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Parametric study and optimal algorithm of a simultaneous estimation in two-dimensional inverse heat conduction problem

A simultaneous estimation of two boundary conditions in a two-dimensional linear heat conduction problem is proposed by numerical approach. The aim is to estimate the evolution of the distributions of the unknown surface heat fluxes from the transient temperature histories taken with several sensors inside a two-dimensional specimen. The inverse numerical algorithm is based on the iterative regularization method and on the conjugate gradient method. Unknown functions are parametrized in the form of a cubic B-spline. The utilization of an optimal choice of the matrix of the descent parameters is at the origin of this method showing an increase in the convergence rate. The effects of the parameters of the cubic B-spline approximation, the number and the position of the sensors and the magnitude of measurement errors on the inverse solutions are discussed.