Heat transfer particle convective component

The particle convective component hpc may be calculated from Eq. (12.39). The heat transfer coefficients of film can be calculated from Eq. (12.48)... 

The particle convection is in general important in the overall bed-to-surface heat transfer. When particles or particle clusters contact the surface, relatively large local temperature gradients are developed. This rate of heat transfer can be enhanced with increased surface renewal rate or decreased cluster residence time in the convective flow of particles in contact with the surface. The particle-convective component hpc can be expressed by the following equation, which is an alternative form of Eq. (12.39) ... 

Figure 4 plots, against suspension density, the heat transfer coefficients measured by Basu (1990) over a wide range of bed temperature for 296 pm sand, by Kobro and Brereton (1986) at a temperature of 850°C for 250 pm sand and by Grace and Lim (1989) at 880°C for 250-300 pm sand. The overall heat transfer coefficient is shown to increase with bed temperature. Before radiation becomes dominant in heat transfer, the observed rise in heat transfer coefficient with bed temperature may be explained as follows. The gas convective component is expected to decrease mainly because of the inverse dependence of gas density on temperature. On the other hand, the particles convective component will increase with temperature, thus leading to an increase in gas conductivity, because the latter is dominant for... 

In most dense gas-solid fluidization systems, particle circulation (e.g., induced by the bubbles) is the primary cause of particle convective heat transfer. The heat transfer rate is high when there is an extensive solids exchange between the in-bed region and the region near the heat transfer surface. In light of the relative importance of the particle convective component, more discussion is focused on particle convective heat transfer in the following sections in the context of the heat transfer models and corresponding correlations. 

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. The film model discounts the effects of thermophysical properties such as the specific heat of solids and hence would not be able to predict the particle convective component of heat transfer. For estimating the contribution of the particle convective component of heat transfer, the emulsion phase/packet model given in a subsequent section should be used to describe the temperature gradient from the heating surface to the bed. 

Particle Convective Component. Particle convection, caused by the mixing of the particles within the bed, is important for heat transfer from a surface when the surface is in contact with the suspension instead of the void/bubble phase. Thus the heat transfer coefficient due to particle convection can be defined as... 

In circulating fluidized beds, the clusters move randomly and the heat transfer between the surface and clusters occurs via unsteady heat conduction with a variable contact time. The heat transfer due to cluster movement represents the major part of the particle convective component. Heat transfer is also due to gas flow that covers the surface (or a part of surface) and contributes to the gas convective component. 

The heat-transfer coefficient of most interest is that between the bed and a wall or tube. This heat-transfer coefficient, is made up of three components. To obtain the overall dense bed-to-boiling water heat-transfer coefficient, the additional resistances of the tube wall and inside-tube-waH-to-boiling-water must be added. Generally, the conductive heat transfer from particles to the surface, the convective heat transfer... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Ackeskog et al. (1993) made the first heat transfer measurements in a scale model of a pressurized bubbling bed combustor. These results shed light on the influence of particle size, density and pressure levels on the fundamental mechanism of heat transfer, e.g., the increased importance of the gas convective component with increased pressure. 

Ebert, T., Glicksman, L., and Lints, M., Determination of Particle and Gas Convective Heat Transfer Components in Circulating Fluidized Bed, Chem. Eng. Sci., 48 2179-2188 (1993)... 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The second and the third components become significant only at high temperatures (> 700°C) and low solids concentrations (< 30 kg/m3). In fast fluidized beds, the motion of the particles plays an overriding role in the heat transfer process, since the solids particles have larger heat capacity and higher thermal conductivity. Most of the heat transfer models reported in the literature give emphasis to particle convective transfer. 

The particle convective heat transfer component is usually treated on the basis of the penetration or packet theory originally proposed by Mickley and Fairbanks (1955) assuming that the clusters are formed next to the immersed surface (e.g., Subbarao and Basu, 1986 Basu and Nag, 1987 Zhang et ai, 1987 Liu et ai, 1990). In that case, the clusters of solids and voids or dispersed phase are assumed to come into contact with the heat transfer surface alternatively, and the heat transfer coefficient can be given as follows ... 

Gas Convective Component. The gas convective component is caused by the gas percolating through the particulate phase and the gas bubbles coming in contact with the heat transfer surface. For small particles, though the contribution of gas convective component is small in the in-bed region, it could be important in the freeboard region. The gas convective... 

Ebert T, Glicksman L, Lints M. Determination of particle and gas convective heat transfer components in circulating fluidized bed. Chem Eng Sci 48 2179-2188, 1993. 

Heat transfer models are usually written in terms of either clusters or dense wall layers, based on the hydrodynamics of fast fluidization. For cluster models (Fig. 26), heat can be transferred between the suspension and wall by (1) transient conduction to particle clusters arriving at the wall from the bulk, supplemented by radiation (2) convection and radiation from the dispersed phase (gas containing a small fraction of solid material). The various components are usually assumed to be additive, ignoring interaction between the convective and radiation components. 

Heat transfer in circulating beds occurs by a combination of mechanisms solids convection, gas convection, and radiation. Solids convection is dominant at low temperature with radiation becoming dominant at high temperature and low suspension densities. Gas convection is a small component of the total heat transfer for the particle sizes currently used. 

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