Fully-developed, forced convective flow through an annular packed-sphere bed with wall effects

Abstract

An analysis is performed for a fully-developed, forced convective flow through a packed-sphere bed between concentric cylinders maintained at different temperatures. The radial variations of the porosity and permeability in the bed near the walls, known as wall effects, are approximated by exponential functions. The Brinkman model with variable permeability is used as the momentum equation. An analytical solution based on the method of matched asymptotic expansions is obtained for the velocity distribution. It is shown that velocity overshoots occur in the variable permeability bed near the inner and outer cylinders. Because of the non-uniform porosity variation near the walls, the stagnant thermal conductivity of the bed also varies in the radial direction accordingly. A mixing length theory, proposed recently by Cheng and Vortmeyer for the transverse thermal dispersion, is employed to obtain the radial temperature distribution and the Nusselt number of the annular bed. Computations of the heat transfer characteristics were carried out based on three velocity models, i.e. Brinkman's model with variable and constant permeabilities as well as the plug flow model. It is found that with the mixing length theory, theoretical predictions of the heat transfer characteristics based on the three velocity models are in good agreement with the existing experimental data. The predicted temperature profiles, based on the Brinkman model with a variable permeability, agree the best with temperature data.