Effects of radial thermal dispersion on fully-developed forced convection in cylindrical packed tubes

Abstract

The fluid flow and heat transfer characteristics of a fully-developed forced convective flow in a cylindrical packed tube with symmetric heating are analyzed in this paper. The Darcy—Brinkman—Ergun model is used as the momentum equation, with the radial porosity variation of the packed column approximated by an exponential function. The method of matched asymptotic expansions is applied to construct a composite solution for the axial velocity profile of a hydrodynamically fully-developed flow. The interaction of inertial and wall channeling effects on the pressure drop and the axial velocity profile is illustrated. The effects of radial thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation for a thermally fully-developed flow in the packed tube, which is heated circumferentially with constant heat flux or constant wall temperature. A wall function is used to model the wall effect on the transverse thermal dispersion process, and the predicted Nusselt numbers agree with existing experimental data. Numerical results of the corresponding heat transfer characteristics in the packed tubes, without introducing the wall function, are also presented for comparison.