Application of lie-group shooting method to estimate nonhomogeneous thermal conductivity and absorption coefficient

In this study, we are concerned with the estimation of nonhomogeneous thermal conductivity and absorption coefficient in a one-dimensional combined conduction-radiation heat transfer problem. As a novel method for inverse problems, the Lie-group shooting method (LGSM) was introduced to solve the inverse problem of combined conduction-radiation heat transfer for the first time. For the LGSM, no prior information on the functional forms of thermal conductivity and absorption coefficient is required and the initial guesses can be chosen randomly. Nonhomogeneous thermal conductivity was estimated by the temperature profile. The absorption coefficient was reconstructed by the coupled optical (radiative intensity) and thermal information (temperature). Numerical examples with different parameter distributions were examined to convince that the new approach is highly accurate and efficient. Meanwhile, the estimated results are still accurate and robust even with a large measurement noise.