The problem of a thermally developing forced convective flow in a packed channel heated asymmetrically is analyzed in this paper. The flow in the packed channel is assumed to be hydrodynamically fully developed and is governed by the Brinkman–Darcy–Ergun equation with variable porosity taken into consideration. A closed-form solution based on the method of matched asymptotic expansions is obtained for the axial velocity distribution, and the wall effect on pressure drop is illustrated. The energy equation for the thermally developing flow, with transverse thermal dispersion and variable stagnant thermal conductivity taken into consideration, was solved numerically. To match the predicted temperature distributions with existing experimental data, it is found that a wall function must be introduced to model the transverse thermal dispersion process in order to account for the wall effect on the lateral mixing of fluid. The variations of the local Nusselt number along the streamwise direction in terms of the appropriate parameters are illustrated. The thermal entrance length effect on forced convection in a packed channel is discussed.

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]

Numerical solution based on the control volume method is presented for the study of heat transfer for forced convective flow in a channel filled with a fluid saturated porous media. The solution of the conservative differential equations governing the flow is performed using the SIMPLE algorithm. The wall effects on the variation of porosity and thermal dispersion have been considered. In calculating the thermal dispersive conductivity, a general expression has been obtained taking into account the flow geometry and flow Reynolds number. The expression appears to serve well in the present investigation and also in reproducing the results of previous studies. The analysis includes predictions of temperature profiles and heat flux for the constant wall temperature condition at the wall and have been compared with available experimental data.