Kazuhiko Kudo

Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index

The ray-tracing technique has the main difficulty in solving radiative transfer in the medium with variable spatial refractive index. Recently, three methods have been developed for the application of the ray-tracing technique in those medium. To compare and discuss the numerical characteristics of those methods, a semitransparent slab with variable spatial refractive index is taken as an example, and the reflectivity and the transmissivity of the slab are computed by the curved ray-tracing method, the multi-layer approach, and the discrete curved ray-tracing method, respectively. As the result, it is shown that, the discrete curved ray-tracing method gives the result with good accuracy and convergence characteristics than the multi-layer approach. Due to accounting physically inexistent reflection on the interface between sublayers, the multi-layer approach converges slowly.

Development of a method to estimate profiles of equivalent absorption coefficient for gray analysis

Using inverse radiative property value analysis, profiles of gray equivalent absorption coefficient are estimated with results similar to non-gray analysis when the coefficients are used in the corresponding gray analysis. For the inverse analysis, the results of non-gray analysis are used as the input. An approximate method is proposed for the estimation of the profiles of equivalent absorption coefficients without previously knowing the results of non-gray analysis. The profiles of the equivalent absorption coefficients obtained by the new method are compared with that estimated by the inverse analysis for two-dimensional model furnaces. The new method is shown to be useful in estimating the profile of absorption coefficients for gray analysis.

Radiative heat transfer analysis in pure water heater used for semiconductor processing

Abstract A simplified one-dimensional model is presented to analyze the non-gray radiative transfer in pure water heater used in the rinsing processes within semiconductor production lines, and the ray-tracing method is extended to simulate the radiative heat transfer. To examine the accuracy of the simplified model, the distribution of radiation absorption is determined by the ray-tracing method based the simplified model and compared with the data obtained by three-dimensional non-gray model in combination with Monte Carlo method in reference, and the effects of the water thickness on the radiation absorption are analyzed. The results show that the simplified model has a good accuracy in solving the radiation absorption in the pure water heater. The radiation absorption increases with the water thickness, but when the water thickness is greater than 50 mm , the radiation absorption increases very slowly with the water thickness.