Objective Radiative heat transfer is one of the three basic modes of heat transfer and has an important impact on the study of the temperature distribution and infrared radiation characteristics of the outer surface of a space target. For solving the radiation heat transfer between incomplete gray-diffuse surfaces system (both diffuse surfaces and non-diffuse surfaces in the model), there is usually a lack of corresponding analytical solutions. The Monte-Carlo method has the advantage of good calculation accuracy, but it has the disadvantage of long calculation time. In order to solve this problem, this paper proposes a representation of the ray reflection energy of the diffuse surface and a calculation method for the radiative transfer coefficient of the incomplete diffuse surfaces system based on the diffuse reflection characteristics of the diffuse surface. This reduces multiple ray tracing before the ray energy threshold is reached and improves the calculation speed.

Methods A method for expressing the reflected energy of diffuse surfaces is proposed. When the Monte-Carlo method is used to conduct ray tracing, if a ray hits a diffuse surface, the reflection energy of the ray is defined as the diffuse emission beam set in the upper half space of the surface using the diffuse reflection characteristics of the diffuse surface (Fig.2(b)). In addition, modifications were made to the Monte-Carlo tracking process. First, the radiative transfer coefficient of the diffuse surface was calculated using the Monte-Carlo method. Then, when calculating the radiative transfer coefficient of diffuse surfaces, if the light emitted from the surface intersects with the diffuse surface, the radiative transfer coefficient of the other surfaces is multiplied by the reflected energy, and the reflected energy absorbed by the other surfaces is calculated to end the ray tracing process, avoiding subsequent multiple ray tracing and achieving fast calculation of diffuse surfaces to improve the computational efficiency of the entire system (Fig.5).

Results and Discussions  Using the cube model and assuming that the No.1 and No.2 surfaces are diffuse and the rest of the surfaces are specular (Fig.4(a)), the radiative transfer coefficient from each surfaces to the other surfaces (including itself) are calculated using the Monte-Carlo method and the fast algorithm proposed in this paper, and the results of the calculations are shown (Tab.1-2). It can be seen that both of them have the same accuracy, but as for the computation time, the new method is more efficient due to the significant reduction of the number of ray tracing times in Monte-Carlo (Fig.6). In addition, the 13-facet L-type unenclosed cavity model is used as proof to show that the method is also applicable in complex models. Finally, taking the cube model as an example, the advantages of the fast method compared with the Monte-Carlo method are analyzed from the theoretical point of view. For the emitted beam on a non-diffuse surface, the average tracing times of its rays are much smaller than that of the Monte-Carlo method, and the higher the reflectivity of the surface element, the more significant the computational advantages are. For example, if the energy threshold is 0.001, the number of diffuse reflective surfaces in the model is 2. When the surface reflectance is 0.4, the calculation time of the non-diffuse reflective surfaces in the fast calculation method is 0.307 times that of the Monte-Carlo method. When the reflectance of the surface is increased to 0.8, the calculation time of the non-diffuse reflective surface is only 0.081 of that of the Monte-Carlo method, which is more than ten times higher.

Conclusions Aiming at the problem of the traditional Monte-Carlo method in calculating the radiative transfer coefficient between diffuse surfaces and diffuse surfaces for a long time, a fast calculation method is proposed. Firstly, the realization principle of the method and the difference with Monte-Carlo method are introduced, and then the cube model and L-shape unenclosed cavity model are used to compare the calculation results and calculation time of the fast method to Monte-Carlo method, which illustrates the advantages of fast method over Monte-Carlo method in terms of the calculation efficiency, and then the coefficient affecting the calculation advantages of the method are illustrated through the theoretical analysis, and finally the outlook on the next step of how to improve the calculation time of the diffuse surface elements is proposed.