Heat transfer coefficient particle effects

The effective thermal conductivity of a Hquid—soHd suspension has been reported to be (46) larger than that of a pure Hquid. The phenomenon was attributed to the microconvection around soHd particles, resulting in an increased convective heat-transfer coefficient. For example, a 30-fold increase in the effective thermal conductivity and a 10-fold increase in the heat-transfer coefficient were predicted for a 30% suspension of 1-mm particles in a 10-mm diameter pipe at an average velocity of 10 m/s (45). 

The effect of the particle properties on the overall heat-transfer coefficient was investigated in our laboratory (43) for an acrylic precipitation polymerization as shown in Figure 6. 

Botterill et al. (1982) measured the overall heat transfer coefficient as a function of particle size for sand at three different conditions 20°C and ambient pressure, 20°C and 6 atmospheres, and 600°C and ambient pressure. They found that there was a significant increase in h with pressure for Group D particles, but the pressure effect decreased as particle size decreased. At the boundary between Groups A and B, the increase of h with pressure was very small. 

The effect of pressure on the heat transfer coefficient is influenced primarily by hgc (Botterill and Desai, 1972 Xavier etal., 1980). This component of h transfers heat from the interstitial gas flow in the dense phase of the fluidized bed to the heat transfer surface. For Group A and small Group B particles, the interstitial gas flow in the dense phase can be assumed to be approximately equal to Um ed. 6/i s extremely small for... 

Increasing system temperature causes hgc to decrease slightly because increasing temperature causes gas density to decrease. The thermal conductivity of the gas also increases with temperature. This causes h to increase because the solids are more effective in transferring heat to a surface. Because hgc dominates for large particles, the overall heat transfer coefficient decreases with increasing temperature. For small particles where dominates, h increases with increasing temperature. 

Figure 4. Effect ofmixed particle sizes, (a) Particle size distribution, (b) Circumferential-average heat transfer coefficients. (Data ofBiyikli and Chen, 1982).

In contrast to the strong effect of gas properties, it has been found that the thermal properties of the solid particles have relatively small effect on the heat transfer coefficient in bubbling fluidized beds. This appears to be counter-intuitive since much of the thermal transport process at the submerged heat transfer surface is presumed to be associated with contact between solid particles and the heat transfer surface. Nevertheless, experimental measurements such as those of Ziegler et al. (1964) indicate that the heat transfer coefficient was essentially independent of particle thermal conductivity and varied only mildly with particle heat capacity. These investigators measured heat transfer coefficients in bubbling fluidized beds of different metallic particles which had essentially the same solid density but varied in thermal conductivity by a factor of nine and in heat capacity by a factor of two. 

Figure 6. Effect of bed temperature on heat transfer coefficient for bubbling bed of ceramic particles. (Data of Yoshida, Ueno and Kunii, 1974.)...

The interaction of parametric effects of solid mass flux and axial location is illustrated by the data of Dou et al. (1991), shown in Fig. 19. These authors measured the heat transfer coefficient on the surface of a vertical tube suspended within the fast fluidized bed at different elevations. The data of Fig. 19 show that for a given size particle, at a given superficial gas velocity, the heat transfer coefficient consistently decreases with elevation along the bed for any given solid mass flux Gs. At a given elevation position, the heat transfer coefficient consistently increases with increasing solid mass flux at the highest elevation of 6.5 m, where hydrodynamic conditions are most likely to be fully developed, it is seen that the heat transfer coefficient increases by approximately 50% as Gv increased from 30 to 50 kg/rrfs. 

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. 

The parametric effect of bed temperature is expected to be reflected through higher thermal conductivity of gas and higher thermal radiation fluxes at higher temperatures. Basu and Nag (1996) show the combined effect (Fig. 23) which plots heat transfer coefficients as a function of bed temperature for data from four different sources. It is seen that for particles of approximately the same diameter, at a constant suspension density (solid concentration), the heat transfer coefficient increases by almost 300% as the bed temperatures increase from 600°C to 900°C. 

Another parametric effect is the apparent dependence of the heat transfer coefficient on the physical size of the heat transfer surface. Figure 24, from Burki et al. (1993), graphically illustrates this parametric effect by showing that the effective heat transfer coefficient can vary by several hundred percent with different vertical lengths of the heat transfer surface, for circulating fluidized beds of approximately the same particle diameter and suspension density. This size effect significantly contributed to confusion in the technical community since experimental measurements by inves-... 

Biyikli, S., and Chen, J. C., Effect of Mixed Particle Sizes on Local Heat Transfer Coefficients Around a Horizontal Tube in Fluidized Beds, 7th Int. Heat Transfer Conf, Munich, Germany (1982)... 

For G/S particle systems, enhancement in convective heat transfer is achieved at the expense of increased pressure drop in moving the gas at higher velocities. A measure of the relative benefit of enhanced heat transfer to added expenditure for fluid movement can be approximated by an effectiveness factor, E, defined as the ratio of the heat transfer coefficient to some kind of a pressure drop factor. For G/S systems in which particles are buoyed by the flowing gas stream, this pressure drop factor is expressed by the Archimedes number Ar, and E can be written... 

A fluidised bed of total volume 0.1 m3 containing the same particles is maintained at an approximately uniform temperature of 425 K by external heating, and a dilute aqueous solution at 375 K is fed to the bed at the rate of 0.1 kg/s so that the water is completely evaporated at atmospheric pressure. If the heat transfer coefficient is the same as that previously determined, what volumetric fraction of the bed is effectively carrying out the evaporation The latent heat of vaporisation of water is 2.6 MJ/kg. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

In order to take account of the effect of temperature and to determine the heat transfer coefficient at realistic freezing temperatures, rather than the room temperature of the reported experiments, and to extend the model to other particle shapes and sizes, Vazquez and Calvelo (1980) then plotted their data according to the model proposed by Chang and Wen (1966)... 

On the other hand, it has been argued that the resistance to heat transfer is effectively within a thin gas film enveloping the catalyst particle [10]. Thus, for the whole practical range of heat transfer coefficients and thermal conductivities, the catalyst particle may be considered to be at a uniform temperature. Any temperature increases arising from the exothermic nature of a reaction would therefore be across the fluid film rather than in the pellet interior. 

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