Effective conductivity of partially sintered solids

An analytical model to predict the effective conductivity of a partially sintered solid is presented. It is based on an analysis of heat flow through a spherical particle embedded in a self-consistent matrix. Determination of the effective conductivity reduces to solving an integral equation, and a numerical solution of this equation is presented. In the limiting cases wherein the contact size is either small or comparable to the particle size, approximate analytical results are obtained which agree very well with the numerical solution. Furthermore, when pieced together, the two solutions are found to describe the effective conductivity over the entire range of contact sizes. © 2004 American Institute of Physics. @DOI: 10.1063/1.1630360#