Ind. Eng. Chem. Res. 1996, 35, 4781-4787
4781
Thermal Entrance Effect for Heat Transfer in Up-Flowing Gas-Particle Suspensions Xiao S. Wang,* Munir Ahmad, and Bernard M. Gibbs Department of Fuel and Energy, Leeds University, Leeds LS2 9JT, England
Derek Geldart Department of Chemical Engineering, Bradford University, Bradford BD7 1DP, England
Martin J. Rhodes Department of Chemical Engineering, Monash University, Victoria 3168, Australia
This paper presents an experimental investigation of thermal development for fully-developed gas-particle suspensions in a 0.161 m i.d. circulating fluidized bed. Results indicated that local heat-transfer coefficients at the lower and upper ends of the heat-transfer surface were higher than those in the middle. This effect was more significant with increasing suspension density but was insensitive to increasing superficial gas velocity and increasing temperature. Analysis suggests that thermal development at the lower end of the heat-transfer surface is caused by the convection of the up-flowing gas augmented by the presence of fine particles, while thermal development at the upper end of the heat-transfer surface is the result of the convection of downflowing particles near the riser wall. Introduction
Experimental Section
The circulating fluidized bed (CFB) is a device for bringing about contacting of solid particles with a gas. CFBs are increasingly used for applications such as coal combustion and solid-gas catalytic reactions. In the design of a CFB the suspension-to-wall heat-transfer coefficient needs to be estimated with reasonable accuracy since heat-transfer surfaces often constitute part of the riser wall. In recent years the topic of heat transfer in CFBs has attracted the attention of many researchers, and, as a result, a number of mechanistic models and empirical correlations are now available in the literature. However, many important issues concerning heat transfer in CFBs are yet to be satisfactorily addressed. To the authors’ knowledge, the mechanism behind the widely reported “length effect” (i.e., the length-average heat-transfer coefficient decreases with increasing vertical length of the heat-transfer surface) still remains very much unknown. This may partly be due to the fact that there is a dearth of published studies on the length effect, and that detailed measurements which would enable us to see how the local heat-transfer coefficient varies along the heat-transfer surface are extremely limited. In addition, a degree of confusion exists among the reported results. For example, Nag and Ali Moral (1990) and Wu et al. (1989) reported decreasing heat-transfer coefficient with increasing length of the heat-transfer surface, while Wirth (1995) observed no effect of the length of the heat-transfer surface. It is difficult to assess the apparent deviations among these studies since no measurement of local heattransfer coefficients was reported in Nag and Ali Moral (1990) and Wirth (1995). The objective of this work was to elucidate, based on the measurement of local heattransfer coefficients along a section of stainless steel riser, the mechanism behind the length effect of heat transfer in gas-particle risers.
1. The CFB Experimental Facility. Since measurements were made in gas-particle suspensions in a CFB riser, it may be helpful here to describe briefly the CFB experimental facility. A schematic diagram of the CFB apparatus is shown in Figure 1. It comprised a 0.161 m i.d. and 6.2 m tall riser, two high-efficiency cyclones in series, an external heat exchanger (EHE), and an L-valve. The whole system was made of stainless steel and was insulated on the outside surface. Hot solids from the primary cyclone were fed to the EHE through a dipleg. After exchanging heat with the fluidizing air and water (flowing through stainless steel tube coils) in the EHE, the solids were returned to the riser via the L-valve at a controlled rate. The whole system was warmed up by a propane gas-burner positioned upstream of the water-cooled air distribution plate. The temperature in the riser was controlled, at a selected burner output, by adjusting heat-transfer surfaces (i.e., the stainless steel tube coils) immersed in solids in the EHE, thus controlling the temperature of recycling particles. Therefore, the temperature in the riser could be controlled independently of the gas velocity. The riser was equipped with pressure tappings to enable pressure profiles to be determined (from which mean suspension concentrations could be derived). The powder used in all experiments was silica sand with a particle density of 2500 kg/m3 and a surface-volume mean diameter of 100 µm. The size distribution of the powder is given below:
* To whom correspondence should be addressed. Telephone: (44) 142 387 2019. Fax: (44) 142 387 3375. Email:
[email protected].
