External Heat Transfer Coefficient in Agitated Vessels Using a Radial

Article pubs.acs.org/IECR

External Heat Transfer Coefficient in Agitated Vessels Using a Radial Impeller and Vertical Tube Baffles Vitor da Silva Rosa,*,†,‡ Marlene Silva de Moraes,† Juliana Tófano de Campos Leite Toneli,‡ and Deovaldo de Moraes Júnior† †

Department of Chemical Engineering, Santa Cecília University, Santos, SP 11045-907, Brazil The Engineering, Modeling and Applied Social Sciences Center (CECS), UFABC, Santo André, SP 09210-580, Brazil

‡

ABSTRACT: There are several correlations used to predict the external heat transfer coefficient in tanks equipped with vertical tube baffles in batch operations, but little information concerning the external heat transfer coefficient in steady state operations. The objective of the present article is to experimentally determine a correlation of the external heat transfer coefficient based on the model proposed by Sieder and Tate (Ind. Eng. Chem. 1936, 1429−1435) in a steady flow rate in a vessel equipped with a radial impeller, turbine type, with six flat blades. The study was carried out in a 50 dm3 working capacity acrylic vessel, fitted with vertical tube baffles made of copper, in which water and sucrose solutions at mass concentrations of 20% and 50% were heated. Heating temperatures varied from 28 to 45 °C, whereas the rotations varied from 90 to 330 rpm. From the Nusselt, Reynolds, and Prandtl similarity parameters, a correlation was obtained which yielded excellent results of the observed data−a maximum deviation of 21% between the observed and predicted data for the external heat transfer coefficient. In addition, one could also observe that the radial impeller raises the heat transfer to as much as 70% compared to the axial impeller for the same study conditions.

1. INTRODUCTION Heat exchange in agitated tanks and vessels are commonly used in heat transfer in chemical, petrochemical, and pharmaceutical industries mainly as chemical reactors. The agitated vessels usually operate in a steady state, using jackets and internal coils as heat transfer surfaces.1 In what concerns the industry, it is preferable to design the tanks and vessels to run continuously so as to maintain a constant production, without the need to stop to feed or discharge as in batch processes. The heat transfer surfaces are designed using the classic Sieder−Tate2 (eq 1), the dimensionless function Nusselt, Reynolds, and Prandtl. Nu = K Re aPr b Vi c

the literature are designed for tanks running in batch operations. On the basis of the lack of project data in the literature about the tube baffles in steady state operations, the goal of this article was to determine the parameters of eq 1 for the external coefficient of heat transfer in a tank whose sucrose solution was heated through the vertical tube baffles, equipped with a radialflow impeller, turbine type, with six flat-blade disk turbines.

2. THEORY OF ENERGY IN AGITATED VESSELS In a given tank running in a steady state in a heat transfer process the outflow temperature of the heated or cooled fluid varies as a function of the heat transfer elapsed time. This temperature is mainly influenced by the thermal effects while the mechanical variable, represented here by the rotation of the impeller, is very small compared to the above-mentioned variables and therefore is negligible and will cause no significant errors.15 Hence, the first law of thermodynamics can be written solely as a function of the thermal variables as shown in eq 2.

(1) 3

Many researchers such as Uhl and Gray, Bourne, Dossenbacyh, and Post,4 Karcz and Strek,5 Cummings and West,6 De Maerteleire,7 Havas, Deak, and Sawinsky,8 Couper et al.,9 Dias et al.,10 Pratt,11 and Kumpinsky12 have determined the parameters of eq 1 through experiment for tanks in a steady state and batch operations, using jackets and internal coils as surfaces. These two techniques need additional baffles to avoid the formation of a vortex, which indicates a low mixture and thermal efficiency.13 The surfaces called vertical tube baffles are connected to each other in banks. They prevent swirling and vortex formation and contribute to stimulate increased turbulence and heat exchange.1 According to Mohan, Emery, and Al-Hassan14 the vertical tube baffles raise the heat transfer coefficient by 37% in the turbulent region in relation to the vessels equipped with jackets and helical coils. Nevertheless, there is a design problem of the vertical tube baffles in determining the heat transfer coefficient parameters. Because of this drawback, most equations found in © XXXX American Chemical Society

Q h = Q c + Q p + Q ac

(2)

The rate of accumulated heat is written as a function of the amount of fluid contained in the tank. Thus, by expanding the terms of eq 2 a differential ordinary equation of first order is obtained, which represents the energy variation in an overall sense (eq 3). Received: February 28, 2014 Revised: August 15, 2014 Accepted: August 18, 2014

A

dx.doi.org/10.1021/ie5008618 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

Article

Figure 1. Location of the internal and external convection coefficients.

