Heat Flux

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### Abstract

The inverse problem of determining a temperature-dependent thermal conductivity coefficient is studied. The study is based on the Dirichlet boundary value problem for the two-dimensional nonstationary heat equation. The cost functional is defined as the rms deviation of the surface heat flux from experimental data. For the numerical solution of the problem, an algorithm based on the modern fast automatic differentiation technique is proposed. Examples of solving the posed problem are given.

## Keywords:

heat conduction inverse coefficient problems gradient heat equation adjoint equations numerical algorithm## Notes

### ACKNOWLEDGMENTS

This work was supported in part by the Russian Foundation for Basic Research, no. 17-07-00493a.

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