Identification of a moving boundary for a heat conduction problem in a multilayer medium

2010 ◽  
Vol 46 (7) ◽  
pp. 779-789 ◽  
Author(s):  
Y. S. Li ◽  
T. Wei
Keyword(s):  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Multilayer Medium

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2009 ◽  
Author(s):  
Hosein Molavi ◽  
Ali Hakkaki-Fard ◽  
Alireza Pourshaghaghy ◽  
Mehdi Molavi ◽  
Ramin K. Rahmani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

Estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using the numerical experiments with the simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to conjugate gradient method with adjoint problem and variable metric method with adjoint problem. The obtained results show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Hosein Molavi ◽  
Ramin K. Rahmani ◽  
Alireza Pourshaghaghy ◽  
Ebrahim Sharifi Tashnizi ◽  
Ali Hakkaki-Fard
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

The estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with an adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using numerical experiments with simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to the conjugate gradient method with an adjoint problem and variable metric method with an adjoint problem. The results obtained show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Sign in / Sign up

Export Citation Format

Share Document