ABSTRACT
Two regularization methods are compared in this article. These methods are used to calculate a heat transfer coefficient distribution on a cylindrical pipe located in a transverse flow, starting from internal temperature measurements. The first inversion method corresponds to a Tikhonov regularization (applied to surface heat flux density). The direct problem is solved by separating the variables in the usual space domain (two-dimensional steady-state problem). The second method uses an inversion in a transformed domain, the space Fourier domain (experimental transforms of the temperature distribution, which relies on the thermal quadrupole method for solving the direct problem). This second method requires the setting of only one parameter: the desired number of harmonics. The agreement between these two inversion techniques is very good. It is also shown that the second method (regularization by spectrum truncation) constitutes a singular value decomposition of the operator of the direct problem, with analytical singular values.
