Performance Characteristics of CO2 Capture Using ... - ACS Publications

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Performance Characteristics of CO2 Capture Using Aqueous Ammonia in a Single-Nozzle Spray Tower Youngbok Lim,† Munkyoung Choi,† Kunwoo Han,‡ Minyoung Yi,§ and Jinwon Lee*,† †

Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, 790-784 South Korea Department of CO2 Project and§Department of Energy and Resource, Research Institute of Industrial Science & Technology, Pohang, 790-330 South Korea

‡

ABSTRACT: Spray towers are an effective means of capturing condensable or absorbable gases and vapors, and they have long been used in a variety of applications. However, the use of a spray towers in CO2 capture is a recent development, and the limited number of studies, to date, have reported experimental data only on the capture efficiency for systems with a fixed size, flow rate, and CO2 concentration of the gas mixture, as well as a fixed flow rate and absorbent concentration of the liquid mixture. Systematic investigations of the parameter space have not been reported. In this study, the capture of CO2 from a CO2/air mixture using aqueous ammonia as the absorbent medium with a single nozzle was experimentally measured over a wide range of operating conditions. Relationships between the capture efficiency and the operating parameters are reported for the first time. We also report the experimental observation of the optimum tower diameter for a given spray nozzle.

1. INTRODUCTION Carbon dioxide (CO2) is one of the most important species in the atmosphere affecting global warming, and numerous efforts are currently underway worldwide to reduce CO2 emissions.1,2 Capturing CO2 from gas mixtures containing CO2 is an important method to reduce emissions. Several techniques have been demonstrated to remove CO2 from industrial gas effluents, including gas absorption, cryogenic separation, membrane separation, and adsorption. Gas absorption using alkanolamine solutions is one of the most well-developed techniques for capturing CO2; however, cost issues remain.3 Cost reduction can be achieved by improving the efficiency of absorption, which requires favorable absorbent media and an efficient absorption unit. Alkanolamine solutions such as monoethanolamine (MEA), diethanolamine (DEA), diisopropanolamine (DIPA), methyldiethanolamine (MDEA), and 2-amino-2-methyl-1-propanol (AMP) are commonly used for CO2 absorption; however, these compounds have problems including a high regeneration temperature (∼140 °C), degradation, erosion, and high cost. Aqueous ammonia can be used to capture CO2, and it has many advantages over alkanolamine, including reduced cost, improved chemical stability, a higher CO2 capacity, and a reduced energy requirement for regeneration.4 The absorption performance is strongly affected by the design of the absorption reactor. There are two commonly used types of absorption towers. The first consists of a packed bed, where the reactor column is filled with a solid packing material and the absorbing liquid forms a thin layer on the surface of the packing solids. The gas mixture flows through the pores and is absorbed onto the liquid film. The second consists of a spray tower, where no solid packing material exists inside the reactor volume and the absorbing liquid is supplied as spray droplets. A packed tower and a tray column are typical packed-bed reactors, and these have long been used in chemical and ferrous industries for scrubbing and stripping. Numerous studies have been carried out on their performance characteristics, and the © XXXX American Chemical Society

effects of different packing materials and absorbents for CO2 capture.5−12 However, packed towers suffer from various operational problems, including a high gas-phase pressure drop, liquid channeling and flooding, disintegration of the packing materials caused by the high temperatures, and deposition onto the packing material and subsequent clogging of the voids. In addition, a very large system is required to handle the large gas volume and high CO2 concentrations in commercial power plants, resulting in expensive construction and maintenance. A packing-free spray tower, on the other hand, does not require any space or material for packing, and so is inherently advantageous over a packed tower in that there is a lower pressure drop for the gas flow and a wider possible range of liquid−gas loading ratios. Also, the structure is simpler and the costs for construction and maintenance are lower.13,14 Spray towers have been used mainly for desulfurization and acidic gas removal.14 Several recent studies have assessed the relative benefits of different absorbent materials and designs of the tower and spray nozzle.15−17 The use of spray towers for CO2 capture is a relatively recent development, and most studies of CO2 capture using spray towers have focused on the characteristics of the absorbents.14,18−20 Studies of the performance characteristics are more scarce: the effects of the gas flow characteristics on the masstransfer characteristics were studied for the capture of low concentrations (∼3 vol%) of CO2 in air,21 while Qing23 reported the capture of a high concentration (∼15 vol%) of CO2 in air. However, no rigorous study of the effect of the various design and operating parameters on the CO2 capture performance has been reported to date. Received: June 23, 2013 Revised: August 15, 2013 Accepted: September 30, 2013

