COMPARISON OF THREE NUMERICAL METHODS FOR EVALUATION OF RADIANT ENERGY TRANSFER IN SCATTERING AND HEAT GENERATING MEDIA

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Abstract
A plane-symmetric, gray model of coal particle suspensions is developed to test the accuracy of the low-order discrete ordinates and flux methods and of the differential approximation for calculating the radiant energy transport in multiply scattering and heat generating media bounded by diffusely reflecting surfaces. Results obtained by these three approximate techniques are compared with those computed by a high-order discrete ordinates method. In this study, the internal heat generation function is represented by a constant model and a diffusion-limited Arrhenius model; however, the solution method presented is applicable to arbitrary nonlinear and temperature-dependent heat production rates, ft is shown that the accuracy of flux methods decreases while the accuracy of the differential approximation increases with increasing optical thickness of the suspension. The approximate methods are found to yield more accurate results for temperature profiles than for profiles of the radiation intensity. With the Arrhenius heat generation model, particle suspensions are shown to ignite only if their optical thickness exceeds a critical value, which varies with the temperature and reflectivity of the bounding walls. The differential and flux methods tend to overpredict the critical size of the system required for ignition.