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

Abstract

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. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method 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.

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

“…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 research of inverse heat conduction problem has a very wide application background.…”

Boundary Shape Inversion of Two-Dimensional Steady-State Heat Transfer System Based on Finite Volume Method and Decentralized Fuzzy Adaptive PID Control

“…There are inverse heat conduction problems (IHCPs) that are well known to be ill posed. The IHCP has been successfully applied in many industrial and engineering fields [1][2][3][4][5][6][7][8][9][10][11].…”

Solving of Two-Dimensional Unsteady Inverse Heat Conduction Problems Based on Boundary Element Method and Sequential Function Specification Method

“…The inverse heat conduction problems (IHCP) are to measure the temperature at the heat conduction system boundary or internal point or points by using the experimental method to obtain partial temperature information and inverse some unknown parameters: the boundary condition, material thermophysical parameter, internal heat source and boundary geometry, and so on [1][2][3][4]. The IHCP researches have wide application background and are nearly applied in all fields of science engineering: the aerospace engineering, bioengineering, power engineering, machine manufacturing, chemical engineering, nuclear physics, metallurgy, material processing, equipment geometry optimization, nondestructive testing, and so on [5][6][7][8][9].…”