Inverse problem of simultaneously estimating the timewise-varying strengths of two plane heat sources

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used for simultaneously estimating the timewise-varying strengths of two plane surface heat sources located inside a plate with insulated boundaries. No prior information is used for the functional forms of timewise variation of the source strength. Transient temperature recordings taken at the boundaries of the region, modified by addition of random errors, served as the simulated experimental data for the inverse analysis. In order to examine the accuracy of the estimation under most strict conditions, timewise variation of the source strength is chosen in the form of rectangular, triangular, and sinusoidal functions. Several different combinations of pulse shapes and location of the heat sources were studied. For situations in which the two heat sources were located close to each other, difficulty was experienced in the estimation of source strengths.