Modeling of the effective thermal conductivity and diffusivity of a packed bed with stagnant fluid

Abstract

Beginning with a model of radial energy transport in a fluid saturated porous medium formed by a cubic array of cylinders with a stagnant fluid, a generalized method for determining overall effective conductivity, volumetric specific energy capacity, and effective thermal diffusivity is derived. The resulting model is not limited to any particular geometry, since it requires only the physical properties of the fluid and solid, and the void fraction as input. Comparisons demonstrate that the model agrees well with both experimental and theoretical values for the effective conductivity, while requiring no empirical or theoretical model parameters. Results for effective thermal conductivity and effective thermal diffusivity as functions of void fraction and as functions of the ratio of solid to fluid thermal conductivity are presented.