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The mechanism of convection in the melt, conduction in the crystal and radiation from the melt free surface and crystal was investigated using a thermal-capillary dynamic numerical model for Czochralski growth of silicon single crystal. It was found that the shapes of the crystal/melt interface, free surface and moving crystal are regulated by the balance of energy and stresses. Results also showed that the diameter of the crystal can remain constant or vary with time based on the approaches used to govern the growth process.

Researchers have developed a general two-dimensional non-stationary semicausal model for the simulation of mixture fraction. This model allows the inclusion of the contributions to the mixture fraction simulation from past locations in geometric space. It has been applied to the mixture fraction simulation for turbulent diffusion carbon monoxide/hydrogen/air flames. It is easy to extend the model to three- and four-dimensional models.

The YIX and Monte Carlo methods have been shown to be capable of solving complicated radiative heat transfer problems that have nonhomogeneous and nongray participating media. However, it was later observed that the difference between the two methods are within 5%. It is proven that the discrepancy is mainly due to the difference in spectral integration procedures using a series of gray nonhomogeneous media with and without anisotropic scattering.

A study used the dicrete transfer model to solve the radiative heat transfer problem in two- and three-dimensional rectangular enclosures containing absorbing-emitting and scattering mediums. The discrete transfer method showed very good results when scattering was taken into consideration, but when scattering was not considered the number of representative directions had to be reduced. The results of the discrete transfer method can be attributed to the 'ray effect,' and the best way to reduce the ray effect is to increase the number of rays which cross each cell, and to work towards optimization of the number of grid cells and rays.

Research is conducted to examine an adaptive quadrature method applied to jet fire radiation modeling. The use of adaptive quadrature is considered against the additional complexity of implementation for a model that can be employed in many different reacting flows. Another consideration is the easy automation of the adaptive quadrature technique. The method can be used successfully in other reacting flows where radiative heat transfer is dominated by a small hot emitting volume.