International Journal of Heat and Mass Transfer 53 (2010) 12–17
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Heat transfer of nanofluids in a shell and tube heat exchanger B. Farajollahi, S.Gh. Etemad *, M. Hojjat Department of Chemical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
a r t i c l e
i n f o
Article history: Received 6 January 2009 Received in revised form 15 September 2009 Accepted 15 September 2009 Available online 2 November 2009 Keywords: Nanofluids Nanoparticles Shell and tube heat exchanger Heat transfer
a b s t r a c t Heat transfer characteristics of c-Al2O3/water and TiO2/water nanofluids were measured in a shell and tube heat exchanger under turbulent flow condition. The effects of Peclet number, volume concentration of suspended nanoparticles, and particle type on the heat characteristics were investigated. Based on the results, adding of naoparticles to the base fluid causes the significant enhancement of heat transfer characteristics. For both nanofluids, two different optimum nanoparticle concentrations exist. Comparison of the heat transfer behavior of two nanofluids indicates that at a certain Peclet number, heat transfer characteristics of TiO2/water nanofluid at its optimum nanoparticle concentration are greater than those of c-Al2O3/water nanofluid while c-Al2O3/water nanofluid possesses better heat transfer behavior at higher nanoparticle concentrations. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Due to the limitation of fossil fuel in the world, subject of energy consumption optimization in various industrial processes becomes very important. In chemical processes one of the most important devices related to energy and heat transfer is heat exchanger. For decades, efforts have been done to enhance heat transfer, reduce the heat transfer time, minimize size of heat exchangers, and finally increase energy and fuel efficiencies. These efforts include passive and active methods such as creating turbulence, increasing area, etc. Most of them are limited by inherent restriction of thermal conductivity of the conventional fluids (such as water, mineral oil and ethylene glycol). The poor heat transfer properties of the employed fluids in the industries are obstacles for using different types of heat exchangers. Since solid particles have thermal conductivity higher than that of common fluids, when they are dispersed in the fluids result in higher heat transfer characteristics. There are many types of particles such as metallic, nonmetallic and polymeric. However, due to large size of micro and macro-sized particles, they will face some problems in using of these suspensions, such as clogging of flow channels due to poor suspension stability, erosion of heat transfer device, and increasing in pressure drop. Modern material technology helps us to produce nanometersized particles that their mechanical and thermal properties are different from those of the parent materials. Recently, there has
* Corresponding author. Present address: Department of Chemical and Biological Engineering, University of Ottawa, Ottawa, Ontario, Canada K1 N 6N5. Tel.: +1 613 8623981; fax: +1 613 5625172. E-mail address:
[email protected] (S.Gh. Etemad). 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2009.10.019
been interest in using nanoparticles to modify heat transfer performance of suspensions. Nanofluids are stable suspension of nanometer-sized particles (smaller than 100 nm in at least one dimension) in conventional heat transfer fluids. Nanofluids are suitable for engineering applications and show several potential advantages such as better stability, dramatically high thermal conductivity and no extra pressure drop compared to other suspensions. Since thermal conductivity is one of the important parameters for heat transfer enhancement, some studies have been done on thermal conductivity of nanofluids. All experimental results have indicated the enhancement of thermal conductivity by addition of nanoparticles. For example Wang et al. [1], Lee et al. [2], and Das et al. [3] measured the thermal conductivity of nanofluids