S0888-5885(96)00314-4 CCC: $12.00
size (µm)
mass (% undersize)
180 150 125 105 90 75 63
100 96.14 79.89 50.82 20.71 10.47 3.02
2. Measurement of Heat-Transfer Coefficient. 2.1. Apparatus. Some details of the apparatus used © 1996 American Chemical Society
4782 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
2.2. Calculation of Heat-Transfer Coefficients. It is assumed that the heat absorbed by the flowing water in the heat-transfer tube equals the heat transferred from the gas-particle suspension to the heattransfer surface. The heat absorbed by the flowing water between axial positions i and j (i ) A, B, C, or D; j ) B, C, D, or E) can be expressed by:
Qij ) Cpmw(tj - ti)
(1)
where Cp is the specific heat of water, mw is water mass flow rate, and ti and tj are water temperatures at axial positions i and j, respectively. The suspension-to-wall heat-transfer coefficient for section i-j of the heattransfer tube can be calculated by:
hij ) Qij/[(tij,sus - tij,s)Aij]
Figure 1. Schematic diagram of the 6.2 m tall circulating fluidized-bed experimental facility.
for measuring suspension-to-wall heat-transfer coefficients are given in Figure 2. It basically comprised three identical stainless steel box tubes, 800 mm long, 10 × 10 mm cross section, and 1 mm thick. These tubes were installed in parallel. The middle tube was used for heat-transfer measurement, and the other two were guard coolers. A water tank with constant water-head (4 m above the lower end of the heat-transfer tube) was used for supplying water to the heat-transfer tube as well as the guard coolers. The temperature of the cooling water entering the guard coolers was therefore the same as that entering the heat-transfer tube. The heat-transfer tube and the guard coolers were installed in such a way that one side of the tube was uninsulated and was flush with the riser inner surface, while the other sides were insulated using high-grade kaowool mastic. To minimize possible heat exchange between the heat-transfer tube and its surroundings, the water flow rates in the heat-transfer tube and the guard coolers were adjusted to be approximately equal. This ensured that heat transfer from gas-particle suspensions to the heat-transfer tube occurred solely through the uninsulated side of the tube. Temperatures of the water, the heat-transfer surface, and the gas-particle suspensions were measured at five axial positions (A, B, C, D, and E) using 1 mm o.d. thermocouples. Pressure drops of the gas-particle suspension across these axial positions were measured using differential pressure transducers, which enabled the suspension density in the measurement section to be calculated. Measurements of the heat-transfer coefficient reported in this paper were made with the heat-transfer tube positioned at an angular position 90° anticlockwise to the inlet of the L-valve (when viewed from above) and with the lower end of the heat-transfer tube at an axial position 2 m above the air distribution plate.
(2)
where tij,sus and tij,s is the mean temperature of the suspension and the heat-transfer surface for heattransfer section i-j, respectively, and Aij is the area of the heat-transfer surface i-j. Equations 1 and 2 allow the local as well as length-average heat-transfer coefficients to be calculated. 2.3. Validity of the Method. (a) Comparison with Published Correlation. To verify the validity of the experimental method, tests were first performed with single-phase gas flow. Superficial gas velocity and temperature in the measurement section were fixed at 4 m/s and 430 °C, respectively. Results are shown in Figure 3 where the local convective heat-transfer coefficients are plotted as a function of dimensionless axial coordinate (with x/D of 0 and 5 being the lower and upper end of the heat-transfer tube, respectively). The variable x was measured from the lower end of the heattransfer tube (referring to Figure 2), and D is the inner diameter of the riser. It can be seen that for this singlephase case there exists an entrance-region effect for heat transfer at the lower end of the heat-transfer surface. For comparison, the prediction using the correlation of Reynolds et al. (1969) for single-phase turbulent convection in the entrance region of the heat-transfer tube is also plotted in Figure 3 (the continuous curve). Results shown in Figure 3 suggest that the current experimental method is technically reliable. (b) Experimental Errors. The main experimental errors introduced in the measurement included those associated with the measurement of temperature and water mass flow rate. In this work all the thermocouples were made to British Standard BS4937, Part 4, 1973, giving rise to an error of (1.5 °C or 0.004 times the temperature, whatever is greater. Water mass flow rate was taken from the average of four measurements (each with 60 s duration), and the error introduced was found to be less than 1%. Experimental errors may be estimated using eqs 3 and 4, which are derived based on eqs 1 and 2. Calculation shows that the experimen-
∆Qij ) ∆hij )
|
|
|| || | || || |
∂Qij ∂Qij ∂Qij ∆mw + ∆tj + ∆ti ∂mw ∂tj ∂ti
∂hij ∂hij ∂hij ∆Qij + ∆tij,sus + ∆t ∂Qij ∂tij,sus ∂tij,s ij,s
(3)
(4)
tal errors for the local heat-transfer coefficients were higher than those for the length-average heat-transfer coefficients and that the estimated experimental error decreased with increasing suspension density. Typical
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4783
Figure 2. Some details of the apparatus for measuring suspension-to-wall heat-transfer coefficients (dimensions: mm; asterisk denotes arc distance).
