Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems

A hybrid numerical algorithm of the Laplace transform technique and finite-difference method with a sequential-in-time concept and the least-squares scheme is proposed to predict the unknown surface temperature of two-sided boundary conditions for two-dimensional inverse heat conduction problems. In the present study, the functional form of the estimated surface temperatures is unknown a priori. The whole time domain is divided into several analysis sub-time intervals and then the unknown surface temperatures in each analysis interval are estimated. To enhance the accuracy and efficiency of the present method, a good comparison between the present estimations and previous results is demonstrated. The results show that good estimations on the surface temperature can be obtained from the transient temperature recordings only at a few selected locations even for the case with measurement errors. It is worth mentioning that the unknown surface temperature can be accurately estimated even though the thermocouples are located far from the estimated surface. Owing to the application of the Laplace transform technique, the unknown surface temperature distribution can be estimated from a specific time.