containing Al2O3 and CuO nanoparticles and investigated the effect of the base fluid on the thermal conductivity of the nanofluids. Xie et al. [4,5] examined the effect of base fluid on thermal conductivity of Al2O3 nanofluid. Li and Peterson [6] investigated on the temperature dependency of thermal conductivity enhancement of Al2O3/water and CuO/water nanofluids. There are several published studies on the forced convective heat transfer coefficient of nanofluids and most of them are under the constant heat flux or constant temperature boundary conditions at wall of tubes and channels. In shell and tube heat exchangers the real heat boundary condition is different from the aforementioned boundary conditions and wall temperature and/ or heat flux is not constant. The experimental results for forced convection inside a channel show that convective heat transfer coefficient of nanofluids is enhanced compared to base fluid. These studies include investigation on convective heat transfer of c-Al2O3/water and TiO2/water nanofluids for turbulent flow in a
B. Farajollahi et al. / International Journal of Heat and Mass Transfer 53 (2010) 12–17
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Nomenclature A Cp D d h k L _ m Nu Pe Pr Q Re T U V
heat transfer area (m2) specific heat (kJ kg1 K1) tube diameter (m) nanoparticle diameter (m) convective heat transfer coefficient (W m2 oC1) thermal conductivity (W m1oC1) tube length (m) mass flow rate (kg s1) Nusselt number (Dimensionless) Peclet number (Dimensionless) Prandtl number (Dimensionless) heat transfer rate (W) Reynolds number (Dimensionless) temperature (oC) overall heat transfer coefficient (W m2 oC1) velocity (m2/s)
stainless steel tube [7], copper nanoparticles suspended in water for turbulent flow in a brass tube [8], suspensions of c-Al2O3 nanoparticles in water for laminar flow in a copper tube [9], graphite nanoparticles dispersed in two base fluids for laminar flow in a horizontal tube exchanger [10], CuO/water and Al2O3/water nanofluids for laminar flow in a copper tube [11], aqueous suspensions of TiO2 nanoparticles and nanotubes flowing upward through a vertical pipe in both laminar and turbulent flow regimes [12,13]. The objective of the present study is to investigate on the heat transfer characteristics (such as overall and convective heat transfer coefficients, and Nusselt number) of c-Al2O3/water and TiO2/water nanofluids for turbulent flow in a horizontal stainless steel shell and tube heat exchanger. 2. Experimental setup Fig. 1 shows the flow loop of constructed system. The system mainly includes two flow loops (nanofluids and water flow loops).
Greek symbols DTlm logarithmic mean temperature difference(oC) a thermal diffusivity (m2/s) q density (kg m3) t Kinematic viscosity (m2/s) nanoparticle volume concentration (Dimensionless) um Subscripts f fluid i inside in inlet m mean nf nanofluid o outside out outlet p particles w wall
It contains a stainless steel shell and tube heat exchanger, a heating tank (15 L), a nanofluids cooling system, a nanofluids reservoir tank (5 L), by-pass-line, two pumps in order to provide required flow rates, thermocouples, and two flow meters. The test section is a shell and tube heat exchanger where nanofluid passes through the 16 tubes with 6.1 mm outside diameter, 1 mm thickness, and 815 mm length and water flows inside the shell with 55.6 mm inside diameter. The tube pitch is 8 mm and the baffle cut and baffle spacing are 25% and 50.8 mm, respectively. The heat exchanger and pipe lines are thermally insulated to reduce heat loss to the surrounding. The flow rates are controlled by two valves, one at the main flow loop and the other at the by-passline (Fig. 1). The flow meters of water and nanofluids were calibrated by weighting collected water and nanofluids over a certain period of time. Four thermocouples (K type) were inserted in the inlet and outlet pipes of heat exchanger. Thermocouples were calibrated by PT100 type thermocouple. The error in measurement of the fluid temperature by the K type thermocouple was ±0.1 °C. Two
Fig. 1. Experimental setup.