Z* = exp(( −S − X + (YZ))/MCpc)

mh Cph(T1 − T ) = mcCpc(t − t1) + h00A 00(t − t00) + MCpc(dt/dθ)

The solution for eq 7 implies determining the global coefficient U, which depends on the conduction mechanics and convective heat transfer. It is known that in agitated vessels conduction is negligible in relation to convective heat transfer, because the conductivity of the material of the tube is high, usually metal. Hence the overall coefficient of heat transfer is only a function of local internal (hi) and external (ho) convective heat transfer.16

(3)

The term on the left of eq 3 represents the heat rate measured from the heated fluid, which can be written as a function of the global heat transfer coefficient (eq 4). mh Cph(T1 − T ) = UA(T1 − T )/(ln((T1 − t)/(T − t))) (4)

Solving for T, T = t + (T1 − T )/(exp(UA /mh Cph))

1/U = 1/h i + 1/ho

(5)

mh Cph[T1 − (t + (T1 − T )/(exp(UA /mh Cph))] = mcCpc(t − t1) + h00A 00(t − t00) + MCpc(dt /dθ ) (6)

The boundary conditions of eq 6 are given by t(0) = t1 and θ(0) = 0. By applying these conditions into eq 6 and integrating it, an expression is obtained to monitor the temperature t in any given time (eq 7).

Nu = 0.027Re 0.8Pr1/3(μ/μw )0.14

(7)

h i = 1429(1 + 0.0146Tm)u 0,8/Di 0,2

where (8)

S = −h00A 00

(9)

X = mcCpc

(10)

Y = mh Cph

(11)

Z = 1 − 1/(exp((UA /mh Cph)))

(12)

(15)

Geankoplis17 presented a simplified correlation to determine the internal coefficient of heat transfer for the flow rate of water inside the tubes at temperature intervals of 4 and 104 °C (eq 16).

t = R(((St00 + Xt1 + (YTZ 1 )) + (( − S − X − (YZt1)Z*))

R = 1/( −S − X + (YZ))

(14)

The internal coefficient of convective heat transfer depends on the internal geometry of the heat transfer surface, the kind of flow (laminar or turbulent), and the physical properties of the fluid. Sieder and Tate introduced the classic equation to calculate the internal coefficient of convective heat transfer inside the turbulent flow in tubes at Reynolds higher than 10000 (eq 15).

Substituting eq 5 in eq 3, the latter comes down to one single variable (t), as shown in eq 6.

− (St 00 + Xt1 + (YTZ 1 )))

(13)

(16)

The external coefficient of convective heat transfer depends on numerous factors such as the type of geometry of the tank and mechanical impeller, the position of the impeller, level of agitation, and the physical properties of the fluids, all of which makes the determination a painstaking task. As a result of the complexity in determining the external coefficient of the convective heat transfer, the solutions of the differential equations governing distribution temperatures are specific.18 As an alternative, the coefficients are calculated through eq 1. B



Article

Figure 2. Sketch of experimental unit: (1) tank of cold fluid; (2) pump for transportation of cold fluid; (3) sphere valve; (4) rotameter (variable-area flowmeter); (5) preheater; (6) inlet temperature of hot fluid; (7) outlet temperature of cold fluid; (8) radial impeller; (9) vertical tube baffles; (10) vessel; (11) outlet temperature of hot fluid; (12) inlet temperature of cold fluid; (13) tachometer; (14) motor supported by bearings and a frequency inverter; (15) thermal controller.

Figure 3. (a) Geometric layout of the main parameters; (b) location of baffles.

Nu = 0.494Re 0.67Pr 0.33(μ/μw )0.14

Figure 1 shows the location of the internal and external convection coefficients for a stirring system with heat transmission. Havas, Deak, and Sawinky19 developed a model for the heating of water and some viscous oils in a tank fitted with a radial impeller, turbine type, and tube baffles made of copper with a bank of five tubes running in a batch operation. Nu = 0.208Re 0.65Pr 0.33(μ/μw )0.40

(18)

Dostál, Petera, and Rieger21 obtained a model for the coefficient of the convective heat transfer of water in a 0.2 m diameter tank, using two banks of tubes with a radial impeller, turbine type, and an axial impeller with two 45° pitched blades and the impeller diameter at 1/3 of the diameter of the tank.

