Wall Heat Transfer in Stirred Tank Reactors - American Chemical

Ind. Eng. Chem. Res. 2005, 44, 4949-4958

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Wall Heat Transfer in Stirred Tank Reactors Rune Engeskaug,† Elisabeth Thorbjørnsen,‡ and Hallvard F. Svendsen*,‡ SINTEF Materials and Chemistry, 7465 Trondheim, Norway, and Department of Chemical Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Local wall heat-transfer coefficients have been measured for water and for the non-Newtonian systems consisting of 0.3, 0.6, and 1.0 wt % carboxymethylcellulose in water. The results were compared to existing correlations, and good agreement was found for the water system outside the impeller region. In the impeller region, deviations were large. For the non-Newtonian systems, a functional dependence between the Reynolds number and the heat-transfer coefficient, given by Nu/(Pr0.33Vi0.14) ∝ Re0.8, was found to fit the data well. Support for this was found by a closer examination of the existing literature. This is in contrast to the currently accepted dependence on a Reynolds number exponent of 0.67-0.68. On the basis of the data, a new correlation for non-Newtonian fluids has been suggested. Radial temperature profiles for the wall region were also measured and presented. Introduction Batch and continuous stirred tank reactors are very common in the process and pharmaceutical industries. Often these reactors operate on systems that require strict temperature control under high heat fluxes, and in batch mode, often the heat flux changes direction during the batch cycle. The heat transfer, characterized by a heat-transfer coefficient h, normally takes place via an internal heat-transfer area as inserted coils or by wall heat transfer from a reactor jacket. Industrially, the transfer of heat in and/or out of a stirred tank reactor is a very frequently encountered problem. The wall heat-transfer coefficient depends on a number of factors such as the type and geometry of the tank and impeller, the position of the impeller, the degree of turbulence created, and, of course, the physical properties of the reacting system. There exist a number of correlations for predicting the wall heat-transfer coefficient, but in view of the importance of the process, there is a surprisingly small number of investigations of the wall heat-transfer coefficient in the literature over the last 50 years and in particular for non-Newtonian fluids. This work presents an experimental investigation of the wall heat transfer into Newtonian and non-Newtonian fluids, and existing correlations for heat-transfer coefficients for 1D reactor models are tested and improved. Background Any heat-transfer coefficient correlation is directly connected to the model for which and by which it is developed. This means that one should not use correlations for 1D models in 2D or 3D models, such as in computational fluid dynamics (CFD) calculations. For these purposes, new correlations must be developed that take into account the spatial resolution offered by the CFD model and the transport of energy inherently modeled by the better resolution. The wall heat transfer will depend on the impeller speed, the physical properties of the system, and the † ‡

SINTEF Materials and Chemistry. Norwegian University of Science and Technology.

geometry of the tank and impeller. The general form of the empirical equation used is

Nu ) k × ReaPrbVic

(1)

The Re number in this equation is taken to be the impeller Re number. To increase the domain of validity of this correlation, geometrical properties such as the impeller and tank diameter, impeller geometry and position, and baffle size and number and in many cases also the inclusion of other elements such as internal heat-transfer areas are considered. In the following, there is a short review of correlations for wall heattransfer coefficients in agitated tanks. Newtonian Fluids. For Newtonian fluids, Mohan et al.1 have given an excellent review for both global and local heat-transfer coefficients in Newtonian systems up to this point in time and only the most relevant papers are referred to here and also only in the realm of local coefficients. Local Heat-Transfer Coefficients. The heat transfer is basically a local phenomenon, and the local heattransfer coefficient will vary significantly with position in a stirred tank. Developing equations for local heattransfer coefficients has the advantage that, in principle, only the local flow structure, for instance, that characterized by the time-averaged velocity and turbulence intensity, should affect the transfer. Therefore, considerations of the geometry could be avoided. On the other hand, using local coefficients demands knowledge of these local properties and an integration of the local values over a whole reactor/tank. Of course, local values are much more suited for use with CFD codes. As pointed out by Mohan et al.,1 the first ones to study local heat-transfer properties were Akse et al.2 They used a heat flux meter and also measured the local flow properties in the tank. Their conclusion was that the local heat-transfer coefficient varied with the axial position in the tank; the highest values were found at the impeller level and decreased, moving both upward and downward from this level. They developed a correlation or a set of correlations for the different positions in the tank:

