Transient Temperature Computation of Spheres in Packings With Multi-Neighbors

Abstract

Packed sphere systems commonly involve heat transfer processes, such as catalytic beds and insulations. Most of the time, these types of systems were considered as porous media. In fact, porous medium approach has been successfully used for application involving considerable amount of spheres with corresponding resolution and, typically in geothermal system study. In recently years, researchers have started to investigate the problem in a finer length scale formulation because of the relevant application requirement, such as powder sintering processes. Using thermal constriction resistance for solving transient temperature of individual sphere in a packing was one of the attempt to achieve the finer resolution of temperature. It has been found that a special formulation is required in order to take care the finite heat diffusion mechanism between spheres. However, available correlations and governing equations from literature were only applicable for spheres with two neighbors. It is obviously not sufficient for solving temperatures of spheres within realistic packing. Furthermore, the interaction of the finite diffusion amoung spheres should be more complicated in three dimensional packing situation. Therefore, this work focuses on the enhancement of the approach of using constriction resistance for realistic packing of spheres. The formulation of the governing equation with the consideration of multi-neighbor arrangement was performed. A finite difference code was developed and using for solving the governing equation. It has been verified to be applicable to multi-neighbor situation few regular packing situations. Computation of sphere temperatures of a packing involving a thousand of spheres was also performed for illustrating the application.