Inverse Reconstrucction of Absorption-Coefficient Distribution in a Two-Dimensional Radiative Medium from the Knowledge of Wall Heat Fluxes

Document Type : Research Article

Authors

1 Shahid Bahonar University of Kerman

2 Mechanical Engineering, Shahid Bahonar University of Kerman

Abstract

In this article, an inverse radiation analysis is presented to reconstruct the absorption coefficient distribution from the knowledge of wall heat fluxes for a two-dimensional, absorbing-emitting medium with black walls. The inverse approach aims to find the location of inclusion with a different absorption coefficient. For this purpose, the study is divided into two parts; the direct and the inverse problems. In the direct problem, the radiative transfer equation is solved by the discrete transfer method from the knowledge of the absorption coefficient distribution and we obtain heat fluxes over the walls. Then the measured data are simulated virtually by adding the random errors to heat fluxes. The conjugate gradient method is used to solve the inverse problem to estimate the absorption coefficient distribution. As the measured data are less than the estimated parameters, a multi-step procedure is adopted to restrict the search region. Results show that the absorption coefficient distribution is well recovered in the medium with a low absorption coefficient by a two steps procedure. The results show that the location of inclusion may be found even by noisy data with 1% and 3% measurement errors. However, as the absorption coefficient increases, the location of inclusion is reconstructed in a three steps procedure and the inverse estimation becomes less efficient and time-consuming.

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