Numerical method for hyperbolic inverse heat conduction problems

The Laplace transform technique and control volume method in conjunction with the hyperbolic shape function and least-squares scheme are applied to estimate the unknown surface conditions of one-dimensional hyperbolic inverse heat conduction problems. In the present study, the expression of the unknown surface conditions is not given a priori. To obtain the more accurate estimates, the whole time domain is divided into several analysis sub-time intervals. Afterward, the unknown surface conditions in each analysis interval are estimated. To evidence the accuracy of the present method, a comparison between the present estimations and exact results is made. Results show that good estimations on the unknown surface conditions can be obtained from the transient temperature recordings only at one selected location even for the cases with measurement errors.