Inverse determination of convective heat transfer between an impinging jet and a continuously moving flat surface

In this study an inverse method is developed to determine the heat flux distribution on a moving plane wall. The method uses a thin layer of material (the measurement medium) glued on the conveyor belt. The heat flux distribution on the moving wall is then determined by an inverse method based on the temperature measurement by infrared thermography on the upper surface of the measurement medium. A finite element based inverse algorithm of a steady state heat conduction advection in the Eulerian frame is performed. The algorithm entails the use of the Tikhonov regularization method, along with the L-curve method to select an optimal regularization parameter. Both the direct solution of moving boundary problem and the inverse design formulation are presented. The accuracy of the inverse method is examined by simulating the exact and noisy data with four different values of the surface-to-jet velocity ratio, and two different materials (PVC and Aluminum) for the measurement medium. The results show a greater sensitivity to the convective heat flux allowing a better estimation of heat flux distribution for the PVC layer. An alternative underdetermined inverse scheme is also studied. This configuration allows a different extend between the retrieval heat flux surface and the measurement temperature surface.