Figure 3. Local heat-transfer coefficients for single-phase gas flow.
Figure 4. Variation of local heat-transfer coefficients with suspension density.
experimental errors were found to be around 20% for the operating conditions investigated. (c) Repeatability of Experiments. Selected operating conditions (e.g., at superficial gas velocity 3.6 m/s, bed temperature 520 °C, suspension density 0-20 kg/ m3) were repeated, and it was found that the deviations in the local heat-transfer coefficients between the repeated experiments were typically less than 10%. 2.4. Operating Conditions. The riser was operated in the range of superficial gas velocity and temperature of 2.6-4.6 m/s and 275-520 °C, respectively. The suspension density in the measurement section varied from 0 to 30 kg/m3, which is in the range used in largescale CFB boilers. Variations in the temperature and suspension density (inferred from pressure drop measurements) along the measurement section were found to be negligible.
conditions are shown in Figures 4-6. The local heattransfer coefficients at axial positions x ) 0.1, 0.3, 0.5, and 0.7 m represent the heat-transfer coefficients at the middle point of sections AB, BC, CD, and DE of the heattransfer tube, respectively. It can be noted from these figures that, for all the operating conditions examined, the local heat-transfer coefficients at the lower and upper ends were higher than those in the middle of the heat-transfer tube. This suggests that there exists a thermal development length at the entry regions of the heat-transfer tube. In the discussion that follows, this effect is defined as thermal entrance and is termed “lower thermal entrance” and “upper thermal entrance”, respectively, for the lower and upper entry regions of the heat-transfer tube. The effect of suspension density on the thermal entrance is shown in Figure 4. Superficial gas velocity and temperature were 3.6 m/s and 520 °C, respectively, and the suspension density was varied from 1.0 to 17.4 kg/m3. Several points can be noted from this figure. First, local heat-transfer coefficients at both the lower and upper ends of the heat-transfer tube increased with
Experimental Results 1. Local-Heat Transfer Coefficients. Variations of the local heat-transfer coefficients with operating
4784 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
Figure 5. Variation of local heat-transfer coefficients with superficial gas velocity.
Figure 6. Variation of local heat-transfer coefficients with bed temperature.
increasing suspension density. Second, the elevation in heat-transfer coefficient at the upper end increased with suspension density. Third, this elevation is relatively insensitive to suspension density at the lower end, except for extremely dilute conditions (e.g., at suspension density 1.0 kg/m3). Figure 5 shows an example of the variations of the local heat-transfer coefficients with superficial gas velocity. Temperature and suspension density were 310 °C and 21.3 kg/m3, respectively, and the superficial gas velocities used were 2.6 and 4.6 m/s. It shows that the effect of superficial gas velocity on the local heattransfer coefficients and thus on the thermal entrance was negligible. An example of the variations of the local heat-transfer coefficients with temperature is shown in Figure 6. Superficial gas velocity and suspension density were 3.6 m/s and 18.3 kg/m3, respectively, and temperatures were 275 and 520 °C. It can be seen that the heat-transfer coefficients increased with temperature at all locations but that the effect was less significant at the lower end of the heat-transfer surface. The apparently high contribution of radiation shown in Figure 6 may be attributed to partly low solids concentration and partly experimental errors. 2. Length-Average Heat-Transfer Coefficients. The length-average heat-transfer coefficients corresponding to conditions in Figure 4 are shown in Figure
Figure 7. Variation of length-average heat-transfer coefficients with suspension density.
