Application of an inverse solution to the thermal conductivity identification using the finite element method

The application of an inverse method for the determination of the thermal conductivity is presented. The method enables a thermal conductivity calculation of a well-conducting solid from measured temperature profiles inside the heated body. The finite element method (FEM) has been used to solve the heat conduction equation. The optimization problem has been solved by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) variable metric method. The solution has been verified by comparison of the numerical results to those obtained from the analytical solution. A good correlation between the closed form solution and numerical results has been obtained. The experimental verification of the solution has been also carried out. Results of experimental and numerical calculations are found to be in excellent agreement. The method can be used for the determination of the thermal conductivity over a wide temperature range on the basis of a single experiment.