Estimation of unknown boundary functionsin an inverse heat conduction problem using a mollified marching scheme

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

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Solution of the Inverse Heat Conduction Problem From Thermal Strain Measurements

Journal of Heat Transfer ◽

10.1115/1.2822579 ◽

1996 ◽

Vol 118 (4) ◽

pp. 842-849 ◽

Cited By ~ 16

Author(s):

G. Blanc ◽

M. Raynaud

Keyword(s):

Heat Conduction ◽

Heat Conduction Problem ◽

Thermal Strain ◽

Sensitivity Coefficient ◽

Inverse Heat Conduction Problem ◽

Temperature Measurements ◽

Unknown Boundary ◽

Inverse Heat Conduction ◽

Numerical Predictions ◽

Unknown Boundary Conditions

Another approach for the solution of the inverse heat conduction problem is presented. The unknown boundary conditions are recovered from thermal strain and temperature measurements instead of temperature measurements only. It is required to calculate both the temperature field and the strains induced by this field. The sensitivity coefficient analysis and the results of two benchmark test cases show that it is possible to recover higher temporal frequencies when the inversion is done from strains instead of temperatures. An experimental setup was specially designed to validate the numerical results. The numerical predictions are verified. Special attention is given to the strain gage measurements.

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BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain

Journal of Pressure Vessel Technology ◽

10.1115/1.1523890 ◽

2003 ◽

Vol 125 (1) ◽

pp. 109-117 ◽

Cited By ~ 6

Author(s):

Chang-Yong Choi ◽

Jong Chull Jo

Keyword(s):

Heat Conduction ◽

Boundary Element ◽

Measurement Errors ◽

Heat Conduction Problem ◽

Boundary Surface ◽

Inverse Heat Conduction Problem ◽

Unknown Boundary ◽

Inverse Heat Conduction ◽

Minimal Energy ◽

Element Analysis

This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

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