Galerkin approach for estimating boundary data in Poisson equation on annular domain with application to heat transfer coefficient estimation in coiled tubes

We investigate the problem of reconstructing internal Neumann data for a Poisson equation on annular domain from discrete measured data at the external boundary. By applying a Galerkin’s collocation method to the direct problem, the reconstruction problem is formulated as a linear system and boundary data are determined through a singular value decomposition (SVD)-based scheme. The SVD of the coefficient matrix is explicitly determined, and thus regularization methods such as truncated singular value decomposition (TSVD) and Tikhonov regularization (TR) are readily implemented. Numerical examples using both synthetic and experimental data are presented to illustrate the efficiency of the method, including an application to the experimental estimation of heat transfer coefficients in coiled tubes; the regularization parameter for TSVD and TR is determined by the discrepancy principle.