An extension of the reciprocity functional approach to the estimate of two-dimensional spatially dependent thermal contact conductances using regularization via TSVD: numerical and experimental results

A method based on the reciprocity functional is presented to estimate a two-dimensional spatially dependent thermal contact conductance between two materials without the use of intrusive measurements. In order to perform the estimation, two auxiliary problems are needed. The first one determines the temperature jump and the second one the heat flux, both at the inaccessible interface between the two materials. Besides the solution of the auxiliary problems, the application of this method requires the solution of ill-conditioned linear systems. This paper is an extension of our previously presented technique to two-dimensional interfaces. This paper also presents some new treatment for the numerical solution of the auxiliary problems. The TSVD method is used to solve the linear systems and a methodology to find the best truncation parameter is proposed. In addition to a test case with computationally simulated temperature measurements, an experimental case is also evaluated with good results.