Estimation of heat source term in three-dimensional heat conduction problem from temperature measurements

Estimation of heat source term in three-dimensional heat conduction problem from temperature measurements is a typical Inverse Heat Conduction Problem (IHCP). In this paper, based on the numerical simulation of three-dimensional steady heat conduction problem with the Finite Volume Method (FVM), this three-dimensional IHCP is converted to an optimization problem, and the inversion method for estimation of heat source term is developed from sensitivity analysis. After applying this method to a typical test case, it can be seen that the estimation method is feasible and is not sensitive to the measurement noise. Moreover, the role of the stop criterion in the estimation process of cases with measurement noise is investigated. By analyzing the change of difference between the estimated heat sources and the exact values along with the decreasing of the objective function, it is shown that the decreasing of the objective function does not certainly mean the closer agreement between the estimated heat sources and exact values due to the ill-posedness of the IHCP. This ill-posedness can be overcome by choosing a proper specification of stop criterion to simulate the regularization effect in IHCP.