A

dx.doi.org/10.1021/ie401981u | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

Article

injected from the top of the tower through the spray nozzle, forming a counter-current flow arrangement between the gas and liquid. The spray nozzle was a pressure-swirl atomizer (Model TGO.3, Teejet Spraying Systems) with an orifice diameter of 0.5 mm. The angle of the ejected full cone spray varied between 50° and 61°, depending on the ejection pressure and the flow rate. Aqueous ammonia was supplied to the spray nozzle using a centrifugal pump, and the flow rate was controlled with a calibrated rotameter. The concentration of CO2 in the gas mixture was controlled using two mass flow controllersone for the air and one for the CO2and the gas mixture was fed through a sufficiently long mixing tube to ensure an even distribution of species in the gas. The gas was introduced into the tower through a distribution panel installed at the bottom to ensure a uniform gas velocity, as shown in Figure 1b. A demister panel made of polypropylene was installed on the ceiling of the tower to capture small droplets in the exiting gas flow, as shown in Figure 1c. The concentration of CO2 in the gas mixture was continuously measured at both the gas inlet and the gas outlet, using an infrared CO2-analyzer (IR600, Hitech Instruments); the measurement error was ±2%. The experiments were repeated three times to monitor the reproducibility of the results. 2.2. Experimental Conditions. The dimensions of the spray tower are listed in Table 1, and the operating conditions are listed in Table 1; these are in the same range as those reported in refs 23−26. Three different 1.0-m high towers were used, with diameters of 0.1, 0.2, and 0.3 m, to investigate the effects of the tower geometry. The following parameters were controlled, as detailed in Table 1: the CO2 concentration (CG) was varied over a range of 6.6−35.7 vol %, the flow rate of gas mixture (QG) was varied over a range of 25−150 L/min, the ammonia concentration (CL) was varied over a range of 5−20 wt %, and the flow rate of aqueous ammonia solution (QL) was varied over a range of 0.20−0.65 L/min. The temperature of the system was fixed at 15 °C. A gas flow rate of 100 L/min corresponded to a velocity of 0.053 m/s in the 0.2-mdiameter spray tower. The Reynolds number (Re) of the gas flow in the 0.2-m-diameter system was in the range of 167−1000 for the gas flow rates used. The spray nozzle can be considered as an orifice with a discharge coefficient of Cd ≈ 0.7. The ejection pressure required for various liquid flow rates and the angles of the full-cone spray for the nozzle are summarized in Table 1. Also shown in the table is the ejection velocity (Ud), the mean droplet diameter (d), and the stopping distance of the generated droplets (S), which were calculated using the following relationships:27−29

The objective of this study was to investigate the performance characteristics of a spray tower for CO2 capture using experimental measurements over a wide range of operating conditions, with the purpose of arriving at empirical relationships between the capture efficiency and the operating parameters. Aqueous ammonia was used as the absorbent, because of its low cost and low energy for regeneration. When ammonia is used to capture CO2, it is converted into ammonium bicarbonate (NH4HCO3) through a series of intermediate products and processes.22 A single spray nozzle was used. The gas flow rate, CO2 concentration, liquid flow rate, and NH3 concentration were varied over a wide range. Three towers with different diameters were used to determine the effects of the tower dimensions.

2. EXPERIMENTAL METHOD 2.1. Experimental Setup. The system used in the experiments was a simple spray tower with a single spray nozzle, as shown in Figure 1. The tower was made from transparent

Ud = Cd

d32 ̅ =

2ΔpL ρl

(1)

2.25σ 0.25μL 0.25Q L 0.25 pL 0.5 ρg 0.25

(2)

and Figure 1. Schematic diagram showing the experimental setup: (a) overall layout, (b) gas distributor, and (c) demister.

