Estimation of applied heat flux at the surface of ablating materials by using sequential function specification method

This paper presents an inverse analysis in one-dimensional ablation problem with the presence of a moving boundary to estimate the unknown applied heat flux at the surface of ablating materials. The estimated heat flux was used to obtain the location of moving front surface. The Sequential function specification method (SFSM) was implemented to minimize the least square objective function. Simulated temperature measurements at specific sensor positions inside the ablating materials were used in the inverse analysis. Due to the ill-posedness of the problem the number of future time steps was used as the regularizing parameter. We show that only a small number of future time steps is required to deal with the great nonlinearity of an inverse problem. The accuracy of applied inverse analysis was examined by functions containing sharp corners and discontinuities. Despite high nonlinearity, good estimations were obtained.