Heat transfer coefficient single particle

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

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 ... 

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... 

Because of the rather complex temperature patterns, the true average temperature difference for the dryer as a whole is not easy to define. Sometimes, in fact, the outlet temperature of solids and gas are so nearly the same that the difference between them cannot be measured. Heat-transfer coefficients are therefore hard to estimate and may be of limited utility. One general equation that is useful in drying ealculations is Eq. (12.70) for heat transfer from a gas to a single or isolated spherical particle ... 

It should be noted that As/for a heated single particle in an otherwise uniform temperature field is expected to be significantly different than that for particles in packed beds. Also, since, in general, the thermal conductivity of the solid is not large enough to lead to an isothermal surface temperature, the conductivity of the solid also influences the temperature field around it. Therefore, the interstitial convection heat transfer coefficient obtained from a given fluid-solid combination is not expected to hold valid for some other combinations... 

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). 

Heat transfer in gas-fluidized bed can occur by conduction, convection, and radiation depending on the operating conditions. The contribution of the respective modes of heat transfer to the coefficient of heat transfer depends on particle classification, flow condition, fluidization regimes, type of distributor, operating temperature, and pressure. Heat transfer between a single particle and gas phase can be defined by the conventional equation of heat transfer ... 

The valne of heat transfer coefficient of a single particle in a flnidized bed system is generally not high. It is in the range 1-700 W/(m K). However, due to the large interfacial snrface area, in the order of 3,000-45,000 m /m extremely high rates of heat transfer are achieved in this system. The heat capacity is in the order of 10 J/(m K). As a resnlt, thermal eqnilibrinm is reached quickly. In designing FBDs, an isothermal condition is often assumed. 

Similar results are reported from the drying of bark and peat in superheated steam in a pilot-plant pneumatic conveying dryer [22], The results are presented as a convective apparent heat-transfer coefficient, defined with the assumption that the temperature of the particle surface coincides with the saturation temperature of the transport steam. This transfer coefficient shows a clear dependence on the moisture content of the particles and the particle sizes. Fyhr [23] presented a model for a pneumatic conveying steam dryer. The dryer model consists of two submodels, one for the single particle and the other for the hydrodynamics of gas and particles in the dryer. 

Quasi-continuum models Of these, the quasi-continuum model is the most common. Here, the solid-fluid system is considered as a single pseudo-homogeneous phase with properties of its own. These properties, for example, diffusivity, thermal conductivity, and heat transfer coefficient, are not true thermodynamic properties but are termed as effective properties that depend on the properties of the gas and solid components of the pseudo-phase. Unlike in simple homogeneous systems, these properties are anisotropic, that is, they have different values in the radial and axial directions. KuUcami and Doraiswamy (1980) have compiled all the equations for predicting these effective properties. Both radial and axial gradients can be accounted for in this model, as well as the fact that the system is really heterogeneous and hence involves transport effects both within the particles and between the particles and the flowing fluid. 

Heat transfer between particles and gas in a fluidized bed may be compared to gas convection from a single fixed particle, and to gas convection from a packed bed of fixed particles. A common definition of the heat transfer coefficient can be used for all three cases, based on the surface area of a single particle (op),... 

It should be noted that the Prandtl number term in these two equations is somewhat speculative, since the experimental data did not cover a sulficient range for good correlation. Equations (12) and (13) include Pr to the 0.33 power, based on the expectation that dependence is similar to that for single spheres, as shown in Eq. (11). In applying heat transfer coefficients calculated by Eqs. (12) and (13), it is important to use a model that considers the particles to be well mixed and the gas to be in plug flow, in order to be consistent with the definition of as discussed above. 

Many different models and correlations have been proposed for the prediction of the heat transfer coefficient at vertical surfaces in FFBs. At time of this writing, no single correlation or model has won general acceptance. The following discussion presents a summary of some potentially useful approaches. It is helpful to consider the total heat transfer coefficient as eomposed of convective contributions from the lean-gas phase and the dense-particle phase plus thermal radiation, as defined by Eqs. (15) and (16). All eorrela-tions based on ambient temperature data, where thermal radiation is negligible, should be considered to represent only the convective heat transfer coefficient hr. 

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