S=

acrylic, so that visual observations of the spray were possible. The gas-phase mixture of air and CO2 was supplied from the bottom through a uniform distributor plate, and aqueous ammonia was

ρl d ⎡ 1/3 ⎢Re0 − ρg ⎢⎣

⎛ Re 1/3 ⎞⎤ 6 arctan⎜⎜ 0 ⎟⎟⎥ ⎝ 6 ⎠⎥⎦

(3)

where ΔpL is the nozzle ejection pressure, ρl the liquid density, σ the liquid surface tension, μL the liquid viscosity, QL the liquid B



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Table 1. Characteristic Conditions of the Experimental System parameter

value Geometry

tower diameter (m) tower height (m)

0.1, 0.2, 0.3 1.0 Operating Conditions

gas flow rate, QG (L/min) gas concentration, CG (vol %) liquid flow rate, QL (L/min) liquid concentration, CL (wt %) temperature, T (°C) flow rate (L/min) pressure (MPa) spray angle (deg) droplet velocity, Ud (m/s) droplet diameter, d (μm) stopping distance, S (m)

25−150 6.6−37.5 0.20−0.65 5−20 15 0.16 0.15 50 12.4 115 0.173

Spray Characteristics 0.23 0.3 58 17.5 88 0.139

0.36 0.7 61 26.7 65 0.11

0.45 1

0.6 2

32 57.5 0.101

45.2 43.7 0.08

Figure 2. Effect of the operating conditions on the CO2 capture efficiency for the 0.2-m-diameter system: (a) gas flow rate, (b) CO2 concentration, (c) aqueous ammonia flow rate, and (d) ammonia concentration.

flow rate, ρg the gas density, and Re is the Reynolds number (Re0 = ρgUdd/μ). The CO2 capture efficiency (η) was calculated using the CO2 concentrations measured at the inlet and the outlet of the gas flow, according to the following relationship: η (%) =

CCO2,in − CCO2,out CCO2,in

3. RESULTS AND DISCUSSION 3.1. Effect of the Operating Conditions on the Capture Efficiency. The change in the capture efficiency in response to the operating conditions was experimentally measured with the 0.2-m-diameter system first. Figure 2a shows the results obtained as a function of the flow rate. The gas flow rate (QG) was increased from 25 L/min to 150 L/min under the following fixed conditions: CG = 18%, QL = 0.60 L/min, and CL = 10%. The CO2 capture efficiency decreased from 86.6% to 37.3%. This can be

× 100 (4) C



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The low efficiency of the 0.1-m-diameter tower was attributed to the shorter residence time of the gas flow. The reduced efficiency of the 0.3-m-diameter, with respect to the 0.2-m-diameter tower, however, cannot be explained based on the residence time. The difference in performance of different diameter towers resulted from a differing distribution of droplets over the flow cross-section. Although the droplets were ejected from the nozzle at a high velocity, the droplet velocity rapidly approached terminal velocity soon after ejection. After a short period of time, the radial velocity component was almost zero, and, for the majority of their trajectory, the droplets simply fell vertically downward. If the tower diameter was too large, the droplets could not reach the wall, so that the gas flowing near the wall did not have a chance to be absorbed onto droplets. If the tower diameter was too small, part of the ejected droplets impinged on the wall shortly after ejection, and therefore could not absorb CO2. For optimum capture performance, the droplets forming the outskirts of the spray pattern should just reach the wall of the tower with a small radial velocity. If this is achieved, droplets will not impinge on the walls without absorbing sufficient CO2, and the flow cross-section will be filled with droplets, leaving no channels for gas flow at the edges of the tower. As shown in Table 1, the stopping distance for droplets generated with the nozzle used in this study was ∼0.173 m at the lowest liquid flow rate of 0.16 L/min. Therefore, the radial extent of the droplets ejected at the largest ejection angle of 60° was ∼0.087 m. Thus, the optimum tower diameter is expected to be 0.173 m. Trajectories of the droplets ejected at a variety of angles in three towers of different diameters were calculated using the CFD package Ansys Fluent v13; the results are shown in Figure 4. The gas flow rate was 50 L/min, and liquid flow rate was 0.16 L/min to ensure the longest possible stopping distance. These results support the optimum diameter given above. The radial extent of the droplets changed, depending on the liquid flow rate; therefore, the optimum diameter or geometry was dependent on the operating conditions. 3.3. Relationship between the Capture Efficiency and Operating Parameters. In the experimental data shown in Figure 2, only one parameter was varied while the other three parameters were kept constant for a given dataset. However, a more general set of relationships reflecting the variation of all of the parameters is more useful for system design and optimization. If mass transfer through diffusion gradients both in and out of the absorbent droplets is fast enough, and chemical equilibrium is quickly established, the entire absorption process can be assumed to occur in a quasi-steady-state equilibrium, and the overall performance can be represented by the relative chemical inertias between CO2 and ammonia. The ratio of mass fluxes of CO2 and ammonia is then a good candidate for a parameter describing the capture efficiency.31 Plotting the experimental data in the form of efficiency versus mass flux ratio, the variation of the liquid conditions at fixed gas conditions was in good agreement with the mass flux ratio description, as shown in Figure 5a; however, the variation of gas conditions under fixed liquid conditions was not, as shown in Figure 5b. This result is to be expected, because the overall masstransfer coefficient is strongly dependent on the concentration boundary layer formed around the droplets, which are, in turn, affected by the gas concentration and gas flow velocity. The following empirical relationship was found to fit all of the experimental data, including variation of all four operating parameters:

