Augmentation of heat transport in laminar flow of polystyrene suspensions. II. Analysis of the data

Abstract

It has been experimentally demonstrated in the preceding paper, I, that heat transport is augmented in the laminar flow of suspensions of 100‐ and 50‐μ polystyrene spheres. The augmentation has been seen to be as much as 200% and depends on the shear rate and several other parameters. Here the experimental data are analyzed by proposing a model based on the particle rotations and the entrained fluid, and by presenting similarity arguments. It is shown that the augmentation in heat transport resides in the inertia of the entrained fluid rotating with the particle which is manifest in two parameters, namely, Reynolds (ωa²/ν_f) and Peclet (ωa²/α_f) numbers, where ω is the angular velocity of the particle, a is the radius of the sphere, and ν_f and α_f, respectively, are the kinematic viscosity and the thermal diffusivity of the suspending fluid. The other parameters on which the augmentation in heat transport depends are the particle volume fraction, tube‐radius–to–particle‐radius ratio, tube‐length–to–particle‐diameter ratio, and the doublet collision frequency ratio which is the cube of the ratio of the particle radius to 50 μ (taking a sphere of diameter 100 μ as a reference particle). Based on the experimental data, a relationship between the augmentation in the thermal conductivity of the flowing suspensions and the various parameters is proposed.