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

Shoubin Wang,Rui Ni

doi:10.1155/2019/7432138

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.

Highlights

The Inverse Heat Conduction Problem is able to retrieve the unknown parameters such as boundary conditions, material thermophysical parameters [1,2,3], internal heat sources, and boundary geometry by measuring the temperature information at the boundary or at some point in the heattransfer system [4, 5]
The Inverse Heat Conduction Problem usually involves the multiple deduction of the forward problem, and its inversion accuracy is directly affected by the calculation accuracy of the forward problem
The explicit Finite Difference Method (FDM) is used for direct problem, when the measurement point in boundary is closer to the boundary angular point, which, imposes a little impact on the inversion result

Summary

Introduction

The Inverse Heat Conduction Problem is able to retrieve the unknown parameters such as boundary conditions, material thermophysical parameters [1,2,3], internal heat sources, and boundary geometry by measuring the temperature information at the boundary or at some point in the heattransfer system [4, 5]. Zhao Luyao combined the particle swarm optimization (PSO) and conjugate gradient method and applied the combined method to the inversion of the heat-transfer coefficient of one-dimensional unsteady-state system. Zhou et al solved the heat conductivity coefficient in the two-dimensional transient inverse problems by using the BEM and gradient regularization method and obtained the relatively accurate inversion results [26]. Li Yanhao resolved the heat-flow problem found in the two-dimensional transient inverse problem by using the model prediction control algorithm and inversion result was relatively precise [27]. Fan Jianxue adopted the model prediction control algorithm to solve the heat-transfer coefficient in the inner wall of two-dimensional transient steam drum and achieved good calculation results [28]. Residual principle is introduced to optimize the regularization parameter during the inversion process, thereby improving the efficiency of inversion in terms of speed and time

Unsteady-State Direct Problem

Unsteady-State Problem

Numerical Experiment and Analysis

Conclusion

Conflicts of Interest