attributed to the reduced gas residence time due to the increased flow velocity. Figure 2b shows the results of varying the CO2 concentration of the gas mixture from CG = 6.6% to CG = 35.7% under the same absorbent conditions and a gas flow rate of 50 L/min. The capture efficiency decreased from 80.9% to 56.2%. The reduction in capture efficiency at higher CO2 concentrations was mainly due to the rapid depletion of ammonia close to the inside surface of the droplets with CO2 absorption from a CO2-rich gas.30 Figure 2c shows the effect of varying the flow rate of the absorbent solution (QL) from 0.20 L/min to 0.65 L/min under the fixed conditions of CL = 10%, CG = 18.5%, and QG = 50 L/min. The capture efficiency increased from 41.6% to 70.4% when the flow rate was increased, because of the slower decrease in ammonia concentration within the droplets due to the enhanced liquid-togas flow rate ratio, and the enhanced absorption mass-transfer rate from the additional increase in surface area of the droplets due to the decreased droplet size at the higher liquid injection rate. Figure 2d shows the effect of varying the ammonia concentration (CL) from 5% to 20% under the fixed conditions of QL = 0.5 L/min, CG = 18.5%, and QG = 50 L/min. Increasing CL resulted in an increase in η from 45.2% to 92.9%. This increase in efficiency at higher ammonia concentrations can be explained by the rate of decrease in ammonia concentration due to absorbing CO2, which will be slower when there is more ammonia. The behavior described above is to be expected based on simple mass transfer principles, and is in broad agreement with previous reports.22,23,26 3.2. Effect of the Tower Geometry. The geometry of the tower affects the gas flow and the distribution of the absorbent droplets. The effects of the tower length are not particularly interesting: the contact time increases roughly proportionally with the length of the tower. However, the mass-transfer pattern is strongly affected by diameter of the vessel, because of the effect on the gas flow and distribution of the droplets. In order to examine the effects of the geometry on the capture performance, experiments were carried out using vessels that were 0.1, 0.2, and 0.3 m in diameter, all with a fixed height of 1.0 m. The capture efficiency at various gas flow rates was markedly different between the towers with different diameters, as shown in Figure 3. The 0.2-m-diameter tower showed the

Figure 3. Capture efficiency as a function of the gas flow rate for the three different diameter towers, with the following parameters kept constant: CL = 10%, QL = 0.65 L/min, and CG = 17.5%.

highest capture efficiency for all of the gas flow rates tested, and the 0.1-m-diameter tower showed the lowest capture efficiency.

η = 1 − exp( −AX ) D

(5)



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Figure 4. Trajectories of the droplets injected at different angles in the three towers. The droplet velocities are shown in different colors for the different diameter towers.