(17)

Nu = 0.571Re 0.67Pr 0.33(μ/μw )0.40

Karcz and Strek20 developed an equation to determine the external coefficient of convective heat transfer by using an axial mechanical impeller with three pitched blades in nonstandard dimension conditions of the vertical tube baffles. The model can be found in eq 18.

(19)

The authors Rosa et al.22 calculated the parameters of eq 1 to determine the external coefficient of heat transfer in an agitated vessel for a steady state condition, with an axial impeller, four 45° pitched, blade turbine, and vertical tube baffles (eq 20). C


Industrial & Engineering Chemistry Research Nu = 17.88Re 0.27Pr 0.29(μ/μw )0.36

Article

temperatures of the study were also obtained from Green and Perry’s Handbook.24

(20)

3. MATERIALS The sketch of the experimental unit used to determine the external coefficient of convective heat transfer is shown in Figure 2. The unit is composed of a transparent acrylic tank that has a working capacity of 50 dm3, a mechanical radial impeller, turbine type, with six flat blades and four vertical copper tubes, each with three tubes, used as baffles. The vertical tube baffles internal diameters (Di) are 11.25 mm and their external diameters (De) are 12.6 mm. The geometric relationships of the tank are presented in Figure 3 and the figures in Table 1 are the relationship of Rushton and Everett.23

Table 3. Physical Properties of Hot Fluid at 60°C from Green and Perry24

size (mm)

dimensional relations

Dt Da H E W J

400 130 400 130 26 40

Da/Dt = 0.325 H/Dt = 1.000 E/Dt = 0.325 W/Dt = 0.065 W/Da = 0.200 J/Dt = 0.100

Table 4. Overall Coefficient of Heat Transfer and External Coefficient of Convective Heat Transfer fluid water

The experimental unit also has a motor supported by bearings with a 2240 W, two boilers, each with 5000 W, a PID thermostat bath control, and two pumps, one for hot fluid displacement and the other for cold fluid.

sucrose 20%

4. EXPERIMENTAL PROCEDURE Water and sucrose solutions at a mass concentration of 20% and 50% were used for heating purposes. Water was used as hot liquid. Temperatures were taken at the inflow and outflow of cold liquid and the inflow and outflow of hot liquid of the vertical tube baffles. The experimental conditions of the study were as follows: the inflow temperature of the cold fluid was between 28−45 °C and the rotation was 90−330 rpm. The constant parameters were the inflow of hot liquid at 60 °C and the flow rate at 0.023 dm3/s. The cold fluid reached the system at a constant flow rate of 0.017 dm3/s. Equation 7 was used to determine the experimental time elapsed, aiming at a steady state operation, which was 100 min for the total mass in the tank. Fifteen trial runs were conducted, 5 for water, 5 for the sucrose solution at 20%, and 5 for sucrose solution at 50%. The outflow temperatures were monitored every 2 min. Table 2 presents the physical properties of the cold fluids, as for example at 32 °C, one of the points used in the work and Table 3 presents the physical properties of hot fluid at 60 °C. The properties of the the fluids at other

sucrose 50%

property

water

sucrose 20% (w/w)

sucrose 50% (w/w)

8 × 10−4 992.22 4177.50 0.650

1.51 × 10−3 1078.2 3640.0 0.470

1.92 × 10−2 1233.60 2820.00 0.449

t1 (°C)

t (°C)

rotation (rpm)

U (W/m2°C)

h0 (W/m2°C)

28 32 36 41 45 28 32 36 41 45 28 32 36 41 45

44.8 47.4 49.2 51.4 53.4 46.2 48.0 49.6 52.4 55.0 46.2 49.6 51.0 53.4 54.2

90 150 210 270 330 90 150 210 270 330 90 150 210 270 330

892.60 1031.90 1081.90 1148.40 1049.30 982.40 1013.60 1204.80 1102.10 1204.80 547.00 700.62 696.50 789.90 741.50

2120.58 3071.02 3508.64 4226.06 3087.15 2689.48 2901.14 5200.90 3626.51 4892.06 841.87 1263.23 1249.10 1567.66 1384.04

