Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach

Abstract

In this paper, a numerical method to solving the one-dimensional inverse heat transfer problem in Cartesian and Cylindrical coordinates, which is combination of the Haar wavelet collocation and Tikhonov regularization approach, has been used. The audit consisted in comparing the heat transfer in reality with numerical result as a noisy data, in order to identify errors of 1%–5% has been presented. In this study, the Haar functions, in addition to estimating the unknown functions, are also used to reduce output noises. Based on the obtained results, two main advantages of the repeated method have been proven, first, the precision of this method in estimating the unknown boundary condition and the second, processing speed due to the lack of need for wavelet functions to be collocated at low intervals. This suggested that this method, also has a high speed. According to the obtained results, it can be asserted that the present method by applying a small error in the input data, is preserved its stability.