An inverse analysis for the estimation of boundary heat flux in a circular pipe employing the proper orthogonal decomposition

An inverse algorithm based on the proper orthogonal decomposition technique is developed in this paper. The performance of the present inverse algorithm is examined by an inverse forced convection problem of identifying the unknown space-dependent heat flux at the outer boundary of a circular pipe. The inverse problem is resolved in a functional optimisation way by the Fletcher-Reeves conjugate gradient method. The effects of the convection, the location of the thermocouples and the measurement error on the performance of the inverse algorithm are studied thoroughly. It was shown that the present POD-based inverse algorithm is very accurate as well as efficient. A large time saving is also found by using the present inverse algorithm.