Simple Numerical Method for Multidimensional Inverse Identification of Heat Flux Distribution

Abstract

In this paper, the inverse heat conduction problem is solved for the identification of the distribution of the heat flux applied to a flat plate based on the surface temperature measurement at the opposite boundary. The modified one-dimensional correction method, along with the finite volume method, is employed for solving the inverse problem. A series of two-dimensional and three-dimensional numerical experiments are conducted to verify the effectiveness of the method. The effects of the factors such as the temperature measurement error, the stopping criterion of the iteration, and the thermal conductivity of the flat plate on the identification results of the heat flux distributions are also studied. The numerical experiments conclude that the method is simple, stable, and accurate for this inverse heat conduction problem. The identification results are not sensitive to the temperature measurement error, whether uniform or random. Better identification results can be obtained for the test pieces with small thermal conductivity, because the temperature distribution at the inspection surface of this small conductivity plate has a larger temperature difference, which more easily reflects the distribution rule of the heat flux.