The Runge–Kutta ray-tracing method is combined with the Monte Carlo method to analyze the radiative transfer in a three-dimensional graded-index media. The analytical solution of the trajectory of a ray in a refractive index distribution of a Maxwell fisheye lens is obtained. The temperature field, heat flux, and apparent emissivity calculated by the analytical solution of the trajectory of a ray are treated as the standard solution to verify the results of the Runge–Kutta ray-tracing methods. The third-order fixed-step, fourth-order fixed-step, and third-order variable-step Runge–Kutta ray-tracing methods are discussed here. More accurate results can be obtained by using a higher-order Runge–Kutta algorithm; however, the third-order variable-step-size Runge–Kutta ray-tracing method has better precision than the fourth-order fixed-step Runge–Kutta formula for the temperature field. The maximum relative error of the temperature as compared to the standard solution is less than 0.19%, the integrated mean relative error is less than 0.06%, and the maximum relative error of the emissivity is less than 0.94% in the case of . The Runge–Kutta ray-tracing method can effectively solve the radiative transfer in a three-dimensional graded-index media.
Runge–Kutta Ray-Tracing Technique for Radiative Transfer in a Three-Dimensional Graded-Index Medium
Journal of Thermophysics and Heat Transfer ; 32 , 3 ; 747-755
2018-07-01
Article (Journal)
Electronic Resource
English
AIAA | 1997
|Explicit Runge- Kutta Integration
NTIS | 1966
|Multi-Step Runge- Kutta Methods
NTIS | 1968
|Multi-step Runge-Kutta methods
TIBKAT | 1968
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