Bed-to-Surface Heat Transfer Coefficient

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). 

The radiant heat transfer coefficient becomes important above about 600°C, but is difficult to predict. Baskakov et al. (1973) report that depending on particle size, hr increases from approximately 8% to 12% of the overall heat transfer coefficient at 600°C, to 20 to 33% of h at 800°C. 

Botterill et al. (1982) measured the overall heat transfer coefficient as a function of particle size for sand at three different conditions 20°C and ambient pressure, 20°C and 6 atmospheres, and 600°C and ambient pressure. They found that there was a significant increase in h with pressure for Group D particles, but the pressure effect decreased as particle size decreased. At the boundary between Groups A and B, the increase of h with pressure was very small. 

The effect of pressure on the heat transfer coefficient is influenced primarily by hgc (Botterill and Desai, 1972 Xavier etal., 1980). This component of h transfers heat from the interstitial gas flow in the dense phase of the fluidized bed to the heat transfer surface. For Group A and small Group B particles, the interstitial gas flow in the dense phase can be assumed to be approximately equal to Um ed. 6/i s extremely small for 

Increasing system temperature causes hgc to decrease slightly because increasing temperature causes gas density to decrease. The thermal conductivity of the gas also increases with temperature. This causes h to increase because the solids are more effective in transferring heat to a surface. Because hgc dominates for large particles, the overall heat transfer coefficient decreases with increasing temperature. For small particles where dominates, h increases with increasing temperature. 

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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). 

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... 

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)]. 

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... 

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... 

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. 

The heat transfer behavior in a spouted bed is different from that in the dense-phase or circulating fluidized bed system due to the inherent differences in their flow structures. The gas-to-particle heat transfer coefficient in the annulus region is usually an order of magnitude higher than that in the central spout region. The bed-to-surface heat transfer coefficient reaches a maximum at the spout-annulus interface and also increases with the particle diameter. 

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] ... 

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

Characterized by high fluidized bed-to-surface heat transfer coefficients that result in compact heat exchanger surface even with the lower temperature driving forces relative to stokers and pulverized fuel-fired combustors. 

The bed-to-surface heat transfer coefficient (about 85 280 W/m °C) by solids convection and radiation is lower in circulating bed AFBC than in bubbling bed AFBC due to the lower bed density and vertical heat transfer surface orientation, and the heat transfer coefficient decreases with increased height. The dilute zone of the furnace is water-walled, with the heat transfer surfaces placed at the perimeter of the rectangular vessel enclosure. Additional vertical heat transfer surface walls or wing walls may be hung within the vessel to increase its heat removal capacity. Another means to increase the heat transfer surface is to place an exter-... 

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