7. The axial coordinate of Figure 7 represents the length of the heat-transfer surface (i.e., L) measured from the lower end of the heat-transfer tube, so that L ) 0.2, 0.4, 0.6, and 0.8 m represents sections AB, AC, AD, and AE of the heat-transfer tube, respectively. It can be seen from Figure 7 that, for the operating conditions, the length-average heat-transfer coefficient decreased as L was increased from 0.2 to 0.6 m; it then increased as L was increased from 0.6 to 0.8 m. This is to be expected because of the change in the relative importance of the thermal entrance in the lengthaverage heat-transfer coefficients. It should be noted that, as far as the thermal entrance is concerned, sections AB, AC, and AD are not independent heat-transfer surfaces since they do not have an independent upper thermal entrance. This is because water-cooling of the heat-transfer surface continued to occur beyond axial positions B, C, and D. Only section AE represents an independent heat-transfer surface since water-cooling ended at axial position E and there existed independent lower and upper thermal entrances for section AE. This is of significance to design engineers since it implies that, at a given heat-transfer surface length, the length-average heat-transfer coefficient for an independent heat-transfer surface would be higher than that for a nonindependent heat-transfer surface. In addition, we would expect the influence of the thermal entrance on the length-average heattransfer coefficient to be more significant for a short (independent) heat-transfer tube than for a longer one. Therefore, the length-average heat-transfer coefficient for a short (independent) heat-transfer tube tends to be higher than that for a longer one; i.e., there exists a length effect for heat transfer in CFB risers. When the length of the heat-transfer surface is sufficiently large, however, the length-average heat-transfer coefficient may become insensitive to the increase in the heattransfer surface length as suggested by the results of Wu et al. (1989), since the thermal entrance would no longer prevail in the length-average heat-transfer coefficient. Discussion on the Thermal Entrance The existence of thermal entrance in fully-developed flow of a single phase (gas or liquid) has been mentioned in a number of heat-transfer textbooks (e.g., Janna, 1988). Malina and Sparrow (1964) observed for turbu-
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4785
Figure 9. Comparison between local heat-transfer coefficients for gas flow and gas-particle suspensions. Figure 8. Illustration of thermal development along a tube at the riser wall for (a) up-flowing gas and (b) down-flowing particles.
lent flow of water and oil in a circular tube that the local heat-transfer coefficients were very large in the neighborhood of the tube entrance and decreased continuously with increasing downstream distance. The thermal entrance for low Reynolds number gas-phase turbulent flow was observed by Black and Sparrow (1967) and McEligot et al. (1965). Theoretical understanding of the thermal entrance for low Reynolds number turbulent flow was first proposed by Reynolds et al. (1969). The present work (Figure 3) and that of Burki et al. (1993) have confirmed that thermal entrance is relevant to gas flow in a CFB riser at ambient as well as elevated temperatures and that the correlation of Reynolds et al. (1969) is also applicable for CFB risers. Thermal entrance for single-phase flow is physically plausible since the thermal boundary layer grows along the heat-transfer surface and the local heattransfer coefficient is approximately inversely proportional to the local thickness of the thermal boundary layer, as evidenced by experimental observations (e.g., Black and Sparrow, 1967; McEligot et al., 1965). Thermal entrance for gas-particle suspensions, however, has not received much attention. Although it was reported in early studies (e.g., Wu et al., 1989) that the local suspension-to-wall heat-transfer coefficient decreased with increasing distance from the upper end of the heat-transfer surface, it was not until Burki et al. (1993) that this effect was referred to as a thermal entrance problem. 1. Lower Thermal Entrance. The observed existence of a lower thermal entrance in the fully-developed region of the riser suggests that the riser wall is not completely covered by particles and that gas convection must still occur. Gas would flow upward over the riser wall, which causes the thermal boundary layer to grow along the heat-transfer tube and hence results in a thermal entrance near the lower end of the heat-transfer tube, as illustrated in Figure 8a. In order to evaluate the relative importance of the gas convection to the lower thermal entrance, an example of the local heattransfer coefficients for the gas phase, calculated using the correlation of Reynolds et al. (1969), together with those for the gas-particle suspension (at a suspension density of 18.3 kg/m3) are shown in Figure 9. Superficial gas velocity and temperature were 3.6 m/s and 275
