Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. Thefactors ofmeasuring error and the number ofmeasuring points zero errorwhich impact the measurement result are discussed and compared with L-MMmethod in inverse problems. Instance calculation and analysis prove that themethod applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points' number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.