Estimation of space-dependent thermophysical properties in participating media by using a Lie-group shooting method

Estimation of space-dependent thermal conductivity and absorption coefficient in a one-dimensional participating medium was investigated in this study. For the forward problem, discrete ordinate method was used to solve the radiative transfer equation. The conduction-radiation energy equation was decoupled by the radiative source term and solved by the finite difference method. Lie-group shooting method (LGSM) was introduced to retrieve the space-dependent thermal conductivity and absorption coefficient from the coupled optical (radiative intensity profile) and thermal (temperature profile) information. LGSM was employed to solve the inverse problem of combined conduction-radiation heat transfer for the first time. This method does not require priori information about the functional form of thermal properties and initial guesses can be selected randomly. Numerical examples of the thermal conductivity and absorption coefficient under different distributions were examined to show that the new approach is highly accurate and efficient, even for identifying highly discontinuous and oscillatory parameters. The estimation was conducted in the presence of the random measurement noise. However, the estimated results still showed high accuracy, robustness and low susceptibility to the shape of property distributions.