Discrete formulation using thermal resistance for conduction heat transfer analysis of sphere packings

Systems of contacting spheres are common in engineering applications. For such systems, the heat transfer analysis can be quite complicated due to the complex geometrical contact arrangement. As such, most of the previous works have typically applied a porous medium approach, which is only valid for resolution of two to three orders of magnitude larger than the sphere. Thus, for applications requiring a finer spatial resolution, porous medium approach is generally not applicable. If direct solving of energy equation is used as an alternative method, a high computational power is required due to its required iteration operation for coupling the temperature solutions at the interfaces between spheres. In this present work, a new formulation was developed to provide sufficient fine spatial resolution with any given packing structure. The computational efficiency of this new formulation has been shown. Furthermore, an experimental setup was designed and built for studying the contact resistance between spheres. The applicability of the new formulation was demonstrated with determination of effective conductivity of different packings. In addition, the effects of the contact resistance and the packing structure on the effective conductivity of sphere packings were studies. By using the new formulation, the effective conductivity of any packing with given packing structure can be determined