10.1021/ie049178a CCC: $30.25 © 2005 American Chemical Society Published on Web 02/11/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005

Above and below the impeller [|h| > (1/2)w] Nu ) 0.54Re0.68Pr0.33(h/D)-0.33(µ/µw)0.14

(2)

For the region close to the impeller [|h| < (1/2)w] Nu ) 0.12Re0.85Pr0.5

(3)

Here, h is the distance from the impeller center plane and w is the impeller width. The dimensionless groups were all based on the physical properties of the liquid at bulk temperature. These results were later confirmed by Balakrishna and Murthy3 and Bourne et al.4 Akse et al.2 also presented correlations for the spatially averaged heattransfer coefficient. Man et al.5 developed a similar set of correlations for different positions in the vessel, and Lu et al.6 described experimentally the axial heattransfer profiles but developed correlations only for the averaged values. Haam et al.7 also measured local heattransfer coefficients and focused on the variation as a function of the azimuthal position between the baffles. Non-Newtonian Fluids. Non-Newtonian fluids are quite common in the process industry, but still only a small number of studies on heat transfer in stirred tanks with these systems exist. The main thrust among the studies to be found relates to pseudoplastic fluids. In most studies, the Newtonian viscosity in the dimensionless groups in eq 1 is substituted with an apparent viscosity. To obtain a good estimate for the apparent viscosity for power law fluids, one needs a good estimate of the liquid shear. In a few cases, new Re and Pr number correlations are developed. Metzner and Otto,8 Metzner et al.,9 Calderbank and Moo-Young,10 and Gluz and Pavlushenko11 assumed proportionality between the impeller speed and the apparent viscosity. In the first and last works, a constant proportionality factor was assumed for all fluids and later also used by Lu et al.,6 whereas the third work uses a factor that depends on the flow behavior index, n. Carreau et al.12 defined the viscosity for the Pr number in the heat-transfer coefficient correlation to be the high shear rate viscosity, i.e., the derivative of the shear stress with respect to the shear rate as the shear rate goes toward infinity. In addition, they used a generalized Re number, similar to the one suggested by Metzner13 for non-Newtonian flow in pipes. This Re number included the flow behavior index and the impeller speed. Hagedorn and Salamone14 presented a large amount of data for non-Newtonian fluids with several types of impellers. Using dimensional analysis, they obtained a new correlation for the Nu number. Sandall and Patel15 and Mizushina et al.16 assumed that the shear rate was proportional to the impeller speed, whereas Tang et al.17 refined this slightly. Bourne et al.18 showed that the linearity between the shear rate and impeller speed is only correct for laminar conditions and suggested a more complex relationship where the flow behavior index and the impeller diameter also enter. Wang and Yu19 go even further and suggest a new model for calculating the apparent viscosity, assuming that the impeller torque and the average wall shear stress are proportional. They introduce the energy dissipation rate into the Re number and also include geometrical properties for the various impellers tested.

Kawase et al.20 studied heat transfer under laminar conditions using specially designed large-scale impellers. For characterizing the apparent liquid viscosity, they also adopted the approach of Metzner and Otto8 and Metzner et al.,9 assuming proportionality between the stirrer speed and the average shear rate. Experimental Section The experimental setup with the tank used is shown in Figure 1. The inner diameter D of the tank was 488 mm, and the tank was equipped with four vertical baffles with width WB equal to D/10 located on the wall. The impeller used was a six-bladed Rushton turbine with diameter DI equal to 161 mm. The impeller position, HA, used was D/3 above the bottom. The impeller blade length, L, and width, w, were 44 mm. The impeller drive was an adjustable drive, where the rpm’s could be kept constant independent of the torque. The bulk temperature was kept constant during the individual experiments by using a thermostat. The bulk temperature was controlled by a PT100 element placed between the impeller and the tank wall opposite the temperature controller. A heat-transfer element for local heat-transfer measurements was designed and used. The element could simultaneously measure the heat flux, the surface temperature, and the liquid temperature at chosen distances, from 0.25 to 15 mm from the wall. The heating element, as shown in Figure 2, was built with two sections, an inner circular section for temperature and flux measurements and an outer one that ensured the buildup of a stable thermal boundary layer. The heat element was 70 × 100 mm and was well insulated from both the tank walls and the outside. The insulation between the inner and outer sections was 2 mm thick, and the whole element was polished so as not to disturb the thermal boundary layer buildup. The inner and outer heating elements were heated separately. The outer heating element provided insulation for the inner element such that the flux measurements became more accurate, and as mentioned, it ensured a fully developed thermal boundary layer when the flow reached the inner element. Akse et al.2 showed that the thermal boundary layer is fully developed at a distance z if

