Heat transfer in the bed

The performance of a fluidized bed combustor is strongly influenced by the fluid mechanics and heat transfer in the bed, consideration of which must be part of any attempt to realistically model bed performance. The fluid mechanics and heat transfer in an AFBC must, however, be distinguished from those in fluidized catalytic reactors such as fluidized catalytic crackers (FCCs) because the particle size in an AFBC, typically about 1 mm in diameter, is more than an order of magnitude larger than that utilized in FCC s, typically about 50 ym. The consequences of this difference in particle size is illustrated in Table 1. Particle Reynolds number in an FCC is much smaller than unity so that viscous forces dominate whereas for an AFBC the particle Reynolds number is of order unity and the effect of inertial forces become noticeable. Minimum velocity of fluidization (u ) in an FCC is so low that the bubble-rise velocity exceeds the gas velocity in the dense phase (umf/cmf) over a bed s depth the FCC s operate in the so-called fast bubble regime to be elaborated on later. By contrast- the bubble-rise velocity in an AFBC may be slower or faster than the gas-phase velocity in the emulsion... 

Adsorption is an exothermic process, and a bed temperature rise of 10 to 50°C may result when treating vapors with only 1 percent adsorbable component. In small-diameter beds, heat loss will limit the temperature rise, but a large unit will operate almost adiabatically, and significant differences in performance could result. In such cases, a large-diameter pilot column should be used or detailed calculations made to account for heat release and heat transfer in the bed. 

Early attempts to get a correlation for similar to the correlations for pipe flow showed wide variations in the exponents for the dimensionless groups and even differences in the equations for heating and cooling [26,27]. Such variations are understandable when we consider the different mechanisms of heat transfer in the bed itself and in the gas film at the wall. 

Heat transfer in the bed of a rotary kiln is similar to heat transfer in packed beds except that in addition to the heat flow in the particle assemblage of the static structure (Figure 8.3), there is an additional contribution of energy transfer as a result of advection of the bed material itself. The effective thermal conductivity of packed beds can be modeled in terms of thermal resistances or conductance within the particle ensemble. As shown in Figure 8.3 almost all the modes of heat transfer occurs within the ensemble, that is, particle-to-particle conduction and radiation heat transfer as well as convection through the interstitial gas depending upon the size distribution of the material and process temperature. Several models are available in the literature for estimating the effective thermal conductivity of packed beds. 

Equation (4.10.157) may also be used to estimate the maximum temperature difference that we have to expect in the radial direction within the bed. Instead of the overall heat transfer coefficient to the wall, we then only have to consider the heat transfer in the bed and not the one located in the small region near the wall. If we use 8Xnd/dp instead of l/h in Eq. (4.10.158) we obtain ... 

The bed and the fluid are considered as a pseudo-homogeneous medium, and the heat transfer in the bed up to the internal side of the wall is represented by two parameters, the radial effective conductivity snd the internal wall heat transfer coefiident aw,int- The introduction of aw.mt allows us to take into account a weaker heat transfer (smaller effective radial heat transfer coefficient X ad) close to the wall due to less mixing and a higher void fraction of the bed (Figure 4.10.64). Thus, combines the interplay of convective flow at the wall and of conduction by contact between the bed and the heat exchange surface (internal wall), and assumes a jump in temperature direcily at the wall. For relative simple modeling, the consequence of the introduction of mt is also that we use a constant value of within the bed. 

As explained in Section 4.10.7.3, Eq. (6.13.20) considers the bed and the fluid as a pseudo-homogeneous medium, and the heat transfer in the bed up to the internal side of the wall is represented by a constant radial effective conductivity and the... 

The characteristic length for heat transfer in the bed is Zq = Fp CJhaS = vpCJha... 

The applieation of aetivated earbons in adsorption heat pumps and refrigerators is diseussed in Chapter 10. Sueh arrangements offer the potential for inereased efficiency because they utilize a primary fuel source for heat, rather than use electrieity, which must first be generated and transmitted to a device to provide mechanical energy. The basic adsorption cycle is analyzed and reviewed, and the ehoiee of refrigerant-adsorbent pairs discussed. Potential improvements in eost effeetiveness are detailed, including the use of improved adsorbent carbons, advanced cycles, and improved heat transfer in the granular adsorbent earbon beds. 