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of the thermocouples, 1 and 2, measure the nanofluid temperatures at the inlet and outlet of heat exchanger tube side, and the other two thermocouples, 3 and 4, measure the water temperatures at the inlet and outlet of heat exchanger shell side. Error analysis was carried out by calculating the error of measurements. Results show that the maximum error for the overall heat transfer coefficient is about 4.2%. Two series of nanofluids were prepared using two different types of nanoparticles, c-Alumina (c-Al2O3) and Titanium dioxide (TiO2) with mean diameters of 25 and 10 nm, respectively, while water used as base fluid. Table 1 contains the other properties of these nanoparticles. To prepare stable nanofluids, ultrasonic vibration was used to reduce the particle agglomeration. The nanofluids with different particle volume concentrations were prepared to investigate the effect of the nanoparticle concentrations on the heat transfer performance of the nanofluids. The nanoparticle volume concentrations of c-Al2O3/water and TiO2/water nanofluids vary in the range of 0.3–2% and 0.15–0.75%, respectively. 3. Data processing The experimental data were used to calculate overall heat transfer coefficient, convective heat transfer coefficient and Nusselt number of nanofluids with various particle volume concentrations and Peclet numbers. The thermophysical properties were calculated based on mean bulk temperature of nanofluids. The heat transfer rate of the nanofluid is
_ pnf ðTout Tin Þ Q ¼ mC
qnf ¼ ð1 uv Þqf þ uv qp
ð2Þ
Subscripts f, p, and nf refer to the base fluid, the nanoparticles, and the nanofluid, respectively. uv is the nonoparticle volume concentration. C pnf is the effective specific heat of the nanofluid which can be calculated from Xuan and Roetzel relation [14]:
ðqC p Þnf ¼ ð1 uv ÞðqC p Þf þ uv ðqC p Þp
ð3Þ
The heat transfer coefficient of the test fluid, hi, can be calculated by the following equation [15]:
Do 1 1 Di Ln Di Di 1 ¼ þ þ 2kw U i hi D o ho
hi Di knf
ð6Þ
where the effective thermal conductivity (knf) of the nanofluids can be evaluated by Maxwell’s model that is given as following [17]:
knf ¼ kf
kp þ 2kf 2uv ðkf kp Þ kp þ 2kf þ uv ðkf kp Þ
ð7Þ
Maxwell’s formula shows that the effective thermal conductivity of nanofluids (knf) relies on the thermal conductivity of spherical particles (kp), the thermal conductivity of base fluid (kf) and volume concentration of the solid particles (uv). 4. Results and discussions To evaluate the accuracy of the measurements, experimental system was tested with distilled water before measuring the convective heat transfer of nanofluids. Fig. 2 shows the comparison between the measured overall heat transfer coefficient and prediction of Eq. (4) in which hi is evaluated by Gnielinski correlation for turbulent flow through a tube [18]:
Nu ¼ 0:012ðRe0:87 280ÞPr0:4
ð8Þ
As shown in Fig. 2, the good agreement exists between the experimental data and predicted values. 4.1. Convective heat transfer of nanofluids Figs. 3 and 4 present the overall heat transfer coefficient of the cAl2O3/water and TiO2/water nanofluids versus Peclet number for various volume concentrations respectively. From the results, the overall heat transfer coefficient of nanofluids increases significantly with Peclet number. For both nanofluids the overall heat transfer coefficient at a constant Peclet number increases with nanoparticle concentration compared to the base fluid. As clearly shown in Fig. 3, the maximum enhancement of the overall heat transfer coefficient of c-Al2O3/water nanofluids occurs at 0.5% volume concentration and the enhancement at the Peclet number about 50,000 is approximately 20%. At this Peclet number (50,000) the enhancement of the overall heat transfer coefficient at 0.3%, 0.75%, 1%, and 2% nanoparticle volume concentrations are about 14%, 16%, 15%, and 9%, respectively. For TiO2/water nanofluids the maximum enhancement is
ð4Þ 5000
ð5Þ
where Ai = pDiL and DTlm is the logarithmic mean temperature difference.
