Inverse analysis of heat transfer across a multilayer composite wall with Cauchy boundary conditions

Abstract

The paper proposes a procedure to solve Cauchy inverse problems of dynamic heat transfer across a multilayer composite wall. The corresponding forward numerical model uses a meshfree method based on radial basis functions (RBFs) approximation in both time and space in a unified fashion. The Tikhonov regularization technique is used to mitigate the ill-posedness of the inverse problem to ensure a stable and reliable inverse solution. Because the time is also considered as a dimension in our RBF approximation, a parameter is introduced and adjusted to deal with the relationship between the time and the space discretization. In addition, because our unified space–time approximation scheme does not use the usual layer-by-layer recursion procedure, possible error accumulation is naturally avoided. In order to obtain better accuracy, a procedure is adapted to minimize the error on the given boundary by selecting a shape parameter c for the RBF in each layer. Intensive numerical experiments are conducted and the results are presented to demonstrate accuracy, effectiveness and stability with respect to noise-contaminated Cauchy data.