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The Reverse Monte Carlo coupled with Runge-Kutta ray tracing (RMCRKRT) method is developed to solve the radiative heat transfer problems in semitransparent media with graded index. Due to the fact the curved ray trajectory determined by Fermat principle almost can’t be expressed as the simple explicit functions except for a few special refractive index distributions. In RMCRKRT, the Runge-Kutta ray tracing technique is employed to obtain the ray trajectory numerical solution of graded index medium, and the Reverse Monte Carlo method is employed to solve the radiative heat transfer problems. The correctness and accuracy of RMCRKRT is validated by comparing with the benchmark numerical solutions. The diffuse, specular and bidirectional reflectance distribution function (BRDF) surfaces are considered, and the effects of diffuse, specular and BRDF surfaces on radiative heat transfer are investigated by using the RMCRKRT developed in this work. Calculation results show that significant differences exist in the radiative intensity under different boundary conditions. Therefore, BRDF should be used instead of diffuse reflection and mirror reflection in practical application.

A hybrid algorithm of extended Kalman filtering and recursive least-square estimator (EKF-RLSE) is developed to solve the nonlinear inverse heat conduction-radiation problems in participating medium. By measuring the time-resolved temperature signals from a thermocouple installed on the other boundary of the participating medium, the proposed EKF-RLSE algorithm can realize real-time retrieval of the time-varying heat flux on the medium surface. The influence factors of the sampling interval, measurement and process covariance, forgetting factor, and medium thickness on the reconstruction accuracy and stability of the EKF-RLSE are investigated by numerical experiments. All the estimated results show that the present algorithm is robust and accurate in real-time estimating transient heat flux. If the nonlinear coupled conduction and radiation heat transfer problems is regard as the linear problems, the unknown time-dependent heat flux predicted by the KF-RLSE are also illustrated in this work.