Ω ) azt/δ2v g 0.2

(4)

The highest liquid velocity at the wall can be estimated by v ≈ NDI2/D, which in our case was found to be 0.056 m/s. This value is confirmed by our own Laser Doppler Velosimetry (LDV) measurements. The thickness of the thermal boundary layer can be estimated from the velocity boundary layer and the liquid Pr number. This gave a laminar sublayer thickness estimate of about 30 mm. Using the thermal diffusivity of water and an entrance length of 40 mm gave an Ω of above 100. This implies that the assumption of an established thermal boundary layer is valid. Using the procedure by Akse et al.2 gives the same conclusion. There were a total of 15 thermocouples on the heating elements. All elements were of the K type and 0.5 mm in diameter. The thermocouples placed on the inner element were used for surface temperature measurements, whereas the ones in the outer element were only used for checking the surface temperature and thereby the buildup of the thermal boundary layer.

Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 4951

Figure 1. Experimental tank and impeller.

Figure 2. Double heating element.

The thermocouples were calibrated against each other at temperature intervals of 10 °C in the whole operating range, and these calibrations were used to normalize the readings from the individual elements. The accuracy of the normalized individual readings was estimated to be better that (0.05 °C. At the center of the element was placed one thermocouple that could be positioned at different distances, as mentioned 0.25-15 mm, from the element surface using a micrometer screw. The reproducibility of these fluid temperature profiles was tested using typically three repetitions. The temperature reproducibility was found to be within (0.01 °C. Typical response times for uncovered elements were about 0.15 s. Elements imbedded in the plate were tested by placing an uncovered element on the top of each of them. The element pairs were found to follow each other completely within the used sampling fre-

quency of 2 Hz. The temperatures and the heat flux required to keep the central element temperature constant were recorded online. To obtain a good statistical base, 3-500 measurements were used. The control system was able to maintain the surface temperature, fluctuating within a maximum of (0.2 °C over a period of about 6 s. The bulk temperature typically varied within (0.05 °C. From this, the accuracy of the average surface/bulk temperature differences could be determined within an estimated accuracy of (0.1 °C. To check the potential heat loss to the surroundings, the natural convection loss and the radiation loss were calculated. Natural convection could give rise to a loss of about 80 W/m2, whereas radiation could give a loss of about 200 W/m2. This was calculated from the heat element in direct contact with air, whereas in reality the element was very well insulated. The average heat flux from the element was 11-15 103 W/m2, so the heat

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Table 1. Rheological Properties for CMC Solutions Used liquid

K (N‚sn/m2)

N

0.3 wt % CMC 0.6 wt % CMC 1 wt % CMC

0.0328 0.1493 0.6232

0.947 0.8703 0.7771

loss to the surroundings can safely be disregarded. The bulk temperature was kept constant at 20 °C, whereas the heating element surface temperature varied in the range of 30-55 °C. The liquids used were tap water and aqueous solutions of carboxymethylcellulose (CMC). These CMC solutions are pseudoplastic, and the viscosity can be described using a power law model:

τ ) Kγn

(5)

The rheological properties of the solutions used were measured using a Physica MCR 300 rheometer using shear stress rates in the range of 0.1-1000 s-1. The parameters were determined at 25 °C for each individual experiment, and Table 1 gives the values found. Aqueous solutions of CMC are well described in the literature; e.g., Muller and Davidson21 and the data in Table 1 agree well with these. Mizushina et al.16 have shown that the thermal properties, k and Cp, and the density of CMC solutions below 4 wt % are very close to the ones of water. We have therefore used the properties of water at the bulk temperature of 20 °C in this study. All experiments were run in the turbulent regime, with Re numbers ranging from 1.4 × 104 to 18.1 × 104. Measurements for water were performed at 33, 43, and 63 rpm. Measurements for the lowest CMC concentration were done at four different vertical positions, 5, 15, 25, and 35 cm from the bottom, at three different positions relative to the baffles, 15, 45, and 75°, and for four different impeller speeds, 63, 120, 180, and 240 rpm.