Experimental
4000
2
Q ¼ U i Ai DT lm
Theory
Ui (W/m K)
where Di and Do are the inner and outer diameters of tubes respectively, Ui is the overall heat transfer coefficient based on the inside tube area, hi and ho are the individual convective heat transfer coefficients of the fluids inside and outside the tubes respectively and kw is the thermal conductivity of the tube wall. Ui is given by:
3000
2000
Table 1 Physical properties of the nanoparticles.
c-Al2O3 TiO2
Nunf ¼
ð1Þ
_ is the mass flow rate of the nanofluid, and Tout and Tin are where m the outlet and inlet temperatures of the nanofluid, respectively. The effective density of nanofluid is
Nanoparticles
The outside heat transfer coefficient can be computed by Bell’s procedure [16]. Nusselt number of nanofluids is defined as:
Mean diameter (nm)
Specific surface area (m2/gr)
Density (kg/m3)
25 10
180 120
3700 3900
Thermal conductivity (W/m K)
Specific heat (kJ/kg K)
46 8.4
880 710
1000 15000
25000
35000
45000
55000
65000
Pe Fig. 2. Comparison between the measured overall heat transfer coefficient and predicted values for distilled water.
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3000
11000
9000
2
2
Ui (W/m K)
3500
Distilled water 0.30% Al2O3 0.50% Al2O3 0.75% Al2O3 1% Al2O3 2% Al2O3
hi (W/m K)
4000
2500
0.50% Al2O3 0.75% Al2O3 1% Al2O3 2% Al2O3
5000
3000
2000
1500 15000
7000
Distilled water 0.30% Al2O3
25000
35000
45000
55000
1000 15000
65000
25000
35000
Pe
3000
11000
0.3% TiO2
9000 2
hi (W/m K)
2
Ui (W/m K)
Distilled water
0.5% TiO2 0.75% TiO2
2500
7000
Distilled water 0.15% TiO2 0.3% TiO2 0.5% TiO2 0.75% TiO2
5000
3000
2000
1500 15000
65000
Fig. 5. Convective heat transfer coefficient of c-Al2O3/water nanofluid versus Peclet number for different volume concentrations.
4000
0.15% TiO2
55000
Pe
Fig. 3. Overall heat transfer coefficient of c-Al2O3/water nanofluid versus Peclet number for various volume concentrations.
3500
45000
25000
35000
45000
55000
65000
Pe
1000 15000
25000
35000
45000
55000
65000
Pe
Fig. 4. Overall heat transfer coefficient of TiO2/water nanofluid versus Peclet number for various volume concentrations.
Fig. 6. Convective heat transfer coefficient of TiO2/water nanofluid versus Peclet number for different volume concentrations.
observed at 0.3% particle volume concentration (Fig. 4). At a certain Peclet number (44,000) the enhancement of the overall heat transfer coefficient at 0.15, 0.3, 0.5, and 0.75 vol.% are about 11%, 24%, 16%, and 13%, respectively. Based on the experimental data the optimum volume concentration of Al2O3 and TiO2 particles in water are 0.5 and 0.3 vol.%, respectively. Although the thermal conductivity of Al2O3 nanoparticle is higher than that of TiO2 nanoparticle (Table 1), the optimum volume concentration of TiO2 nanoparticle in water is less than that of Al2O3 nanoparticle. The difference may be related to the difference between the mean diameters of two nanoparticles. As shown in Table 1, the mean diameter of TiO2 nanoparticle is less than that of Al2O3 nanoparticle. Figs. 5 and 6 illustrate variation of convective heat transfer coefficients with Peclet number for different volume concentrations of Al2O3 and TiO2 nanoparticles, respectively. As shown in Figs. 5 and 6, addition of nanoparticles has strong influences on the convective heat transfer coefficient of both nanofluids. The maximum enhancement of convective heat transfer coefficient with 0.5 vol.% c-Al2O3/water and 0.3 vol.% TiO2/water nanofluids exceeds 50%. This enhancement for 0.3, 0.5, 0.75, 1, and 2 vol.% of c-Al2O3/water are about 46%, 56%, 46%, 38%, and 19%, respectively. The convective heat transfer coefficients of the TiO2/water nanofluid with 0.15, 0.3, 0.5, and 0.75 vol.% of TiO2 nanoparticles are about 20%, 56%, 33%, and 18% higher than those of water.
