Inverse estimation of temperature-dependent refractive index profile in conductive-radiative media

The aim of this paper is to retrieve the temperature-dependent refractive index distribution in parallel-plane semi-transparent media with combined conduction-radiation heat transfer, by the measurement of exit intensities over the boundaries. The finite volume method in combination with the discrete ordinates method is used to solve the energy equation. The results of the direct solution for both linear-spatially and linear-temperature-dependent refractive index distributions are compared and the effects of the main parameters are examined. The results confirm a remarkable difference between the results for spatially and temperature-dependent refractive index profiles. Finally, the refractive index profile is estimated using the conjugate gradient method in an inverse manner. The coefficients of the linear profile are estimated for three cases with different levels of measurement errors; 1%, 3% and 5%. The results show that the temperature-dependent refractive index distribution can be retrieved in a good range of errors for noisy data.