For the higher CMC concentrations, measurements were only done at the middle position between the baffles, but the range of impeller speeds was expanded to cover also 300, 360, and 400 rpm. For most of the experiments, also temperature profiles into the tank were measured for the positions 0.25-15 mm from the wall. The experimental uncertainties of the heat-transfer coefficient measurements vary with the temperature differences between the heating element surface and the bulk. The accuracy in the temperature difference measurements was, as mentioned, found to be (0.05 °C, and the accuracy of the heat flux determination was about (0.5%. The surface/bulk temperature difference ranged from 4 to 25 °C, and the accuracy in the determined heat-transfer coefficients was found to range between 1 and 4%. The highest uncertainties were observed for the highest heat-transfer coefficients. Results and Discussion In Figure 3 are shown data obtained for water at the four different axial positions above the tank bottom. These represent one position in the region below the impeller, one at the impeller (15 cm), and two positions above. The data are compared with correlations developed by Akse et al.2 and Man et al.5 As can be seen from the figure, our data agree reasonably well with the correlation of Akse et al.2 for both of the two regions above and below the impeller. The deviations are in the range of 2-10%. However, in the impeller region, the Akse et al.2 correlation gives very low values compared to both the predicted and experimental ones. The data are also compared to correlations developed by Man et al.5 These correlations give heat-transfer coefficients far below both the experimental data and the correlations of Akse et al.2 given in eqs 2 and 3. In the treatment of the CMC solution data, the common assumption of proportionality between the

Figure 3. Heat-transfer coefficients for water. Comparison between the experimental data and correlations by Akse et al.2 and Man et al.5


Figure 4. Heat-transfer coefficients for 0.3 wt % CMC in water. Comparison between the experimental data and correlations by Akse et al.2

average shear rate and the rotational speed is used. Metzner et al.9 found that the average shear rate for pseudoplastic fluids with a six-bladed turbine could be given as

(dv/dy)av ) 11N

(6)

The apparent viscosity for the fluid can then be written as

µa ) (11N)n-1K

(7)

This type of relationship was also used by Kawase et al.20 for industrial impellers, but the coefficient in the parentheses was adjusted to the specific type of impeller. In this work, the relationship was used in the calculation of both the Pr and Re numbers entering into the used correlations. The data are presented in Figures 4-6. Predictions using the correlations of Akse et al.2 are also shown. For the data for 0.3 wt % CMC, it can be seen that the Akse et al. correlation describes well the experimental points. The exception again is at the impeller level, where the predictions are far too low. Even for 0.6 wt % CMC, the correlation gives an acceptable fit of the data up to stirrer speeds of approximately 300 rpm. Above this, the correlation seems to underpredict the heat transfer. In Figure 6 are shown the data for 1.0 wt % CMC. Here there is a far larger deviation between data and predictions, particularly for the lower stirrer speeds and far away from the stirrer. It may seem that the influence of the impeller in these regions is limited at lower speeds, which is reasonable taking into account the shear thinning behavior of the fluid. It is therefore not surprising that a correlation for Newtonian fluids breaks down under these circumstances.

The temperature profiles along the tank height were compared to the corresponding profiles given by Karcz22 and Lu et al.6 The geometrical proportions of the tank and impeller in the work of Lu et al.6 were identical with those of the apparatus used in this work, but the size, i.e., the linear dimensions, were only half. Local heattransfer coefficients from Lu et al.6 obtained for water at a position 45° between the baffles and an impeller speed of 100 rpm were found to be significantly lower than those obtained in this work for an impeller speed of 63 rpm for positions up to slightly above the impeller. Above this, the 100 rpm data from Lu et al.6 are very close to our data for 63 rpm. This implies that the data of Lu et al.6 do not agree with the correlation of Akse et al.2 The results from Karcz22 are for a taller tank where the height was twice the tank diameter. Apart from this, the proportions were the same as those in our work. For the results, however, only a qualitative agreement with our tests could be established because these were run up to 63 rpm and Karcz’s22 results were for 300 rpm and above. Most correlations developed for wall heat transfer in agitated vessels from Newtonian fluids are of the type given in eq 1. Early work by Strek23 found the exponent for the Re number to be 0.67. Exponent values of 0.670.68 have later been supported by results from many authors such as Akse et al.,2 Karcz,22 and Lu et al.6 Le Lan et al.24 obtained a value of 0.65, which is in line with the work of Chapman et al.25 Havas et al.26 obtained an exponent of 0.667 for a different geometry and vertical tube baffles. In Figure 7 are shown our data for water where the dimensionless group Nu/(Pr0.33Vi0.14) is plotted as a function of the Re number. Lines for the Re0.67 dependence have been drawn, and the data are seen to support this relationship for all positions in the vessel.

