Heat transfer, fluidized beds walls

The simplest correlations are of the form shown by Eq. (15), in attempts to recognize the strong influence of solid concentration (i.e., suspension density) on the convective heat transfer coefficient. Some examples of this type of correlation, for heat transfer at vertical wall of fast fluidized beds are ... 

Dou, S., Herb, B., Tuzla, K., and Chen, J. C., Dynamic Variation of Solid Concentration and Heat Transfer Coefficient at Wall of Circulating Fluidized Bed, Fluidization VII, 793-801 (1993)... 

The quasi-steady laminar model is now employed to describe the heat transfer near the wall. Note that while the shear stress at the wall can be related easily to the pressure drop for the flow in a tube, it is more difficult to establish a relation between these two quantities for a packed or fluidized bed. However, while for the flow in a tube the dissipated energy is not uniform over the section... 

Figure 1738. Heat transfer coefficient in fluidized beds [Wender and Cooper, AIChE J. 4, 15 (1958)]. (a) Heat transfer at immersed vertical tubes. All groups are dimensionless except kgICgpg, which is sqft/hr. The constant CR is given in terms of the fractional distance from the center of the vessel by CR = 1 + 3.175(r/R) — 3.188(r/R)2. (b) Heat transfer at the wall of a vessel. Lh is bed depth, Ot is vessel diameter.

Compared to the fluidized bed, a spouted bed with immersed heat exchangers is less frequently encountered. Thus, the bed-to-surface heat transfer in a spouted bed mainly is related to bed-to-wall heat transfer. The bed-to-immersed-object heat transfer coefficient reaches a maximum at the spout-annulus interface and increases with the particle diameter [Epstein and Grace, 1997]. 

Yoshida, K., Kunii, D. and Levenspiel, O. (1969). Heat Transfer Mechanisms Between Wall Surface and Fluidized Bed. Int. J. Heat Mass Transfer, 12, 529. 

Packed Bed Thermal Conductivity 587 Heat Transfer Coefficient at Walls, to Particles, and Overall 587 Fluidized Beds 589... 

In the transition zone and the freeboard region, heat transfer between bed and wall is a function of bed density. Shirai et al. (S9, Sll) studied heat transfer from a sphere immersed in the fluidized bed and showed the trend of decreasing heat-transfer coefiicient with decreasing bed density. 

Heat Transfer to the Wall A number of investigations of heat-transfer coefficients at the wall in fluidized beds have been reported, and in all cases the values found for h, were considerably larger than those for an empty tube at the same fluid velocity. Presumably this is because the motion of solid particles near the wall tends to prevent the development of a slow-moving layer or film of gas, and the heat-carrying capacity of the particles themselves as they move between the center and the wall of the reactor is significant. 

Fluidized beds of fine solids are used for catalytic reactions in the petroleum and chemical industries, where the main advantages are nearly uniform temperature, good heat transfer to the wall or immersed surfaces, high effectiveness factors (because of the small particle size), and easy transfer of solids from one vessel to another. Fluidized beds are also used for combustion of coal, reduction of ores, and other solid-gas reactions, and these processes often use moderately large particles. 

Wear (also called wastage and erosion) of surfaces is a serious operational issue in some fluidized-bed reactors. Wear occurs when hard particles (e.g., silica-supported catalyst particles) continually strike fixed surfaces such as heat transfer tubes, reactor walls, or cyclone inner surfaces. The most damaging collisions tend to be those which are oblique (e.g., at 60 ) to the surface, for example, at about the 5 and 7 o clock positions, when bubble wakes slam into the underside of horizontal heat transfer tubes. If corrosion is also a factor, then the combined damage from erosion and corrosion can be considerably more extensive than estimated from the summation of the individual effects. 

In a bubbling fluidized bed the coefficient of heat transfer between bed and immersed surfaces (vertical bed walls or tubes) can be considered to be made up of three components which are approximately additive (Botterill, 1975). 

Solid mass flow flux and velocity also vary across the radius of fast fluidized beds. Experimental measurements obtained by Herb et al. (1992) show that while local solid fluxes are positive upward in the core of the bed, they can become negative downward in the region near the bed wall. The difference between core and wall regions becomes increasingly greater as total solid mass flux increases. The downward net flow of solid in the region near the bed wall has significance for heat transfer at the wall. 

Since gas density is usually negligible compared to solid density, pb is essentially equal to the mass concentration of solid per unit mixture volume. Some examples of this type of correlation, for convective heat transfer at vertical walls of fast fluidized beds, are given below. Due to accumulating evidence that the vertical size of the heat transfer surface affects the average the correlations are divided with regard to short or long surfaces. 

Dou S, Herb B, Tuzla K, Chen JC. Dynamic variation of solid concentration and heat transfer coefficient at wall of circulating fluidized bed. In Potter OE, Nicklin DJ, ed. Fluidization VII. New York Engineering Foundation, 1993, pp 793-801. 

Nag PK, Moral MNA. Effect of probe size on heat transfer at the wall in circulating fluidized beds. J Inst Energy Res 14 965-974, 1990. 

Figure 11 Heat transfer coefficient between wall and liquid for packed bed, fluidized bed, and single-phase flow as a function of superficial liquid velocity. (After Haid et al., 1994 data points from Kato et al., 1981.)... 

FIG. 7.41. Fluctuations of local heat transfer coefficient from wall to fluidized beds [42]. Glass beads, wo == 18.6 cm/sec. 

Zenz and Othmer (see Introduction General References ) give an excellent summary of fluidized bed-to-wall heat-transfer investigations. 

Ostergaard (02) measured the wall-to-bed heat-transfer coefficient in a bed of 3-in. diameter. The media were air, water, and glass ballotini of0.5-mm diameter. It was observed that the heat-transfer coefficient for a liquid fluidized bed near the point of incipient fluidization could be approximately... 

Values for the various parameters in these equations can be estimated from published correlations. See Suggestions for Further Reading. It turns out, however, that bubbling fluidized beds do not perform particularly well as chemical reactors. At or near incipient fluidization, the reactor approximates piston flow. The small catalyst particles give effectiveness factors near 1, and the pressure drop—equal to the weight of the catalyst—is moderate. However, the catalyst particles are essentially quiescent so that heat transfer to the vessel walls is poor. At higher flow rates, the bubbles promote mixing in the emulsion phase and enhance heat transfer, but at the cost of increased axial dispersion. 

General Characteristics. Energy addition or extraction from fast fluidized beds are commonly accomplished through vertical heat transfer surfaces in the form of membrane walls or submerged vertical tubes. Horizontal tubes or tube bundles are almost never used due to concern with... 

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. 

Gabor, J. O., Wall-to-Bed Heat Transfer in Fluidized and Packed beds, AIChE Symp. Series, 66(105) 76-86 (1970)... 

Lints, M., Particle to Wall Heat Transfer in Circulating Fluidized Beds, Ph.D. Dissertation, MIT (1992)... 

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