°C, respectively. It can be noted from Figure 9 that the length of the lower thermal entrance for the gas phase may be comparable to that for gas-particle suspensions and that the lower thermal entrance would still exist if the contribution of gas convection were excluded. This suggests that the convection of up-flowing gas was only partially responsible for the lower thermal entrance. We believe that the lower thermal entrance may be augmented by the presence of fine particles near the heattransfer surface. Nevertheless, the comparable length of the lower thermal entrance for the gas phase and for gas-particle suspensions (shown in Figure 9) suggests that the up-flowing gas near the riser wall may be the driving force for the existence of the lower thermal entrance. In other words, the lower thermal entrance would not exist without the upward flow of gas near the riser wall. The observed negligible effect of increasing superficial gas velocity on the local heat-transfer coefficient may be due to the fact that the contribution of gas convection toward the total heat-transfer coefficient was very small. 2. Upper Thermal Entrance. From previous studies (e.g., Hartge et al., 1988; Rhodes et al., 1988; Weinstein et al., 1986) we know that the flow of the gas-particle suspensions in a CFB riser is characterized by a rapidly rising, dilute core surrounded by a slowlyfalling, denser region adjacent to the walls. By analogy between the flow of gas and particles along a cooling surface, the down-flowing particles near the riser wall in the fully-developed region of the riser must be responsible for the observed thermal entrance near the upper end of the heat-transfer tube, as illustrated in Figure 8b. In order to examine the influence of downflowing particles on the thermal entrance, the net (down-flowing) solids flux at 3 mm from the riser wall immediately above the heat-transfer tube was measured using a nonisokinetic probe described in Wang et al. (1995). Figure 10 shows an example of the effect of the local solids flux on the heat-transfer coefficients near to the lower (x ) 0.1 m) and upper (x ) 0.7 m) ends of the heat-transfer tube. The superficial gas velocity and bed temperature were 3.6 m/s and 520 °C, respectively. It can be noted that the heat-transfer coefficient at the lower end of the heat-transfer tube increased moderately (and linearly) with the local solids flux, which substantiates our statement that the lower thermal entrance is augmented by the presence of fine particles. In contrast, the increase in the heat-transfer coefficient
4786 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
Figure 10. Effect of solids flux at the riser wall on the local heattransfer coefficient near the lower and upper ends of the heattransfer tube.
3. Combined Lower and Upper Thermal Entrance. Since both the up-flowing gas and the downflowing particles (predominantly near the riser walls) exist in the fully-developed region of a gas-particle riser and since the flows of gas and particles result in thermal entrance near their respective entry points at the heattransfer surface, we expect a heat-transfer tube in the fully-developed region of the riser to have both lower and upper thermal entrances. Efforts are being made at the universities of Bradford and Leeds to incorporate the thermal entrance into modeling of heat transfer in CFBs. 4. The Role of Particle Packets. The importance of particle packets in suspension-to-wall heat transfer has been widely recognized (e.g., Wu et al., 1991). Since the residence time of particle packets on the riser wall is very short (Rhodes et al., 1992; Chen, 1995), it would be reasonable to assume that the contact of individual packets on the heat-transfer tube is transient and that the packets would rapidly disintegrate to form a dispersed phase. Therefore, particle packets would not be directly responsible for the observed thermal entrance. The role of particle packets in the fully-developed region of the riser would be that they cause the local heattransfer coefficient to increase evenly along the heattransfer tube. Conclusions
Figure 11. Variation of solids flux at the riser wall with operating conditions.
at the upper end of the heat-transfer tube with increasing solids flux at the riser wall is much more significant. An example of the variation of the net (down-flowing) solids flux (at 3 mm from the riser wall) with operating conditions is shown in Figure 11. The measured solids flux was considered the same along the heat-transfer tube since we are dealing with the region of the riser where the gas-particle flow is fully developed. The operating conditions presented in this figure included superficial gas velocities of 2.6 and 4.6 m/s at a bed temperature of 310 °C and bed temperatures of 310 and 520 °C at a superficial gas velocity of 3.6 m/s. It shows that the solids flux near the riser wall increased almost linearly with suspension density but was insensitive to increasing temperature and increasing superficial gas velocity. This coincides with our experimental observation that the local heat-transfer coefficient at the upper end of the heat-transfer tube increased with increasing suspension density but was insensitive to increasing superficial gas velocity (referring to Figures 4 and 5) and that the length of the upper thermal entrance was insensitive to increasing superficial gas velocity and temperature (referring to Figures 5 and 6). Therefore, the characteristic features of the upper thermal entrance are directly linked to variations of the solids flux near the riser wall.