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In Figure 8, the same dimensionless groups are shown for the CMC systems. Lines with Re number exponents of 0.8 are drawn in the graph and are seen to represent the slope of the data points reasonably well for all positions in the vessel. The consistency of the data

appears to be best for the positions closest to the impeller. These are the positions where the proportionality between the impeller speed and the shear rate would be best represented. For these two positions, 0.15 and 0.25 m above the tank bottom, the heat-transfer


Figure 7. Dimensionless group Nu/(Pr0.33Vi0.14) as a function of the Re number for heat transfer to water. The lines show Re0.67.

Figure 8. Dimensionless group Nu/(Pr0.33Vi0.14) as a function of the Re number for heat transfer to CMC solutions. The lines show Re0.80.

coefficients clearly increase with the CMC content. This may be counterintuitive, but a detailed study of the data from Edney and Edwards27 shows the same tendency. They studied the overall heat transfer to coils. From their data for 0.5, 1.0, and 1.5 wt % CMC, it is clear

that the heat-transfer coefficients increase with the CMC concentration. This is, however, not reflected in the correlation that they developed. The same tendency also appears for their data on poly(acrylamide) solutions.

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Figure 9. Influence of the element position relative to the baffles for 0.3 wt % CMC. Baffle positions are 0 and 90°.

For the positions 0.05 and 0.35 m above the impeller, the increase in the heat-transfer coefficient with the CMC content can be seen for the two lowest CMC concentrations. However, for 1 wt % CMC, the values decrease, and at the highest position, farthest away from the impeller, the two points obtained are very uncertain. This can be explained with a smaller influence of the impeller at the higher CMC concentration. A relationship between Nu/(Pr0.33Vi0.14) and Re0.80 is, as was already mentioned, found to represent the data well. This value is higher than the one for water and also higher than the value found by Edney and Edwards27 for the overall heat-transfer coefficient to coils. In their case, however, they correlated data for both water and non-Newtonian solutions together. Examining their material closely reveals that both the CMC

and poly(acrylamide) data separately show higher exponents than 0.67 for the Re number dependence. As was already mentioned, bulk properties were used in the evaluation of the Nu, Pr, and Re numbers. This is in accordance with the basis for the correlation of Akse et al.2 and also for the work of Edney and Edwards.27 The functional dependence on the position is also found to be slightly changed compared to the results for water. For water, the heat-transfer coefficient dependence on the normalized distance from the impeller, hI/D, is to the power -0.33. For the CMC data, the exponent was found to be -0.5. The final correlation for the CMC data then becomes

Nu ) KCMC(Re0.8Pr0.33Vi0.14)(hI/D)-0.5

(8)


Figure 10. Temperature profiles close to wall as a function of the position. Data are for 63 rpm and 0.3% CMC.

Here KCMC is a function of the CMC concentration, which in this study has the form

KCMC ) 0.124 + 0.1CCMC

(9)

The local heat-transfer coefficient is also a function of the heat surface azimuthal position. Three positions were measured, at 15, 45, and 75° between the baffles. The results for 0.3 wt % CMC are shown in Figure 9. As is seen, the effect of the heating element position varies with the axial position in the vessel. The movement of the impeller from 0 to 90°. At the impeller position, the heat-transfer coefficient is clearly highest directly downstream of a baffle for all impeller speeds, but the effect is most pronounced for the highest speeds. This is in agreement with the results of Haam et al.,7 and they suggest that wake formation is the reason for this. In the lowest position in the tank, the opposite trend is found. Here the coefficients upstream of the baffle are the highest. The reason for this is not fully understood, but at this position, the downward flow will probably play a dominating role. The downward flow may well be strongest where the flow is pushed toward a baffle. In the top section again, the coefficients are largest just downstream of a baffle. One would suspect that the upward flow would be dominating in this region. To explain this in more detail, comparisons with CFD studies would be helpful. At the highest position, the effects are small. Lu et al.6 also give data for the different azimuthal positions but only as averaged data for all axial positions. The averaged effects are small, but there is a slight tendency for higher coefficients upstream of a baffle. Using the adjustable center-point thermoelement of the heating plate, the temperature as a function of the distance from the wall could be measured. Data for 0.3 wt % CMC and 63 rpm are given in Figure 10. As

