Comparison of Gray and Spectral Line-Based Weighted Sum of Gray Gases Models in Inverse Design for Radiative Heat Source in Non-Gray Media

In this study, an optimization technique is performed to obtain the unknown heat source distribution in order to produce the known temperature and heat flux distribution over the design surface. The medium is considered non-gray, absorber-emitter and non-scatter in radiative equilibrium. Discrete ordinate method is used for solving the radiative transfer equation. In order to consider the nongray calculations, both the spectral line-based weighted sum of gray gases approach and the gray model are implemented. The inverse problem involves the minimization of an appropriate objective function which is minimized by the conjugate gradient method. Some examples are presented to prove the ability of the approach for achieving the desired thermal conditions. Although the gray model is a low-computational-time method, the present outcomes showed that using this method results in enormous error. Compared to the gray model, accurate results could be only achieved through using the spectral line-based weighted sum of gray gases model which is a powerful and efficient method.