Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects

Abstract

ABSTRACT. Previous work in chemical engineering literature on the determination of the effective transverse thermal conductivity and Nusselt number for forced convection in packed tubes and channels are reviewed. Discrepancies in existing Nusselt number correlation equations are discussed. Some of the existing experimental data are reanalyzed based on the recent thermal dispersion theory developed by Hsu and Cheng with variable porosity effects Iaken into considmltion in an approximate manner. Numerical results are obtained for forced convection of air and water in packed tubes and channels. For forced convection in a packed column, it is found that the avemge Nusselt number depends not only on the Reynolds number, but also on the dimensionless particle diameter, the dimensionless length of the tube, the thermal conductivity ratio of the fluid phase to the solid phase, and the Prandd number of the fluid. IN1RODUcnONForced convection in packed tubes and channels have been the subject of intensive study in chemical engineering literature during the past six decades [I]. As early u 1931, Colbmn [2] found that the heat transfer rate for forced convection of air through a packed tube is about eight times higher than that of an empty tube. The substantial increase in the heat transfer rate hu been attributed to the mixing of fluid owing to the presence of the solid matrix known u the thermal dispersion process. During the ensuring years, more than thirty experiments have been performed on forced convection through cylindrical , annular [33][34][35]

An Investigation on Transport Properties Near the Wall in Porous Media by Fractal Models

“…In his solutions, φ ∞ = 0.5, C 1 = 0.98, and N 1 = 2 in Equation (1) were used. The empirical constants φ ∞ = 0.36, C 1 = 1.4, and N 1 = 5-6 in Equation (1) were later recommended by Cheng et al [7,8] for the best match between theory and experiment for pressure drop. They then numerically solved the macroscopic momentum and energy equations, together with Equation (1), in a variable porosity medium for an incompressible, hydrodynamically, fully developed flow for velocity and temperature profiles as well as for heat transfer coefficients in porous beds.…”

“…The effective stagnant thermal conductivity k e is usually represented by one of the existing correlations. Cheng et al [7,8] used the following semi-analytical expression in the energy equation for the stagnant thermal conductivity…”

“…The wall effects on fluid flow and heat transfer in porous media have attracted a number of investigators [1][2][3][4][5][6][7][8][9][10][11][12]. Because the porosity of the porous medium near the wall increases drastically from φ ∞ (≈0.36 ∼ 0.4) at the bulk/core region to nearly unity at the wall in packed beds, the transport properties (such as permeability, thermal conductivity, and dispersion) near the wall are significantly different from those in the bulk region.…”

“…The total thermal conductivity in the energy equation is composed of two terms: the effective stagnant thermal conductivity k e of the saturated porous medium, and the thermal dispersion conductivity k d [7,8] due to the microscopic fluid velocity and temperature deviations from the average values. The effective stagnant thermal conductivity k e is usually represented by one of the existing correlations.…”

A thermal dispersion model for single phase flow in porous media

“…Understanding and predicting the thermal dispersion is one of the major concerns for both fluid mechanics and thermal science researchers. Cheng and colleagues [1] provided an extensive review on thermal dispersion and derived a thermal dispersion tensor for convection in a porous medium by averaging the velocity and temperature deviations in the pores over a representative volume [2]. Koch and Brady [3] proposed a correlation of the transverse and longitudinal thermal dispersion conductivity.…”