Bed-to-surface heat transfer

For the bed-to-surface heat transfer in a dense-phase fluidized bed, the particle circulation induced by bubble motion plays an important role. This can be seen in a study of heat transfer properties around a single bubble rising in a gas-solid suspension conducted 

12 / Heat and Mass Transfer Phenomena in Fluidization Systems 

Particle convection, caused by the particle motion within the bed, is concerned with the heat transfer from a surface when it is in contact with the particulate emulsion phase instead of the void/bubble phase. Thus, the heat transfer coefficient of particle convection can be 

Considering the thermal diffusion through an emulsion packet and assuming that the properties of the emulsion phase are the same as those of minimum fluidization, h, can be expressed by [Mickley etal., 1961] 

The surface-emulsion phase contact time tc can be estimated by assuming that the time fraction for the surface to be covered by bubbles equals the bubble volume fraction in the bed 

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Bed-to-Surface Heat Transfer. Bed-to-surface heat-transfer coefficients in fluidized beds are high. In a fast-fluidized bed combustor containing mostly Group B limestone particles, the dense bed-to-boiling water heat-transfer coefficient is on the order of 250 W/(m -K). For an FCC catalyst cooler (Group A particles), this heat-transfer coefficient is around 600 W/(600 -K). 

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

Bed-to-surface heat transfer, 11 809—810 Beer, 3 561-589. See also Beer brewing Brewing entries brewing process for, 3 563, 564,... 

Normally, the heat-transfer rate is between 5 and 25 times that for the gas alone. Bed-to-surface-heat transfer coefficients vary according to the type of solids in the bed. Group A solids have bed-to-surface heat-transfer coefficients of approximately 300 J/(m2s-K) [150 Btu/(h-ft2-°F)]. Group B solids h ave bed-to-surface heat-transfer coefficients of approximately 100 J/(m2- s-K) [50 Btu/(h-ft2-°F)], while group D solids have bed-to-surface heat-transfer coefficients of 60 J/(m2-s-K) [30 Btu/(hft2 oF)]. 

Figure 12.13. Effect of temperature and pressure on h, hgc, and hmm for bed-to-surface heat transfer (from Botterill et al., 1981).

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) ... 

Compared to the fluidized bed, a spouted bed with immersed heat exchangers is less frequently encountered. Thus, the bed-to-surface heat transfer in a spouted bed mainly is related to bed-to-wall heat transfer. The bed-to-immersed-object heat transfer coefficient reaches a maximum at the spout-annulus interface and increases with the particle diameter [Epstein and Grace, 1997]. 

The bed-to-surface heat transfer coefficient may vary with the radial position in the bed. Wender and Cooper (1958) correlated the data of coefficients for heat transfer to immersed vertical tubes and proposed the following empirical correlation for 0.01 < Rep < 100... 

Geldart4 distinguished these powders as those for which umb/uml- > 1. At gas velocities above wmb bubbles begin to appear, which constantly split and coalesce, and a maximum stable bubble size is achieved. The flow of bubbles produces high solids and gas back-mixing, which makes the powders circulate easily, giving good bed-to-surface heat transfer. 

The overall mass and heat interphasc exchange coefficients can be obtained by summing the resistances from bubble to cloud and from cloud to emulsion (dense phase) in series. The overall bed to surface heat transfer coefficient is assumed to be mostly atuibuted to... 

Bed-to-Surface Heat Transfer. The heat transfer between the bed and the surface in spouted beds is less effective than in fluidized beds. The heat transfer primarily takes place by... 

TABLE 13.6 Influence of Surface Location and Orientation on Bed-to-Surface Heat Transfer Coefficient in a Circulating Fluidized Combustor (from Grace [86])... 

The influence of surface location and orientation on the bed-to-surface heat transfer coefficient in circulating fluidized bed combustors is summarized in Table 13.6. The geometric construction of the combustor and the heat transfer surface is shown in Fig. 13.17. Besides the location and orientation, differences in local heat transfer can also be found on the heat transfer surface/tube. For example, the upper part of the horizontal tube shows the smallest value for the heat transfer coefficient in dense-phase fluidized beds due to less frequent bubble impacts and the presence of relatively low-velocity particles. 

Excellent reviews of heat transfer in fluidized beds have been provided in books by Botterill [34] and Molerus and Wirth [35]. Many empirical and semiempirical correlations are available for predicting bed-to-surface heat transfer coefficients. The recommended one is that of Molerus and Wirth [35] ... 

In the freeboard region for bubbling and turbulent beds, the heat transfer coefficient falls off rapidly with increasing height as the particles, responsible for enhancing heat transfer, are disengaged and fall back onto the bed surface. If reactor temperatures exceed approximately 600°C, radiation also contributes appreciably to the overall bed-to-surface heat transfer. For start-up. 

Bed-to-surface heat transfer coefficient, W/m K Expanded bed height, m... 

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