Estimation of multiple heat sources in two-dimensional heat conduction problems

There have been some recent restrictions in the estimation of location and strength in inverse problems. One of the restrictions is that the problem is limited to the fixed number of heat sources. In other words, the moving sources cannot coincide in the moving path. Therefore, it is necessary to develop a method to estimate the location and the strength of various numbers of moving heat sources. A numerical algorithm combined with simplex method is proposed to determine the problem sequentially. A special feature of this method is that no prior knowledge of the number, the location, and the strength of the heat sources is necessary and that no sensitivity analysis is needed in the algorithm. Two examples are used to demonstrate the characteristics of the proposed method. The examples enable the investigation of the multiple moving sources with some coincided paths that lead to the number of sources varied with respect to the temporal coordinate. The numerical results show that the proposed method is an accurate and efficient method to determine the location and the strength of multiple moving sources in the inverse heat conduction problem.