Figure 5. Change in the capture efficiency expressed in terms of the NH3/CO2 molar flux ratio, (QLCL)/(QGCG): (a) as a function of the absorbent conditions and (b) as a function of the gas flow conditions.

where ⎛ Q ⎞0.7 C 1.0 L X = ⎜⎜ L ⎟⎟ 0.4 Q C ⎝ G⎠ G ⎛ Q C L ⎞0.7 = ⎜⎜ L ⎟⎟ (C LCG)0.3 ⎝ Q GCG ⎠

(6)

(7)

Plots showing the relationships are shown in Figure 6. The parameter X is a dimensionless number that represents the effects of all four operational parameters. Parameter A is an empirical factor that represents the effectiveness of the system design in terms of droplet distribution, related to the relative capture performance for different systems at given operating conditions. Best-fit values are A = 0.65, 1.71, and 1.31 for the 0.1-, 0.2-, and 0.3-m-diameter towers, respectively. This implies that the capture potential of the 0.1- and 0.3-m-diameter towers is ∼40% and ∼80%, respectively, relative to the 0.2-m-diameter system under the same operating conditions. The general performance characteristics conform to the case of very fast

Figure 6. Empirical relationships describing the dependence of the capture efficiency on the operating parameters. The symbols represent the experimental data, and solid lines represent empirical curves.

reaction of Dimiccoli et al.,32 and the mass transfer was much enhanced by the chemical reaction than with pure physical absorption, as was predicted in it. E



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(6) Strigle, R. F. Random Packings and Packed Towers, Design and Applications; Gulf Publishing Company: Houston, TX, 1987. (7) Aroonwilas, A. High Efficiency Structured Packing for CO2 Absorption Using 2-Amino-2-methyl-1-propanol (AMP). M.A.Sc. Thesis, University of Regina, Regina, Saskatchewan, Canada, 1996. (8) Aroonwilas, A.; Veawab, V.; Tontiwachwuthikul, P. Behavior of the Mass-Transfer Coefficient of Structured Packings in CO2 Absorbers with Chemical Reactions. Ind. Eng. Chem. Res. 1999, 38, 2044−2050. (9) Aroonwilas, A.; Tontiwachwuthikul, P.; Chakma, A. Effects of Operating and Design Parameters on CO2 Absorption in Columns with Structured Packings. Sep. Purif. Technol. 2001, 24, 403−411. (10) Aroonwilas, A.; Veawab, A. Characterization and Comparison of CO2 Absorption Performance into Single and Blended Alkanolamines in Packed Column. Ind. Eng. Chem. Res. 2004, 43 (9), 2228−2237. (11) Yeh, J. T.; Pennline, H. W.; Resnik, K. P. Study of CO2 Absorption and Desorption in a Packed Column. Energy Fuels 2001, 15 (2), 74−278. (12) DeMontigny, D.; Tontiwachwuthikul, P.; Chakma, A. Comparing the Absorption Performance of Packed Columns and Membrane Contactors. Ind. Eng. Chem. Res. 2005, 44 (15), 5726−5732. (13) Mehta, K. C.; Sharma, M. M. Mass transfer in spray columns. Br. Chem. Eng. 1970, 15 (11), 1440−1444. (14) Taniguchi, I.; Takamura, Y.; Asano, K. Experimental study of gas absorption with a spray column. J. Chem. Eng. Jpn. 1997, 3 (3), 427−433. (15) Feldkamp, M.; Neumann, J.; Feldkamp, H. Influence of Droplet Collision on the Design of Flue-Gas Desulphurization Scrubbers in Power Plant Technology. Chem. Eng. Technol. 2003, 26 (9), 956−959. (16) Weiss, S.; Ruhland, F.; Kind, R. Flue gas desulphurisation by absorption with lime. Int. Chem. Process. 1990, 11 (1), 157−169. (17) Nguyen, K. D.; Spink, D. R. Turbotak Technology in FGD Scrubbers to Control SO2 Emissions. Int. Pittsburgh Coal Conf. 1993, 10, 812−817. (18) Mehta, K. C.; Sharma, M. M. Mass transfer in spray columns. Br. Chem. Eng. 1970, 15 (12), 1556−1558. (19) Fukunaka, Y.; Inada, A.; Ogawa, A.; Asaki, Z. Absorption of CO2 Gas into Falling Droplets of Aqueous NaOH Solution. Metall. Rev. MMIJ 1992, 9 (1), 33−50. (20) Yeh, N. K.; Rochelle, G. T. Liquid-Phase Mass Transfer in Spray Contactors. AIChE J. 2003, 49 (9), 363−2373. (21) Javed, K. H.; Mahmud, T.; Purba, E. The CO2 capture performance of a high-intensity vortex spray scrubber. Chem. Eng. J. 2010, 162 (2), 448−456. (22) Liu, J.; Wang, S.; Zhao, B.; Tong, H.; Chen, C. Absorption of carbon dioxide in aqueous ammonia. Energy Procedia 2009, 1 (1), 933− 940. (23) Qing, Z.; Yincheng, G.; Zhenqi, N. Experimental studies on removal capacity of carbon dioxide by a packed reactor and a spray column using aqueous ammonia. Energy Procedia 2011, 4, 519−524. (24) Chakma, A.; Chornet, E.; Overend, R. P.; Dawson, W. H. Absorption of CO2 by Aqueous Diethanolamine (DEA) Solutions in a High Shear Jet Absorber. Can. J. Chem. Eng. 1990, 68, 593−598. (25) Kuntz, J.; Aroonwilas, A. Performance of spray column for CO2 capture application. Ind. Eng. Chem. Res. 2008, 47 (1), 145−153. (26) ZhenQi, N.; YinCheng, G.; WenYi, L. Experimental studies on removal of carbon dioxide by aqueous ammonia fine spray. Sci. China Tech. Sci. 2010, 53, 117−122. (27) Han, Z.; Perrish, S.; Farrell, P. V.; Reitz, R. D. Modeling Atomization Processes of Pressure−Swirl Hollow-Cone Fuel Sprays. Atomization Sprays 1997, 7 (6), 663−684. (28) Lefebvre, A. H. Gas Turbine Combustion; Hemisphere Publishing Co.: Washington, DC, 1983. (29) Mercer, T. T. Aerosol Technology in Hazard Evaluation; Academic Press: New York, 1973. (30) Levenspiel, O. Chemical Reaction Engineering; Wiley: New York, 1792. (31) Zhao, B.; Su, Y.; Tao, W.; Li, L.; Peng, Y. Post-combustion CO2 capture by aqueous ammonia: A state-of-the-art review. Int. J. Greenhouse Gas Control 2012, 9, 355−371.

