Transient conduction analysis of multiply contacting spheres in simple three dimensional packing for powder sintering applications

Sintering is a versatile process of powder metallurgy. It is typical for processing materials with high melting point such as ceramics. However, there exists a significant gap between the existing sintering theory and practical application. Consideration of the heating process is a crucial part of this gap. The underlying heat transfer analysis is tremendously complex. Since conduction is the dominant mode at the initial phase of the heating process, and is also the mode which always exists within any solid medium, the first step of the analysis is the study of heat conduction. In this work, the greenware is considered as a packing of spheres with finite contact areas. The objective of this work is to develop the fundamental ground for computing the transient temperature solution of conduction among spheres which are packed into contact. A finite volume formulation was developed for the investigation of computing the bulk temperature of individual spheres within a packing using thermal constriction resistance. The correlations were presented for the required constriction resistance. In addition, an artificial instantaneous diffusion effect was found with the transient computation of bulk temperature. As a result, a new governing equation was proposed and shown to be applicable for simple packed sphere system. The correlations for the required parameters for this new equation, such as thermal constriction capacitance and characteristic time, were presented as well. Furthermore, a numerical algorithm was developed for providing high computational efficiency with speed-up in the order of thousand which is generally greater than most existing methods.