Concept of equivalent diameter for heat and fluid flow in porous media

In this note, we shall propose the concept of the equivalent diameter and the Reynolds number based on it, which can handle both hydrodynamic and heat-transfer aspects associated with fluid flow, and heat transfer in porous media. This concept enables us to extract a series of useful correlations for porous media, such as the friction factor, thermal dispersion and interfacial heat transfer coefficient, from existing correlations available for tube flows and cross flows over banks of cylinders. Prior to the discussion leading to the equivalent diameter, here we revisit the concept of the hydraulic diameter often introduced in conjunction with the Carman-Kozeny theory, to estimate the permeability of a fluid-saturated porous medium (See for example,). The hydraulic diameter dh may best be illustrated in consideration of a bundle of capillary tubes as shown in Figure 1, in which, Hagen-Poiseuille flow may develop. For each tube, the following equation should hold