Measurements of the heat-transfer coefficient along a heat-transfer tube have confirmed the existence of thermal entrance in the fully-developed region of a gasparticle riser suggested by the results of Burki et al. (1993). The lower thermal entrance is induced by the up-flowing gas augmented by the presence of particles while the upper thermal entrance is caused by the convection of down-flowing particles near the riser wall. The link between the upper thermal entrance and the solids flux near the riser wall is clearly established. Analysis suggests that the existence of thermal entrance is responsible for the so-called length effect of heat transfer in gas-particle risers. Acknowledgment The authors thank the Engineering and Physical Science Research Council for their support of the research into circulating fluidized beds. Nomenclature Aij ) area of heat-transfer surface for section i-j, m2 Cp ) specific heat of water, J/kg °C D ) inner diameter of the riser, m Gw ) solids flux near the riser wall, kg/m2s hij ) average heat-transfer coefficient for section i-j, W/m2 K hL ) length-average heat-transfer coefficient, W/m2 K hx ) local heat-transfer coefficient, W/m2 K L ) length of the heat-transfer surface measured from the lower end of the tube, m mw ) water mass flow rate, kg/s Nu ) Nusselt number Nuc ) Nusselt number for fully established conditions Qij ) rate of heat absorption by water in section i-j, W tb ) mean bed temperature, °C ti ) water temperature at position i, °C tj ) water temperature at position j, °C tij,sus ) average suspension temperature for section i-j, °C tij,s ) average surface temperature for section i-j, °C
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4787 U ) superficial gas velocity, m/s x ) variable, measured from the lower end of the heattransfer tube, m Subscripts i ) axial position of the heat-transfer tube (A, B, C, or D) j ) axial position of the heat-transfer tube (B, C, C, or E)
Literature Cited Black, A. W.; Sparrow, E. M. Experiments on Turbulent Heat Transfer in a Tube with Circumferentially Varying Thermal Boundary Conditions. J. Heat Transfer, Trans. ASME, Series C 1967, 89 (3), 258. Burki, V.; Hirschberg, B.; Tuzla, K.; Chen, J. C. Thermal Development for Heat Transfer in Circulating Fluidized Beds. AIChE Meeting, St. Louis, MO, 1993. Chen, J. C. Personal communication, 1995. Hartge, E.-U.; Rensner, D.; Werther, J. Solids Concentration and Velocity Patterns in Circulating Fluidized Beds. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: New York, 1988; p 165. Janna, W. S. Engineering Heat Transfer (SI ed.); Van Nostrand Reinhold (International) Co. Ltd.: London, 1988. Malina, J. A.; Sparrow, E. M. Variable-Property, ConstantProperty, and Entrance-Region Heat Transfer Results for Turbulent Flow of Water and Oil in a Circular Tube. Chem. Eng. Sci. 1964, 19, 953. McEligot, D. M.; Magee, P. M.; Leppert, G. Effect of Large Temperature Gradients on Convective Heat Transfer: The Downstream Region. J. Heat Transfer, Trans. ASME, Series C 1965, 87 (1), 67. Nag, P. K.; Ali Moral, M. N. Effect of Probe Size on Heat Transfer at the Wall in Circulating Fluidized Beds. Int. J. Energy Res. 1990, 14, 965.
Reynolds, H. C.; Swearingen, T. B.; McEligot, D. M. Thermal Entry for Low Reynolds Number Turbulent Flow. J. Basic Eng., Trans. ASME 1969, 91, 87. Rhodes, M. J.; Laussmann, P.; Villain, F.; Geldart, D. Measurement of Radial and Axial Flux Variation in the Riser of a Circulating Fluidized Bed. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: New York, 1988; p 155. Rhodes, M. J.; Mineo, H.; Hirama, T. Particle Motion at the Wall of a Circulating Fluidized Bed. Powder Technol. 1992, 70, 207. Wang, X. S.; Gibbs, B. M.; Rhodes, M. J. Measurement of Local Solids Flux in High Temperature Gas-Particle Suspensions. Proceedings of the First European Conference for Young Researchers in Chemical Engineering, IChemE (UK), 1995; p 731. Weinstein, H.; Shao, M.; Schnitzlein, M. Radial Variation in Solid Density in High Velocity Fluidization. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon Press: Oxford, U.K., 1986; p 201. Wirth, K.-E. Heat Transfer in Circulating Fluidized Beds. Chem. Eng. Sci. 1995, 50, 2137. Wu, R. L.; Grace, J. R.; Lim, C. J.; Brereton, C. M. H. Suspensionto-Surface Heat Transfer in a Circulating Fluidized Bed Combustor. AIChE J. 1989, 35, 1685. Wu, R. L.; Lim, C. J.; Grace, J. R.; Brereton, C. M. H. Instantaneous Local Heat Transfer and Hydrodynamics in a Circulating Fluidized Bed. Int. J. Heat Mass Transfer 1991, 34, 2019.
Received for review June 6, 1996 Revised manuscript received September 26, 1996 Accepted September 27, 1996X IE960314O X Abstract published in Advance ACS Abstracts, November 1, 1996.
