Transient temperature computation for a system of multiple contacting spheres in 180° orientation

Systems of contacting spheres are common in engineering applications. Due to the complexity, most of the previous work in this area have adopted a porous media approach, which is only valid for units cells of two to three orders of magnitude larger than the sphere. Thus, this approach is more suitable for a porous, semi-infinite medium. However, there are many practical applications where the porous medium assumption is not applicable. The objective of this study is to develop a tool to compute the transient behavior of multiple contacting spheres in 180° orientation with application of thermal constriction resistance. A finite volume formulation was developed using non-uniform grids. Since the grid size must be small at the contact surface, the computation time was significant. To alleviate this, a time varying over-relaxation (TOR) scheme was developed. The correlation for transient constriction resistance for a one-sphere system and a two-sphere systems were obtained. It is shown that these resistance cannot be directly used in computing the transient temperature of a multiple sphere system. Instead a correction factor must also be introduced, and this factor is herein called the constriction capacitance. A correlation is presented for this capacitance and its necessity is confirmed for a 20 sphere system