A filter based solution for inverse heat conduction problems in multi-layer mediums

This paper presents a solution for the inverse heat conduction problem (IHCP) in a multi-layer medium based on solutions from individual layers separately. The approach allows for inclusion of known contact resistances between the layers. The temperature histories are assumed known at two points on the inner layer and the heat transfer rate at the far end of the outer layer is the desired unknown parameter. A step-by-step solution is proposed for solving this problem based on minimization of the sum-of-squared errors between the computed and known temperature values and using Tikhonov regularization for stabilizing the solution. A Tikhonov digital filter solution is developed which allows near real-time heat transfer estimation in multi-layer application. The proposed method is tested via numerical experiments using exact solutions and ANSYS to generate synthetic data.