Correlations for heat transfer in packed-beds are still being developed. The current state of the art is represented by... 

Argo and Smith (106, 107) have presented a detailed discussion of heat transfer in packed beds and have proposed the following relation for the effective thermal conductivity in packed beds ... 

Palchonok, G. I., Breitholz, C., Anderson, B. A., and Lechner, B., Heat Transfer in the Boundary Layer of a Circulating Fluidized Bed Boiler, Fluidization... 

Zabrodsky, S. S. Hydrodynamics and Heat Transfer in Fluidized Beds (The M.I.T. Press, 1966). 

In considering heat transfer in gas-solid fluidization it is important to distinguish between, on the one hand, heat transfer between the bed and a heat transfer surface (be it heated bed walls or heat transfer coils in the bed) and, on the other hand, heat transfer between particles and the fluidizing gas. Much of the fluidization literature is concerned with the former because of its relevance to the use of fluidized beds as heterogeneous chemical reactors. Gas-particle heat transfer is rather more relevant to the food processing applications of fluidization such as drying, where the transfer of heat from the inlet gas to the wet food particle is crucial. 

The use of the Plank/Nagaoka model can be illustrated with a simple example. Consider a fluidized bed 0.75 m wide and 5 m long which is used to freeze peas 8 mm in diameter at a rate of 6000kgh k Assume that the peas enter the bed at 12°C, have a freezing temperature of -2°C and that the fluidizing air enters the bed at -35°C and at a velocity such that the heat transfer coefficient (see Heat transfer in fluidized bed freezers, below) is 170Wm K k What is the necessary bed depth ... 

Sheen, S. and Whitney, L.F., Modelling heat transfer in fluidized beds of large particles and its applications in the freezing of large food items, J. Food Eng., 12 (1990) 249-265. 

The staged adiabatic packed bed reactor of Fig. 19.1c presents a different situation. Since there is no heat transfer in the zone of reaction the temperature and conversion are related simply, hence the methods of Chapter 9 can be applied directly. We will examine numerous variations of staging and heat transfer to show that this is a versatile setup which can closely approximate the optimum. 

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) ... 

All types of catalytic reactors with the catalyst in a fixed bed have some common drawbacks, which are characteristic of stationary beds (Mukhlyonov et al., 1979). First, only comparatively large-grain catalysts, not less that 4 mm in diameter, can be used in a filtering bed, since smaller particles cause increased pressure drop. Second, the area of the inner surface of large particles is utilized poorly and this results in a decrease in the utilization (capacity) of the catalyst. Moreover, the particles of a stationary bed tend to sinter and cake, which results in an increased pressure drop, uneven distribution of the gas, and lower catalyst activity. Finally, porous catalyst pellets exhibit low heat conductivity and as a result the rate of heat transfer from the bed to the heat exchanger surface is very low. Intensive heat removal and a uniform temperature distribution over the cross-section of a stationary bed cannot, therefore, be achieved. The poor conditions of heat transfer within... 

Froessling, N. (1938). The Evaporation of Falling Drops. Gerlands Beitr. Geophys., 52,170. Gel Perin, N. I. and Einstein, V. G. (1971). Heat Transfer in Fluidized Beds. In Fluidization. Ed. 

In a well-fluidized gas-solid system, the bulk of the bed can be approximated to be isothermal and hence to have negligible thermal resistance. This approximation indicates that the thermal resistance limiting the rate of heat transfer between the bed and the heating surface lies within a narrow gas layer at the heating surface. The film model for the fluidized bed heat transfer assumes that the heat is transferred only by conduction through the thin gas film or gas boundary layer adjacent to the heating surface. The effect of particles is to erode the film and reduce its resistive effect, as shown by Fig. 12.3. The heat transfer coefficient in the film model can be expressed as... 

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