| Based on the practical requirement and application background, the research on radiative heat transfer within a graded index medium is of great value for understanding the radiative heat transfer process, exploring the radiative heat transfer mechanism and carrying on the radiative analysis correctly. The nature of radiative heat transfer analysis is solving the radiative heat transfer equation, and the key is to obtain the propagation path of the energy bundle. Within a graded index medium, the energy bundle propagates in curved paths which are determined by the Fermat principle and experiences full-reflection. This makes the solving of radiative heat transfer equation within a graded index medium much more difficult than that in an uniform refractive index medium. With the development of the research on radiative heat transfer within a graded index medium, many numerical methods are proposed to solve this problem. However, these methods are challenged by the curved propagation path of the energy bundle, the complication of the problem, the requirement of precise and rapid solving process. It still worth to doing some deep research on how to solve the radiative heat transfer within a graded index medium rapidly, accurately and comprehensively.The aim of this thesis is to establish a high effective, precise and high directional-resolution model for solving radiative heat transfer within a graded index medium, which will provide reliable theoretical support and practical basis for the application of the graded index materials and for the analysis of the graded index optics. Therefore, this thesis tries to extend the DRESOR method to the radiative heat transfer within a graded index medium, sets up a complete solution system for1-D transient and steady heat transfer with simple and complicated graded index distribution medium.The basic solving mechanism of the DRESOR method for radiative heat transfer within a graded index medium, the ray tracing process and the updating of the DRESOR values are deduced. The1-D radiative heat transfer under linear and periodical changed graded index distributions is analyzed and the curved propagation paths are calculated. The comparison of the results shows the accuracy of the DRESOR method, and the results obtained by the DRESOR method can be considered as the precise solution for a non-scattering medium. The existence of the graded index has a strong effect on the radiative heat transfer process, while the influences of the anisotropic scattering albedo and the optical thickness are much weaker and the isotropic scattering albedo has no effect on the radiative heat transfer. As for the periodical changed graded index medium, the ratio of the amplitude to the average value of the graded index is used to adjust the influence of the graded index, and the temperature node of the medium under radiative equilibrium is investigated.After the research on steady radiative heat transfer, the DRESOR method for the transient problem with a pulse irradiation is studied. Under a1-D collimated truncated Gaussian pulse irradiation, the graded index attenuates the time-resolved reflectance and transmittance to some degree and significantly delays the occurrence time of the transmittance. The optical thickness and the anisotropic scattering phase function has effect on the transmittance. The double-peak phenomenon of the time-resolved transmittance becomes more obvious as the increase in the graded index, the scattering albedo and the optical thickness. Besides, the transmittance profile gives much more information about the properties of the participating medium than does the reflectance profile, to which additional attentions needs to be paid.Compared with the traditional diffuse or specular surface assumption, BRDF surface can well describe the radiative character of a real surface. Based on this, the radiative heat transfer problem within a graded index medium coupled with BRDF surfaces is investigated in this thesis. The Minnaert model is utilized to simulate a cement slab, and the corresponding coefficients are optimized and obtained by the Genetic Algorithm, then the DRESOR method and the RMC method are extended to do the solution. Compared with the diffuse surface, the temperature difference of the medium with the BRDF surface increases, and the radiative flux increases significantly by3.5-12%. This indicates the importance of introducing a model that is closer to the real surface in a precise radiative heat transfer analysis. |
