Effective property predictions in multi-scale solidification modeling using homogenization theory

Abstract

Homogenization based upscaling is proposed as a superior technique over conventional volume-averaging methodologies, for effective property predictions in multi-scale modeling of transport phenomena in solidification problems. Differences between the effective diffusion coefficients, as predicted using the above two techniques, are identified over a range of cellular solid fractions. From the results, subtle deficiencies of volume-averaging techniques, with regard to implicit capturing of micro-scale physics in meso-scale formalism, as compared to the proposed methodology, are emphasized upon.