Transient temperature computation of spheres in three-dimensional random packings

In this work, the Discrete Conduction Model (DCM method) was developed. This proposed method is an intermediate approach between the porous medium and PDE methods, as it assumes each sphere to be an isothermal element, and constructs the energy conservation equation in terms of thermal resistances between these contacting spheres. As a result, the governing equations were reduced to a set of simultaneous ODE’s in time. To demonstrate this method, a packing algorithm was utilized to generate 3-D random packed beds, and the results showed the DCM method to have an error of less than 0.9% while attaining a speedup of 105 in comparison with the PDE method. In addition, results for varying packing structures showed the porosity to be insufficient to uniquely characterize a packing structure, but instead presents correlations in terms of CN and γ.