Influence of the wall on transient conduction into packed media

Abstract

Surfaces immersed in moving packed beds and fluidized beds frequently experience a "renewal" type of contact with packed media. If there is heat transfer during surface renewal, it can be modeled as a transient conduction process provided the contribution due to thermal radiation is negligible. There exist two distinct approaches (Mickley and Fairbanks, 1955;Botterill and Williams, 1963) for the prediction of the heat transfer coefficient. Many investigators have subsequently suggested modifications to the basic models cited above so as to achieve good agreement with experimental data (Saxena and Gabor, 1981;Chandran and Chen, 1985).A review of the literature indicated that the model developed by Kubie and Broughton (1975) exhibits satisfactory agreement with experimental data without the use of empirical parameters. However, the model requires a numerical solution and that detracts it from use for design purposes. From an application standpoint, it is desirable to develop a simple closed-form relation for the heat transfer coefficient; such a relation is derived in this note. ANALYSISConsider a disperse system comprising a gas-solid medium with a close-packed matrix of solid particles and stationary gas that comes into contact with a surface at a different temperature for a certain duration. For the case of negligible radiant contribution, heat transfer occurs by unsteady state conduction. In formulating the problem, it is important to (i) account for the influence of the surface or wall on the local packing, and (ii) recognize the heterogeneity of the two-phase medium. The property boundary layer concept introduced by Kubie and Broughton (1975) is used here to account for the wall effect. This translates into the voidage variation shown in Figure 1. The heterogeneous nature of the disperse system, however, is more difficult to deal with. Hence as a first approximation, the stochastic behavior of multiple particles is treated as pseudo-homogeneous in this work.For constant wall temperature, with the usual assumptions, the governing equations for transient conduction into the disperse system can be written in normalized form as: Equations 1 and 2 were obtained by using the relation proposed by Kubie and Broughton (1975) subject to

Modeling of Wall-to-Bed Heat Transfer in a Supercritical Water Fluidized Bed by the Packet Approach

“…An effective approach to account for this is to introduce a thermal resistance between wall and packet. Many researchers have made efforts to deal with wall-to-bed heat transfer in this region. ,,, In the present paper, a simplified spherical particle model is adopted to evaluate the thermal resistance, as shown in Figure . The spherical particle contacting the surface is simplified as an equivalent cylindrical particle with equal diameter and volume, respectively.…”

“…Chandran and Chen studied the parameters in a horizontal tube immersed in a fluidized bed of glass beads and predicted the heat transfer coefficient. Some modification studies on this model under special conditions have also been conducted. , Their research work shows that the packet renewal theory can be applied to predict the wall-to-bed heat transfer coefficient well in gas–solid fluidized beds.…”

“…Some modification studies on this model under special conditions have also been conducted. 28,29 Their research work shows that the packet renewal theory can be applied to predict the wall-to-bed heat transfer coefficient well in gas−solid fluidized beds.…”