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

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 comple...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-9
Main Authors: Jia, Huangchao, Sun, Xiaogang, Zhang, Li, Wang, Shoubin
Format: Article
Language:English
Subjects:
Accuracy
Boundary conditions
Boundary element method
Complex variables
Conduction heating
Conductive heat transfer
Conjugate gradient method
Engineering
Error analysis
Heat conductivity
Heat transfer
Impact analysis
Integral equations
Inverse problems
Mathematical analysis
Mechanical engineering
Nondestructive testing
Nonlinear programming
Optimization algorithms
Science education
Standard deviation
Temperature distribution
Two dimensional analysis
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/2861342