Reverse Monte Carlo coupled with Runge-Kutta ray tracing method for radiative heat transfer in graded-index media

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.