Transient effect on the constriction resistance between spheres

Abstract Systems of contacting spheres are common in engineering applications where the heat transfer analysis can be quite cumbersome due to the transient behavior and the complex geometrical arrangement. As a result, most of the previous works, in this area, have adopted the porous media approach. However, this approach requires the length scale of the representative cell to be roughly three orders of magnitude larger than the size of the spheres. Constriction resistance relations could be useful in accurately computing the temperature distribution within systems of contacting spheres, however many of the requisite relations are not available. Thus, the objective of this study is to develop these relations. In this study, the transient, three-dimensional conduction equation was solved using a finite volume scheme and a non-uniform grid. From the resulting temperature distributions, the steady-state and transient constriction resistance of one-sphere and two-sphere systems were computed and correlated. The results also showed, for the first time, the critical parameters below which the transient variations must be considered.