Heat transfer coefficient gas-particle

For a single sphere in a stagnant environment, i.e. where there is no convection, the limiting value of the Nusselt number can be shown (see, for example, Kay and Nedderman, 1985) to be 

This represents the lowest possible value of the film heat transfer coefficient when no natural or forced convection currents are present. When there is a relative velocity between the sphere and the surrounding fluid the heat transfer coefficient will increase and heat transfer will improve. Thus for heat transfer to and from spherical particles, correlations take the form of equation 2.8 

However, for Re 10 the experimental values of Nu fall sharply with decreasing Reynolds number, well below the theoretical minimum of Nu = 2. This is attributable in part to experimental difficulties, for example fhe problem of measuring particle temperature, and in part to the theoretical interpretation of the data. Botterill (1975) posed the question of what exactly is measured by a bare wire thermocouple inserted in a fluidized bed. Despite the uncertainties in the experimental evidence, Botterill concluded that it probably does indeed measure the particle temperature. This was the assumption of Smith and Nienow (1982) who used bare wire thermocouples to measure bed particle temperatures during fluidized bed granulation. In the region Re 10, as Kunii and Levenspiel (1991) indicate, the data can be represented by an expression due to Kothari 

However, Botterill (1975) suggests that this high dependence on Reynolds number is not consistent with other studies and that, based on the work of Rabinovich with 25 mm particles, a more reasonable index on Re would be 0.77. 

Kunii and Levenspiel (1991) identify two kinds of heat transfer coefficient to describe gas-particle heat transfer. The coefficient for a single particle, or local coefficient. If, is that pertaining to a single particle at high temperature Tj, introduced suddenly into a bed of cooler particles at a temperature and is defined by 

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Kunii and Levenspiel (1991) summarised the experimentally determined values of fhe gas-particle heat transfer coefficient If, and the data are shown in Figure 2.1. At Re > 100 the value of Nu lies between that for a single particle and a fixed bed and these authors suggest that the relevant correlations are those due to Ranz, equations 2.9 and 2.10 respectively ... 

Figure 2.1 Experimental gas-particle heat transfer coefficients. Adapted from Kunii, D. and Levenspiel, O., Fluidization engineering, 1991, with permission from Elsevier.

Table 2.1 Example calculation of gas-particle heat transfer coefficients.

Persson (1967) measured the variation in gas-particle heat transfer coefficient with particle diameter. Figure 3.5 shows the heat transfer coefficient for both an unspecified maximum gas velocity and for Fr = 120. For Fr = 120, h falls from approximately 130 Wm K at a diameter of 3mm to lOOWm K at a diameter of 16mm, these particle sizes corresponding to superficial gas velocities of 1.88ms and 4.33ms respectively. For larger diameters the heat transfer coefficient becomes approximately constant at 85Wm K . ... 

Figure 3.5 Variation in gas-particle heat transfer coefficient with particle diameter (A = fluidized bed at maximum air velocity B = fluidized bed at Fr = 120 C = flat surface velocity as for curve B). Adapted from Persson, ASHRAE Journal, June 1967. American Society of Heating, Refrigerating and Air-Conditioning...

Vazquez, A. and Calvelo, A., Gas particle heat transfer coefficient in fluidized pea beds, /. Food Proc. Eng., 4 (1980) 53-70. 

S.C.S. Rocha, Contribution to the study of pneumatic drying simulation and influence of the gas-particle heat transfer coefficient, Ph.D. Thesis, Sao Paulo University, Sao Paulo, Brazil, (in Portuguese), 1988. 

Littman, H. and Sliva, D. E. (1971). Gas-Particle Heat Transfer Coefficient in Packed Beds at Low Reynolds Number. In Heat Transfer 1970, Paris-Versailles, CT 1.4. Amsterdam ... 

Gas to particle heat transfer coefficients are t3q>ically small, of the order of 5-20 W m K. However, because of the very large heat transfer surface area provided by a mass of small particles (1 m of 100 pm particles has a surface area of 60 000 m ), the heat transfer between gas and particles is rarely limiting in fluid bed heat transfer. One of the most commonly used correlations for gas-particle heat transfer coefficient is that of Kunii and Levenspiel (1969) ... 

Integration of Eq. (6) for S02 in Table V estimates the conversion achieved. Simulation of periodic symmetrical switching between a reactant mixture and air gave an estimate of 99.4% at 12 min after the switch to the S03/S02 reactant mixture in reasonable agreement with the overall conversion of 98.8% measured by Briggs et al. (1977). With respect to model sensitivity, it was found that bed midpoint temperature was sensitive to the wall and gas to particle heat transfer coefficients. An extensive study of sensitivity, however, was not undertaken. 

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... 

One method of improving G/S contacting consists of showering solids in dilute suspension from the top into an upflowing gas stream. Experiments verified that gas/solid heat transfer coefficient for such a system is essentially the same as for the discrete particles, and that pressure drop for gas flow is extremely low. 

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). 

Investigator Type of correlation Phases involved Region associated Rowe and Claxton [82] Gas-to-particle heat transfer coefficient Gas-solid Central spouting region... 

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. 

In general, the average gas-to-particle heat transfer coefficients for ISDs are much higher than those in classical dryers that operate under similar hydrodynamic regimes. For example, when the heat... 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

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