expected, the curves vary markedly over the height of the vessel. The steepest profile is found outside the impeller. The closest measurement possible was at a distance of 0.5 mm, and at the impeller position, the temperature has reached the bulk value already at this distance from the wall. A heat-transfer model based on the boundary layer theory should work well here. At the other positions, however, the temperature profile stretches significantly into the vessel. This is important when using CFD models. If the momentum boundary layer is thin, then a substantial part of the temperature profile may be resolved by the model. If this is the case, one needs to develop new modified correlations for the wall heat-transfer coefficient, taking the resolution into account. One would also have to be very careful when using correlations based on 1D studies. Conclusions An apparatus for the measurement of local wall heattransfer coefficients has been developed. Measurements have been performed for water and for non-Newtonian systems consisting of 0.3, 0.6, and 1.0 wt % CMC in water. The results were compared to the correlation of Akse et el.,2 and a good agreement was found for the water system outside the impeller region. In the impeller region, deviations were large. For the non-Newtonian systems, a functional dependence between the Re number and the heat-transfer coefficient, given by Nu/ (Pr0.33Vi0.14) ∝ Re0.8, was found to fit the data well. Support for this was found by a closer examination of the existing literature. This is in contrast to the currently accepted dependence with a Re number exponent of 0.67-0.68. On the basis of the data, a new correlation for non-Newtonian fluids has been suggested. Radial temperature profiles for the wall region were also measured and presented.

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Acknowledgment The financial support by the Norwegian Research Council Klimatek Program is greatly appreciated. Nomenclature a ) thermal diffusivity of the agitated liquid, m2/s CCMC ) CMC concentration, wt % Cp ) specific heat of the fluid, J/kg‚K DI ) impeller diameter, m D ) vessel diameter, m h ) vertical distance from the impeller, m hw ) heat-transfer coefficient, W/m2‚K HA ) height of the impeller from the tank bottom, m H ) height from the tank bottom, m K ) power law parameter, N‚sn/m2 k ) liquid thermal conductivity, W/m‚K L ) length of the impeller blade, m n ) flow behavior index nb ) number of baffles N ) rotational speed of the impeller, 1/s Nu ) Nusselt number (hDT/k) Pr ) Prandtl number (Cpµ/k) Re ) Reynolds number (FND2/µ) Tm ) average liquid temperature, °C v ) velocity of the main flow along the wall, m/s Vi ) viscosity number, m/mw w ) width of the impeller blade, m wb ) width of the baffles, m y ) length coordinate, m zt ) length of the thermal entrance region, m Greek Symbols γ ) shear rate, 1/s δ ) thickness of the thermal boundary layer, m µ ) viscosity at the bulk temperature, Pa‚s µw ) viscosity at the wall temperature, Pa‚s µa ) apparent viscosity, Pa‚s F ) density, kg/m3 τ ) shear stress, Pa Ω ) test criterion in eq 2

Literature Cited (1) Mohan, P.; Emery, A. N.; Al-Hassan, T. Review heat transfer to Newtonian fluids in mechanically agitated vessels. Exp. Therm. Fluid Sci. 1992, 5 (6), 861-883. (2) Akse, H.; Beek, W. J.; van Berkel, F. C. A. A.; de Graauw, J. The local heat transfer at the wall of a large vessel agitated by turbine impellers. Chem. Eng. Sci. 1967, 22, 135-146. (3) Balakrishna, M.; Murthy, M. S. Heat transfer studies in agitated vessels. Chem. Eng. Sci. 1980, 35, 1486-1494. (4) Bourne, J. R.; Dossenbach, O.; Post, T. Local and average mass and heat transfer due to turbine impellers. Fifth European Conference on Mixing; Stanbury, J., Ed.; 1985; pp 199-207. (5) Man, K. L.; Edwards, M. F.; Polley, G. T. A study of local heat transfer coefficients in agitated vessels. Inst. Chem. Eng. Symp. Ser. 1984, 89, 193-207. (6) Lu, W. M.; Lan, C. M.; Fang, H. W. Local heat transfer in a stirred vessel with and without aeration. J. Chem. Eng. Jpn. 1995, 28 (6), 666-672.

