Heat transfer coefficient radial distribution

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. 

Radial and Axial Distributions of Heat Transfer Coefficient... 

As opposed to the relatively uniform bed structure in dense-phase fluidization, the radial and axial distributions of voidage, particle velocity, and gas velocity in the circulating fluidized bed are very nonuniform (see Chapter 10) as a result the profile for the heat transfer coefficient in the circulating fluidized bed is nonuniform. 

When the particle holdup is high, the contribution of h plays a dominant role and hgc is less important. The radial distribution of the heat transfer coefficient is nearly parabolic, as shown in Fig. 12.16(a). Such a heat transfer profile is similar to the solids concentration profile described in Chapter 10. 

Figure 12.17. Effect of gas velocity on the radial distribution of the heat transfer coefficient in a circulating fluidized bed (from Bi et at., 1989).

Heat transfer studies on fixed beds have almost invariably been made on tubes of large diameter by measuring radial temperature profiles (1). The correlations so obtained involve large extrapolations of tube diameter and are of questionable validity in the design of many industrial reactors, involving the use of narrow tubes. In such beds it is only possible to measure an axial temperature profile, usually that along the central axis (2), from which an overall heat transfer coefficient (U) can be determined. The overall heat transfer coefficient (U) can be then used in one--dimensional reactor models to obtain a preliminary impression of longitudinal product and temperature distributions. 

Lu, H., Yang, L. D Bao, Y. L., and Chen, L. Z. The Radial Distribution of Heat Transfer Coefficient Between Suspensions and Immersed Vertical Tube in Circulating Fluidized Bed (Chinese), The Proceeding of 5th National Conference on Fluidization, pp. 164-167 (1990). 

B. Radial Distribution of Heat Transfer Coefficients 1. Influence of Operating Conditions... 

The effect of gas velocity on radial distribution of heat transfer coefficient is shown in Figs 9 and 10. With increasing gas velocity the heat transfer coefficients decrease. For the lower bed sections (see Fig. 10) the radial distributions are mainly affected by solids concentrations, and for the higher bed sections this trend changes significantly. 

The characteristic axial and radial distributions of heat transfer coefficients computed from the preceding formula are shown in Fig. 12. In the calculation, the sectional average voidage e can be established from any of the known... 

From the preceding discussion the radial distribution of heat transfer coefficient in fast fluidized beds can be distinguished as three types ... 

Figure 20 indicates that the ratio of hjh, between probes B and A, is in the range of 1.1 to 1.8 and keeps almost constant along the axial direction of the probe. The ratio of hjhx is large at low gas velocities, and when the probes are located at the center of the bed (see Fig. 20). This implies that the distribution of heat transfer coefficients, even with rings, along the radial direction of the bed becomes flatter at a higher bed level where solids concentration is low. Stated alternatively, with increasing gas velocity the influence of the rings on heat transfer coefficient diminishes.

In Chapter 5, Z. Yu and Y. Jin of THU describe experimental studies of heat transfer between particle suspensions and immersed surfaces, enumerating the effects of variables and of the radial and axial distribution of the heat transfer coefficient. They then present an analysis of the mechanism of heat transfer, particularly in terms of particle convection. 

Let the rate of energy per unit volume generated in a solid cylinder or a solid sphere be u" (r) = u , the radius and the thermal conductivity of the cylinder or the sphere be R and k(T) = kr (alternate notations ur and kr are used for convenience in the following formulation). Under steady conditions, the total energy generated in the cylinder or sphere is transferred, with a heat transfer coefficient h, to an ambient at temperature Too. This cylinder could be one of the fuel rods of a reactor core, or one of the elements of an electric heater, and the cylinder or sphere could be a bare, homogeneous reactor core. We wish to determine the radial temperature distribution. 

The axial temperature rise in the coolant, Eq. (2.183), the radial temperature drop and the axial temperature distribution in the fuel, the gap, the clad, and the coolant, Eq. (2.188), are sketched in Fig. 2.52. Some typical values encountered in practice for the radial temperature drop are ATpuei 1500 °C, AToap 150 — 300 °C, ATaad 50 °C, and ATbooiam 5 °C (for water). Also, some values for the geometry, thermal conductivity and heat transfer coefficient are ... 

Blasco and Alvarez [28] and Alvarez and Blasco [29] considered the application of flash drying to moisture removal of fish and soya meals. Heat, momentum, aud mass balauce equations were formulated. The model was solved numerically with appropriate coefficients of convective heat and mass transfer. Dilute phase transport of homogeneous radial mono-size particle distribution was considered. The conveying superheated steam was assumed to be an ideal gas. The initial period for heating the particles, during which condensation takes place, was neglected. Using the film theory [30], the effect of the mass transfer on the heat transfer coefficient... 

In the above equations, Cpr and Cp< denote heat capacities of the fluid and solid phases, pb is the bed density and hp is the heat transfer coefficient between fluid and particles. Transport of heat through the fluid phase in the axial direction and in the radial direction of the bed by conduction are described by the effective thermal conductivities, ka,i and kas, while in the solid phase thermal conduction can be assumed to be isotropic and the effective thermal conductivity ka can be used to express this effect. Q i represents the heat evolution/absorption by adsorption or desorption on the basis of bed volume. This model neglects the temperature distribution in the radial position of each particle, which may seem contradictory to the case of mass transfer, where intraparticle mass transfer plays a significant role in the overall adsorption rate. Usually in the case of adsorption, the time constant of heat transfer in the particle is smaller than the time constant of intraparticle diffusion, and the temperature in the particle may be assumed to be constant. 

The process result of heat transfer is a heat transfer coefficient. For dispersion it is a drop or particle size and size distribution. For blending in tanks it is blend time to achieve a certain degree of mixing. The equivalent for mixing in pipeline flow is not as clear. Alloca and Streiff (1980) proposed using a radial coefficient of variation, and this concept is now widely accepted. Since it is unique in the process industries to pipeline flow, it merits some extended discussion. 

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