In the second stage the dimensionless Nusselt and Reynolds numbers for agitation (outside the tube) and Prandtl number were calculated. Calculations ware also performed for the relationship between the fluid viscosity in the homogeneous mass temperature in the tank and the fluid viscosity of the surface temperature during the heat transfer (Vi). The data is shown in Table 5. The exponents a, b, and c and the constant K of eq 1 were found through a log−log plotting described by Figures 4, 5, 6, and 7 based on the above-mentioned dimensionless numbers. This method was used in the classical work by Chilton, Drew, and Jeleens25 and Rosa et al.22 in predicting the parameters for the semiempirical equation, emphasizing that this method is valid for a steady state operation and turbulent flow. The points on the rotations of 90 rpm were excluded from the multiple regression because the agitation of the sucrose solution (50% w/w) is laminar (Reynolds 1970.59); therefore, for comparison, the corresponding points in the water and sucrose solution (20% w/w) were also discarded. From these graphs the effect of each exponent and the constant were found successively, thereby proposing a model for the external coefficient of convective heat transfer described in eq 21.

Table 2. Physical Properties of Cold Fluids at 32°C from Green and Perry24 μ (Pa·s) ρ (kg/m3) cp (J/kgK) k (W/m°C)

water 4.8 × 10−4 977.77 4189.6 0.686

5. RESULTS AND DISCUSSION First the overall coefficient values for heat transfer and for the external coefficient of convective heat transfer were found from the temperature readings of the steady state operation of the unit, according to Table 4.

Table 1. Geometric Parameters of the Tank Applied in the Present Study parameters

property μ (Pa·s) ρ (kg/m3) cp (J/kgK) k (W/m°C)

D



Article

Table 5. Dimensionless Numbers fluid water

sucrose 20%

sucrose 50%

rotation (rpm)

Nusselt

Reynolds

Prandtl

Vi

90 150 210 270 330 90 150 210 270 330 90 150 210 270 330

1258.50 1822.56 2082.28 2508.05 1832.13 2288.92 2469.05 2852.68 3086.39 4163.45 750.00 1125.37 1112.78 1396.58 1233.00

35525.23 63158.84 93580.39 129080.69 167273.00 20518.12 36302.61 53839.86 75005.34 98106.46 1970.59 3774.20 5847.91 8639.50 11554.99

4.27 3.98 3.73 3.46 3.24 10.65 10.03 9.47 8.74 8.16 103.45 90.32 81.80 71.42 65.40

1.40 1.33 1.28 1.21 1.17 1.41 1.35 1.29 1.23 1.17 1.95 1.75 1.59 1.46 1.35

Figure 6. Exponent c.

Figure 4. Exponent a. Figure 7. Constant K.

the change of state; (IV) radial impeller, turbine type, with six flat blades; (V) heating Newtonian fluids with a dynamic viscosity between 5 × 10−4 Pa.s and 2 × 10−2 Pa·s; (VI) copper tube baffles with four tube banks (VII); and a steady state operation. Figure 8 shows a maximum error of 21% between the experimental Nusselt value and the value predicted by eq 21. So as to compare the present model with other equations available in literature with similar conditions, with radial impeller turbine, eq 21 was compared to the models proposed by Havas, Deak, and Sawinky,19 Karcz and Strek,20 and Dostál, Petera, and Rieger.21 Figure 9 illustrates the comparison among the above-mentioned models and the present study. As can be observed in Figure 9 the proposed model in the present study enables a higher heat transfer as compared with the other three models. However, as the present study is the only one performed in a steady state, it is not possible to compare its efficiency with other equations which were studied in batch operations. Nevertheless it is possible to compare the type of mechanical impeller for heat transfer efficiency. Rosa et al.22 performed a study in a tank with the same conditions but with the use of an

Figure 5. Exponent b.

Nu = 25.03Re 0.38Pr 0.11(μ/μw )0.20

(21)

The use of eq 21 considers the following conditions: (I) Reynolds in the interval from 3700 to 170000; (II) Prandtl with variation between 3.0 and 90.3; (III) heating of water without E



Article

impellers. The radial propeller causes more turbulence and channels the fluid directly toward the walls of the tank where the vertical tube baffles are placed. In contrast, the axial impeller channels the fluid to the bottom of the tank where it subsequently rises to the vertical tube baffles. Hence, on the basis of the dispersion obtained in Figure 10, the radial impeller provides an average increase of 70% in heat transfer.

