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 Δ t = 10 3 . The Runge–Kutta ray-tracing method can effectively solve the radiative transfer in a three-dimensional graded-index media.


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    Title :

    Runge–Kutta Ray-Tracing Technique for Radiative Transfer in a Three-Dimensional Graded-Index Medium


    Contributors:
    Qian, Linfeng (author) / Shi, Guodong (author) / Huang, Yong (author)

    Published in:

    Publication date :

    2018-07-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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