Solving of Two-Dimensional Unsteady-State Heat-Transfer Inverse Problem Using Finite Difference Method and Model Prediction Control Method

Abstract

The Inverse Heat Conduction Problem (IHCP) refers to the inversion of the internal characteristics or thermal boundary conditions of a heat transfer system by using other known conditions of the system and according to some information that the system can observe. It has been extensively applied in the fields of engineering related to heat-transfer measurement, such as the aerospace, atomic energy technology, mechanical engineering, and metallurgy. The paper adopts Finite Difference Method (FDM) and Model Predictive Control Method (MPCM) to study the inverse problem in the third-type boundary heat-transfer coefficient involved in the two-dimensional unsteady heat conduction system. The residual principle is introduced to estimate the optimized regularization parameter in the model prediction control method, thereby obtaining a more precise inversion result. Finite difference method (FDM) is adopted for direct problem to calculate the temperature value in various time quanta of needed discrete point as well as the temperature field verification by time quantum, while inverse problem discusses the impact of different measurement errors and measurement point positions on the inverse result. As demonstrated by empirical analysis, the proposed method remains highly precise despite the presence of measurement errors or the close distance of measurement point position from the boundary angular point angle.