6. CONCLUSIONS Numerous empirical correlations based on the model proposed by Sieder and Tate have been developed to predict the external coefficient of convective heat transfer. Most of them were designed for batch operation, containing mainly jackets and internal coils on their surfaces. The prediction of heat transfer for vertical tube baffles is still an exhausting task as there are many limitations to the models from which generalizations cannot be made for all geometric configurations. The proposed model in the present study offers a satisfactory prediction of the external coefficient of convection in a steady state flow of 21% maximum deviation between the observed and predicted values. The employment of a radial impeller in the heat transfer processes with vertical tube baffles results in more heating efficiency as compared to the axial impeller. This finding can lower the project area for tube baffles, saving building material.

Figure 8. Modeling error.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: + 55 13 32027119. Address: Rua Oswaldo Cruz, 277 Santos, SP, Brazil. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS ́ University and the The authors acknowledge the Santa Cecilia unit operations laboratory for all the research support and execution.

■

Figure 9. Comparison among the models: Nusselt vs Reynolds.

axial impeller. Figure 10 illustrates the comparison between the axial and radial impellers. The heating of solutions in tanks equipped with vertical tube baffles and radial impellers is more efficient as opposed to axial

Figure 10. Comparison between the axial and radial impellers. F

NOMENCLATURE a = exponent in eq 1 b = exponent in eq 1 c = exponent in eq 1 A00 = external surface area of the tank (m2) A = heat transfer area, m2, As = π·De·L Cpc = cold fluid specific heat (J/(kg K)) Cph = hot fluid specific heat (J/(kg K)) Da = impeller diameter (m) De = external diameter of vertical tube baffle (m) Di = internal diameter of vertical tube baffle (m) Dt = vessel diameter (m) E = distance of impeller from the bottom of the tank (m) hi = Internal convection coefficient (W/(m2 °C)) ho = external convection coefficient (W/(m2 °C)) h00 = air film coefficient (W/(m2 °C)) J = bank of tubes diameter (m) k = thermal conductivity of fluid (W/(m °C)) K = constant in eq 1 L = tube length (m) mc = mass flow of cold liquid (kg/s) mh = mass flow of hot liquid (kg/s) M = mass of cold fluid in the tank (kg) N = impeller rotation speed (rpm) Nu = Nusselt number, Nu = h·Dt/k dx.doi.org/10.1021/ie5008618 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX


Article

Pr = Prandtl number, Pr = Cp·μ/k Qac = rate of accumulated heat (W) Qc = rate of heat received by the cold fluid (W) Qh = rate of heat supplied by the hot fluid (W) Qp = rate of heat lost (W) Re = Reynolds number of agitation, Re = N·Da2ρ/μ t1 = inflow temperature of cold liquid (°C) t = outflow temperature of cold liquid (°C) T1 = inflow temperature of hot liquid (°C) T = outflow temperature of hot liquid (°C) Tm = average temperature of hot fluid (°C) t00 = outside ambient temperature (°C) u = average flow rate speed at the cross section of the vertical tube baffle (m/s) U = overall heat transfer coefficient (W/(m2 °C)) Vi = viscosity ratio, Vi = μ/μw W = width of impeller blade (m)

(15) Nassar, N. N.; Mehrotra, A. K. Design of a Laboratory Experiment on Heat Transfer in an Agitated Vessel. Education for Chemical Engineers 2011, 6, 83−89. (16) McCabe, W. L.; Smith, J. C.; Harriot, P. Unit Operations of Chemical Engineering, 6th ed.; McGraw-Hill: New York, 2001. (17) Geankoplis, C. J. Transport Processes and Unit Operations, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2008. (18) Pittman, J. F. T.; Richardson, J. F.; Sherrard, C. P. An Experimental Study of Heat Transfer by Laminar Natural Convection between an Electrically Heated Vertical Plate and both Newtonian and Non-Newtonian Fluids. Int. J. Heat Mass Transfer 1999, 42, 657−671. (19) Havas, G.; Deak, A.; Sawinky, J. Heat Transfer Coefficients in an Agitated Vessel Using Vertical Tube Baffles. Chem. Eng. J. 1982, 28, 161−165. (20) Karcz, J.; Strek, F. Heat Transfer in Agitated Vessel Equipped with Tubular Coil and Axial Impeller. MIESZANIE’99 1999, 135−140. (21) Dostál, M.; Petera, K.; Rieger, F. Measurement of Heat Transfer Coefficients in an Agitated Vessel with Tube Baffles. Acta Polytech. 2010, 50 (2), 46−57. (22) Rosa, V. S.; Souza Pinto, T. C.; Santos, A. R.; Moino, C. A. A.; Roseno, K. T. C.; Lia, L. R. B.; Tambourgi, E. B.; Dias, M. L.; Toneli, J. T. C. L.; Moraes Júnior, D. External Coefficient of Heat Transfer by Convection in Mixed Vessels Using Vertical Tube Baffles. Ind. Eng. Chem. Res. 2013, 52, 2434−2438. (23) Rushton, J. H.; Costich, E. W.; Everett, H. J. Power Characteristics of Mixing Impellers. Part 1. Chem. Eng. Prog. 1950, 46, 395−467. (24) Green, D. W. And Perry, R. H. Perry’s Chemical Engineers’ Handbook, 8th ed.; McGraw-Hill: China, 2008. (25) Chilton, T. H.; Drew, T. B.; Jeleens, R. H. Heat Transfer Coefficients in Agitated Vessels. Ind. Eng. Chem. 1944, 36, 6.