(7) Haam, S.; Brodkey, R. S.; Fasano, J. B. Local heat transfer in a mixing vessel using heat flux sensors. Ind. Eng. Chem. Res. 1992, 31, 1384-1391. (8) Metzner, A. B.; Otto, R. E. Agitation of non-Newtonian fluids. AIChE J. 1957, 3 (1), 3-10. (9) Metzner, A. B.; Feehs, R. H.; Ramos, H. L.; Otto, R. E.; Tuthill, J. D. Agitation of viscous Newtonian and non-Newtonian fluids. AIChE J. 1961, 7 (1), 3-9. (10) Calderbank, P. H.; Moo-Young, M. The power characteristics of agitators for the mixing of Newtonian and non-Newtonian fluids. Trans. Inst. Chem. Eng. 1961, 39, 337. (11) Gluz, M. D.; Pavlushenko, I. S. Experimental Investigation of Heat Transfer During Stirring of Non-Newtonian Liquids. J. Appl. Chem. (Leningrad) 1966, 21, 2323. (12) Carreau, P.; Charest, G.; Corneill, J. L. Heat Transfer to Agitated Non-Newtonian Fluids. Can. J. Chem. Eng. 1966, 44 (1), 3. (13) Metzner, A. B. Advances in chemical engineering; Academic Press: New York, 1956; Vol. 1, p 101. (14) Hagedorn, D.; Salamone, J. J. Batch Heat Transfer Coefficients for Pseudoplastic Fluids in Agitated Vessels. Ind. Eng. Chem. Process Des. Dev. 1967, 6 (4), 469. (15) Sandall, O. C.; Patel, K. G. Heat Transfer to NonNewtonian Pseudoplastic Fluids in Agitated Vessels. Ind. Eng. Chem. Process Des. Dev. 1970, 9 (1), 139. (16) Mizushina, T.; et al. Experimental studies of film coefficients of non-Newtonian fluids in agitated vessels. Chem. Eng. Tokyo 1966, 30, 819-826. (17) Tang, F.; et al. Studies on heat transfer to Newtonian and non-Newtonian fluids in agitated vessels. Chem. Ind. Eng. J. (China) 1983, 4, 389-394. (18) Bourne, J. R.; Buerli, M.; Regenass, W. Power and heat transfer to agitated suspensions: use of heat flow calorimetry. Chem. Eng. Sci. 1981, 36, 782-784. (19) Wang, K.; Yu, S. Heat transfer and power consumption of non-Newtonian fluids in agitated vessels. Chem. Eng. Sci. 1989, 44 (1), 33-40. (20) Kawase, Y.; Hoshino, M.; Takahashi, T. Non-Newtonian laminar boundary layer heat transfer in stirred tanks. Heat Mass Transfer 2002, 38, 679-86. (21) Muller, F. L.; Davidson, J. F. Rheology of shear thinning polymer solutions. Ind. Eng. Chem. Res. 1994, 33 (10), 2364-2367. (22) Karcz, J. Studies of local heat transfer in a gas-liquid system agitated by double disc turbines in a slender vessel. Chem. Eng. Sci. 1999, 72, 217-227. (23) Strek, F. Heat transfer in liquid mixerssstudy of a turbine agitator with six blades. Int. Chem. Eng. 1963, 3 (4), 533-556. (24) Le Lan, A.; Laguerie, C.; Angelino, H. Transferts de Chaleur a la Paroi d′une Cuve Mechaniquement Agitee. Chem. Eng. Sci. 1974, 29, 2021-2031. (25) Chapman, F. S.; Dallenbach, H.; Holland, F. A. Heat transfer in baffled, jacketed, agitated vessels. Trans. Inst. Chem. Eng. 1964, 42 (10), T398-T406. (26) Havas, G.; Deak, A.; Sawinsky, J. Heat Transfer in an Agitated Vessel Using Vertical Tube Baffles. Chem. Eng. J. 1982, 23, 161-65. (27) Edney, H. G. S.; Edwards, M. F. Heat Transfer to NonNewtonian and Aerated Fluids in Stirred tanks. Trans. Inst. Chem. Eng. 1976, 54, 160-166.

Received for review September 1, 2004 Revised manuscript received December 10, 2004 Accepted December 15, 2004 IE049178A

Wall Heat Transfer in Stirred Tank Reactors - American Chemical

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