Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

In the paper a solution of the inverse heat conduction problem with the Neumann boundary condition is presented. For finding this solution the homotopy perturbation method is applied. Investigated problem consists in calculation of the temperature distribution in considered domain, as well as in reconstruction of the functions describing the temperature and the heat flux on the boundary, in case when the temperature measurements in some points of the domain are known. An example confirming usefulness of the homotopy perturbation method for solving problems of this kind are also included.

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On Elliptic Inverse Heat Conduction Problems

Journal of Heat Transfer ◽

10.1115/1.4036006 ◽

2017 ◽

Vol 139 (7) ◽

Cited By ~ 7

Author(s):

M. Tadi

Keyword(s):

Boundary Condition ◽

Heat Conduction ◽

Heat Conduction Problem ◽

Inverse Heat Conduction Problem ◽

Initial Guess ◽

Unknown Boundary ◽

Inverse Heat Conduction ◽

Robustness To Noise ◽

Inverse Heat Conduction Problems ◽

New Feature

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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Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2012-0102 ◽

2015 ◽

Vol 23 (2) ◽

Cited By ~ 2

Author(s):

Zhi Qian ◽

Benny Y. C. Hon ◽

Xiang Tuan Xiong

Keyword(s):

Heat Conduction ◽

Numerical Solution ◽

Heat Conduction Problem ◽

Inverse Heat Conduction Problem ◽

Stability And Convergence ◽

Two Dimensional ◽

Inverse Heat Conduction ◽

Convergence Error ◽

Regularization Techniques ◽

Ill Posed

AbstractWe investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modified kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and effective approximation to the solution of the inverse and ill-posed problem.

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