These relationships hold only for the tower geometry and operating conditions used in this study. However, they are expected to be applicable to cases where the system diameter is close to the maximum radial extent of the spray droplets. The effect of the tower height can be considered by multiplying the AX term in eq 5 by L/L0. Equation 5 looks similar to the traditional ε-NTU relationship for heat exchangers in the limiting condition of very small heattransfer coefficient or very small heat capacity ratio between hot and cold streams.33 The term in the first parentheses on the righthand side is equivalent to the heat capacity ratio and the term in the second parentheses plays the role of NTU. This can be an acceptable interpretation, if it is recalled that the conversion rate of CO2 into bicarbonate compound is determined by the concentration of the absorbent and also the resolved CO2 which is proportional to CO2 concentration in the gas phase due to Henry’s law. One important characteristics of chemical absorption in a spray tower is noticed from eq 7 that, if the concentrations of NH3 and CO2 are changed in proportion, CO2 capture efficiency should be higher for conditions of higher concentration of NH3 and/or CO2, which has not been noticed previously.

4. CONCLUSION The efficiency of CO2 capture using aqueous ammonia droplets in a single-nozzle spray tower was experimentally measured over a wide range of flow rates and concentrations of both the gas- and liquid-phase mixtures. Higher efficiency was observed at low gas flow rates and high liquid flow rates, as well as at low CO2 concentrations and high NH3 concentrations. Empirical relationships describing the capture efficiency in terms of the four operating parameters were derived. The effect of the operating conditions could be represented by a single dimensionless parameter describing all four operating parameters. When the gas flow conditions were fixed, the effect of the liquid flow conditions on the efficiency could be described by the ratio of the mass fluxes of CO2 and NH3. It was shown that there exists an optimum tower diameter for maximum capture efficiency, which can be determined by the nozzle characteristics and corresponds to the maximum radial extent of the spray droplets.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-54-279-2170. Fax: +82-54-279-3199. E-mail: jwlee@ postech.ac.kr. Notes

The authors declare no competing financial interest.

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REFERENCES

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(32) Dimiccoli, A.; Di Serio, M.; Santacesaria, E. Mass Transfer and Kinetics in Spray-Tower-Loop Absorbers and Reactors. Ind. Eng. Chem. Res. 2000, 39 (11), 4082−4093. (33) Incropera, F. P.; DeWitt, D. P. Introduction to Heat Transfer; John Wiley & Sons: New York, 1996.

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