Estimating the internal heat transfer coefficient in ducts is becoming increasingly important in many engineering applications. Unlike traditional estimation methods which seek to recover the unknown coefficient by using optimization tools such as iterative methods or linear system solvers, new solution methods based on forward/inverse analytical solutions have gained noticeable interest. Two recently proposed non traditional methods are an explicit Fourier analysis-based (EFA) reconstruction method of Bazán and Bedin and a filtered reciprocity functional (FRF) approach of Mocerino et al. Both methods provide approximate solutions that are expressed as a sum of weighted harmonics where the number of terms used in the reconstruction depends on the noise level in the data and is selected using the Morozov's discrepancy principle (DP). In the present work, these methods are analyzed to identify similarities and differences as well as to introduce improvements. In particular, limitations of the FRF method in determining the truncation parameter are discussed and circumvented. This gives rise to new methods for heat flux estimation that are easy to implement and extremely inexpensive when compared to existing techniques. To illustrate the effectiveness of the new methods we present numerical results on several test problems including an analytical model obtained by synthesizing experimental data reported by Bozzoli et al. and several benchmark problems reported by Mocerino et al.
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