xchange of heat between a rising bubble and the dense phase is a component of the overall gas-particle heat transfer behaviour in E a bubbling fluidized bed. However, surprisingly few measurements and models have been reported on this subject. This is, perhaps, because reactant conversion in fluidized beds is calculated assuming that the bed is isothermal. This is expected to be the case for modelling solid-catalyzed gas-phase reactions where the bubbles represent a dead volume in terms of reaction; the bypassing of reactant in bubbles reduces the conversion per unit bed volume. In fluidized bed combustion, however, the bubble phase may represent a more favourable reaction volume for the combustion of volatile gases released from coal (Agarwal, 1986; Hayhurst and Tucker, 1990; Hesketh and Davidson, 1991). For modelling such systems, an accurate description of the heat exchange between the bubble and dense phases is vital (Srinivasan et al., 1998). In fluidized bed drying systems, the drying media in the bubble phase acts partly as the heat carrier (Chen et al., 1999); modelling such systems also requires accurate heat transfer coefficient between the bubble and dense phases. Kunii and Levenspiel (1991) obtained a model for the heat transfer coefficient between the bubble and dense phases by applying the analogy between heat and mass transfer to their well-established model for mass exchange. However, the large difference in thermal capacities of gas and solids in the fluidized bed implies that the mechanisms for heat and mass transfer need not be analogous. To explain the measurements on gas-particle heat transfer in a fluidized bed, Kunii and Levenspiel (1991) introduced an additional term representing heat exchange between bubble gas and the very small fraction of solids, which may be present within the bubble. The heat transfer coefficient between the particles and the bubble gas was calculated using the Ranz and Marshall correlation (1 952). The volumetric fraction (of the bubble) occupied by solid particles in the bubble was taken, based on measurements in a two-dimensional bed, as yp,B = (1 -2) x 1 0-3 It can be established quite readily that the contribution of the additional term to the total heat transfer far outweighs that from the terms obtained through the application of the heathass transfer analogy.Toei et al. (1 972), comparing the relative contributions of various heat transfer mechanisms to the overall heat transfer coefficient, concluded that the effect of the particles falling through the bubble was the dominant heat transfer mechanism. The contact time between the particles and the bubble gas was taken as the free-fall time of a particle through the bubble. Again, the Ranz and Marshall equation was recommended for the calculation of the heat transfer coefficient between the particles and the bubble gas.*Author to whom correspondence may be addressed: E-mail address: paganVal@ uwyo.edu Heat transfer between the bubble and dense phases of a bubbling fluidued bed plays a very important role in t...
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