EFFECTIVE-MEDIUM CONDUCTIVITY (DIFFUSIVITY) FOR A SPHERE IN A CUBE MODEL

A modified analytical solution for the effective medium conductivity ( or diffusivity) k(eff) for two-phase mixtures yields estimates similar to 0.2 - 26 % lower than the classic model of a sphere in a cube (Jef ferson et al. Ind. Eng. Chem. 1958, 50, 1589) depending on the ratios of phase conductivities and volumes. The difference between the two so lutions lies in the assumption of an isothermal plane at the edge of t he sphere in the original derivation. The temperature contours obtaine d with a finite element method simulation of the model confirm the int uitive judgement that this assumption is not valid.