Greek Letters

μ = dynamic viscosity of cold liquid in the homogeneous tank temperature (Pa·s) μw = dynamic viscosity of cold liquid at the temperature of the wall (Pa·s) ρ = density of agitated liquid (kg/m3) θ = time (seconds)

■

REFERENCES

(1) Engeskaug, R.; Thorbjϕrnsen, E.; Svendsen, H. F. Wall Heat Transfer in Stirred Tank Reactors. Ind. Eng. Chem. Res. 2005, 44, 4949−4958. (2) Sieder, E. N.; Tate, G. E. Heat Transfer and Pressure Drop of Liquids in Tubes. Ind. Eng. Chem. 1936, 1429−1435. (3) Uhl, V. W. Gray, J. B. Mixing Theory and Practice; Academic Press: New York, 1966; Vol. 1, Chapter V. (4) Bourne, J. R., Dossenbach, O., Post, T. Local and Average Mass and Heat Transfer due to Turbine Impellers. Fifth European Conference on Mixing, Wurzburg, West Germany, Stanbury, 1985, 199−207;. (5) Karcz, J.; Strek, F. Heat Transfer in Jacketed Agitated Vessels Equipped with Non-standard Baffles. Chem. Eng. J. 1995, 58, 135−143. (6) Cummings, G. H.; West, A. S. Heat Transfer Data for Kettles with Jackets and Coils. Ind. Eng. Chem. 1950, 42, 2303−2313. (7) De Maerteleire, E., Heat Transfer in Turbine Agitated Gas− Liquid Dispersions. International Symposium on Mixing, European Federation of Chemical Engineering, Mons, Belgium, 1978, XC7− CX35;. (8) Havas, G.; Deak, A.; Sawinsky, J. Heat Transfer to Helical Coils in Agitated Vessels. Chem. Eng. J. 1987, 35, 61−64. (9) Couper, J. R.; Penney, W. R.; Fair, J. R.; Walas, S. M. Chemical Process EquipmentSelection and Design, 2nd ed.; Gulf Professional Publishing: Burlington, MA, 2005. (10) Dias, M. D.; Moino, C. A. A.; Santos, A. R.; Roseno, K. T. C.; Rosa, V. S.; Moraes Júnior, D. Comparaçaõ Experimental da Troca Térmica por Serpentina Helicoidal em Tanques Com Impelidores Mecânicos Tipo Radial e Axial (Comparison of Experimental Thermal Exchange by Helical Coil in Tanks with Mechanical Radial Type and Axial Impellers). Sci. Technol. 2012, 1, 33−38. (11) Pratt, N. H. Heat Transfer in Reaction Tank Cooled by Means of a Coil, Trans. Inst. Chem. Eng., London 1947, 25, 163. (12) Kumpinsky, E. Heat Transfer Coefficients in Agitated Vessel. Latent Heat Models. Ind. Chem. Res. 1996, 35, e-938−e-942. (13) Paul, E. L.; Atiemo-Ubeng, V. A.; Kresta, S. M. Handbook of Mixing, 1st ed.; Wiley-Interscience: New York, 2004. (14) Mohan, P.; Emery, A. N.; Al-Hassan, T. Review Heat Transfer to Newtonian Fluids in Mechanically Agitated Vessels. Exp. Therm. Fluid. Sci. 1992, 5, 861−883. G


External Heat Transfer Coefficient in Agitated Vessels Using a Radial

Recommend Documents