Bed-to-gas heat transfer

For suspension-to-gas (or bed-to-gas) heat transfer in a well-mixed bed of particles, the heat balance over the bed under low Biot number (i.e., negligible internal thermal resistance) and, if the gas flow is assumed to be a plug flow, steady temperature conditions can be expressed as... 

Figure 12.9. Particle-to-gas and bed-to-gas heat transfer coefficients under various flow conditions (from Kunii and Levenspiel, 1991).

Particle-to-Gas and Bed-to-Gas Heat Transfer. The particle-to-gas heat transfer can be quantified by unsteady-state experiments that measure the time required for cold particles of temperature Tp0, mass M, and surface area Sp to reach the bed temperature when they are introduced into the bed. The local particle-to-gas heat transfer coefficient /igp can be given by the equation... 

Investigator Type of correlation Phases involved Kunii and Levenspiel [2] Bed-to-gas heat transfer coefficient Gas-solid... 

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 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... 

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)]. 

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... 

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 particle-to-gas heat transfer coefficient in dense-phase fluidization systems can be determined from correlation Eq. 13.3.1 [2] given in Table 13.3. The correlation indicates that the values of particle-to-gas heat transfer coefficient in a dense-phase fluidized bed lie between those for fixed bed with large isometric particles (with a factor of 1.8 in the second term [49]) and those for the single-particle heat transfer coefficient (with a factor of 0.6 in the second term of the equation). 

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. 

J. Shen, S. Kaguei, and N. Wakao, Measurement of Particle-to-Gas Heat Transfer Coefficients From One-Shot Thermal Response in Packed Beds, Chem. Eng. Sci. (36) 1283,1981. 

Shen, J., Kaguel, S., and Wakao, N., Measurements of particle to gas heat transfer coefficients from one shot thermal response in packed beds, Chem. Eng. Sci., 36(8) 1283-1286,1981. 

For catalytic reactions, particles used in fluidized bed processes are usually in the range of 40 to 100 pm in mean diameter. Similarly, particle-to-gas heat transfer coefficients in dense phase fluidized beds can be estimated by (Kunii and Levenspiel, 1991) ... 

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