An iterative regularization method in estimating the base temperature for non-Fourier fins

An inverse non-Fourier fin problem is examined in the present study by an iterative regularization method, i.e., conjugate gradient method (CGM), in estimating the unknown base temperature of non-Fourier fin based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different temperature distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the base temperature. Moreover, the drawbacks of previous study for this identical inverse problem, such as (1) the inverse solutions become poor when the frequency of base temperature is increased, (2) the estimations depend strongly on the size of grids, (3) the estimations are sensitive to the measurement errors and (4) the uncertainty of using the concept of future time step, can all be avoided by applying this algorithm. Finally, it is concluded that accurate base temperatures can be estimated in the present study.