Clusters heat transfer

Fig. 21. Mechanism of cluster heat transfer (a) at bed axis, (b) near bed wall (Bai et al., 1991).

After venting of the elongated bubble, the region of liquid droplets begins. The vapor phase occupies most of the channel core. The distinctive feature of this region is the periodic dryout and wetting phenomenon. The duration of the two-phase period, i.e., the presence of a vapor phase and micro-droplet clusters on the heated wall, affects the wall temperature and heat transfer in micro-channels. As the heat flux increases, while other experimental conditions remain unchanged, the duration of the two-phase period decreases, and CHF is closer. 

Bowring, R. W., 1967a, HAMBO A Computer Programme for the Sub-Channel Analysis of the Hydraulic and Burnout Characteristics of Rod Clusters, European Two-Phase Heat Transfer Meeting, U.K., Durey Hall, Bournemouth, England. (3)... 

Gaspari, G. P, A. Hassid, and G. Vanoli (CISE), 1970, Some Consideration on Critical Heat Flux in Rod Clusters in Annular Dispersed Vertical Upward Two-Phase Flow, Proc. 1970 Inti. Heat Transfer Conference, Vol 6, Paper B 6.4, Paris, Hemisphere, Washington, DC. (5)... 

Figure 26. Comparison of predictions from cluster-based model to heat transfer data. (From Lints and Glicksman, 1993.)...

An alternate to the concept of cluster renewal discussed above is the concept of two-phase convection. This second approach disregards the separate behavior of lean and dense phases, instead models the time average heat transfer process as if it were convective from a pseudo-homogeneous particle-gas medium. Thus h hcl, hh and hd are not... 

Equation (293) cannot be applied to gas fluidized beds because in the latter case, the fluidized bed contains a large number of bubbles. The rate of heat transfer between the bed and wall is determined in the latter case by the heat transfer in the packets (clusters) of solid particles (through which the gas flows at the minimum fluidization velocity) which are exchanged, because of bubbling, between the wall and the bulk of the fluidized bed [74], The heat transfer coefficient is given in the latter case by an expression similar to Eq. (282) ... 

The suspension-to-wall surface heat transfer mechanism in a circulating fluidized bed (see Chapter 10) comprises various modes, including conduction due to particle clusters on the surface or particles falling along the walls, thermal radiation, and convection due to... 

In circulating fluidized beds, the clusters move randomly. Some clusters are swept from the surface, while others stay on the surface. Thus, the heat transfer between the surface and clusters occurs via unsteady heat conduction with a variable contact time. This part of heat transfer due to cluster movement represents the main part of particle convective heat transfer. Heat transfer is also due to gas flow which covers the surface (or a part of surface). This part of heat transfer corresponds to the gas convective component. 

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) ... 

An alternative treatment for radiative heat transfer in a circulating fluidized bed is to consider the radiation from the clusters (hcx) and from the dispersed phase (i.e., the remaining aspect of gas-solid suspension except clusters, A ), separately [Basu, 1990]... 

In general, small/light particles can enhance heat transfer. The cluster formation in small/light particle systems contributes to the enhancement of hpc. Also the gas film resistance can be reduced by fluidizing with small particles [Wu et al., 1987]. When the temperature is lower than 400°C, the effect of bed temperature on the heat transfer coefficient is due to the change of gas properties, while hr is negligible. At higher temperatures, h increases with temperature, mainly because of the sharp increase of radiative heat transfer. 

Derive the axial profile of the particle convective heat transfer coefficient in a circulating fluidized bed of fine particles using the information given in 10.4.1. It can be assumed in the derivation that particles in the bed are all in a cluster form. 

The local heat transfer coefficients measured by both probe B and probe A are compared in Fig. 19. The local heat transfer coefficient for probe B is evidently larger than that for probe A. This difference in local heat transfer coefficients measured by the two probes gradually decreases from top to bottom of the probes at any radial position in the bed. Such enhancement in heat transfer is attributed to the promotion of cluster layer renewal surrounding the probe, as has been well recognized (Glicksman, 1988 Wu et al, 1989, 1990 Basu, 1990 Leckner, 1991 and Bai et al., 1990). 

In addition to direct contact with clusters, the wall of a fast bed is constantly exposed to the up-flowing gas, which contains dispersed solids (Li et ai, 1988). The gas convective component can be estimated on the basis of correlations for gas flow alone through the column, at the same superficial gas velocity and with the same physical properties. When a tall heat transfer surface is used or the bed is operated at high solids concentrations, errors caused by using different approaches will usually be small since htc is generally much less than hpc, provided the solids concentration is low and temperature high. 

The particle convective heat transfer component is usually treated on the basis of the penetration or packet theory originally proposed by Mickley and Fairbanks (1955) assuming that the clusters are formed next to the immersed surface (e.g., Subbarao and Basu, 1986 Basu and Nag, 1987 Zhang et ai, 1987 Liu et ai, 1990). In that case, the clusters of solids and voids or dispersed phase are assumed to come into contact with the heat transfer surface alternatively, and the heat transfer coefficient can be given as follows ... 

Subbarao and Basu (1986), Basu and Nag (1987) and Basu (1990) derived the expression of cluster residence time lc on the heat transfer surface based on Subbarao s (1986) cluster model, although the model is not widely accepted. Lu et ai (1990) and Zhang et al. (1987) have also obtained empirical correlations independently for predicting cluster residence time based on their heat transfer experiments. However, because of the lack of available and reliable information about the residence time of clusters at the surface and the fraction of the clusters in solids suspension, a significant discrepancy between the results predicted by the different approaches mentioned earlier has been observed. Besides, it should be pointed out that the major shortcoming in the earlier models is that they all take no account of the heat transfer surface length. 

To account for the influence of the length of the heat transfer surface on heat transfer, several cluster-layer type models have been reported in the literature (Glicksman, 1988 Wu et al., 1990 Mahalingam et al., 1991 Basu, 1990). However, all these models can only be applied to heat transfer between the suspension and the walls. 

When the heat transfer surface is immersed in the bed at any radial position, the solids particles form a downflowing cluster layer surrounding the surface. The thickness of the cluster layer grows up to reach a Anal constant value. 

Heat transfer between the cluster layer and the surface is mainly caused by unsteady particle convection. The cluster layer is renewed from time to time by the moving particles and fluidizing gas. 

Equation (7) shows that the local heat transfer coefficient is a function of the thickness and the renewal frequency of the cluster layer. If the gas-solids flow is fully developed and rb dp, Eq. (7) can be simplified to... 

This is based on the assumption that the voidage at the heat transfer surface is mf, and the voidage varies linearly with radial distance within the cluster... 

The renewal frequency of the cluster layer at the heat transfer surface is mainly dependent on the solids exchange rate between the layer and the other suspension, and usually assumed to be proportional to the ratio of the characteristic velocity to the characteristic length. Here we define... 

The parameter C represents the probability of contact between the cluster and the heat transfer surface when the cluster layer velocity remains constant. 

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