Generally the enhancement of convective heat transfer coefficient depends on increasing of the fluid thermal conductivity and decreasing of thermal boundary layer thickness. Thermal conductivity of the nanofluids increases with increasing of the volume concentrations. Decreasing of the thermal boundary layer thickness can be due to mobility of particles near the wall, migration of them to the center of tube, and reduction of viscosity at the wall region. Convective heat transfer coefficient of nanofluids decreases with nanoparticle volume concentration at the concentrations higher than the optimum. This may be associated with the effect of high viscosity at the higher volume concentrations that causes in thickening of thermal boundary layer. In other words, at the higher volume concentrations the effect of increase of viscosity on the heat transfer coefficient is more than the effect of increase of thermal conductivity. Figs. 7 and 8 illustrate the effect of c-Al2O3 and TiO2 nanopaticles concentrations on the Nusselt number of the nanofluids at various Peclet numbers. As shown in Figs. 7 and 8, the enhancement of the convective heat transfer coefficient of both nanofluids is much higher than that of thermal conductivity. The enhancement of the Nusselt number for both nanofluids is particularly significant at their optimum nanoparticle concentrations and is higher than 50%. Based on the results at the lower volume concentrations (<0.3 vol.%) TiO2 nanoparticle possesses better heat transfer
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B. Farajollahi et al. / International Journal of Heat and Mass Transfer 53 (2010) 12–17
100
Nui
60
110
70 50
20
30
25000
2% Al2O3 (Theory) 2% Al2O3 (Exp)
1% Al2O3 2% Al2O3
40
0 15000
0.50% Al2O3 (Theory) 0.50% Al2O3 (Exp)
90
Nui
80
Distilled water 0.30% Al2O3 0.50% Al2O3 0.75% Al2O3
35000
45000
55000
10 15000
65000
25000
35000
45000
Pe Fig. 7. Nusselt number of c-Al2O3/water nanofluid versus Peclet number for different volume concentrations.
80
Fig. 9. Comparison between the experimental results and calculated values from correlation (9) for c-Al2O3/water nanofluids.
100
Distilled water 0.15% TiO2 0.3% TiO2
0.3% TiO2 (Theory) 80
60
40
40
20
20
0 15000
25000
0.3% TiO2 (exp) 0.75% TiO2 (Theory)
0.5% TiO2 0.75% TiO2
Nui
60
65000
0.75% TiO2 (exp)
Nui
100
55000
Pe
35000
45000
55000
65000
0 15000
Pe
25000
35000
Pe
45000
55000
65000
Fig. 8. Nusselt number of TiO2/water nanofluid versus Peclet number for different volume concentrations.
Fig. 10. Comparison between the experimental results and calculated values from correlation (9) for TiO2/water nanofluids.
behavior than c-Al2O3 nanoparticle and at the higher volume concentrations (>0.3 vol.%) c-Al2O3 nanoparticle is more effective than TiO2 nanoparticle in augmenting the heat transfer coefficient. This behavior may be related to the competition of thermal conductivity and particle size of both nanoparticles.
where the thermal diffusivity is given by:
4.2. Comparison between experimental results and available correlations In Figs. 9 and 10 the experimental results for the Nusselt number of c-Al2O3/water and TiO2/water nanofluids are compared with the prediction of Xuan and Li correlation. The correlation was provided by Xuan and Li for turbulent flow of nanofluids inside a tube [8]:
Nunf ¼ 0:0059 1 þ 7:6286u0:6886 Pe0:001 Pr0:4 Re0:9238 v p nf nf
ð9Þ
The particle Peclet number, Reynolds number and the Prandtl number for nanofluid are defined respectively as:
Pep ¼
V m dp
Renf ¼ Prnf ¼
anf V mD #nf #nf
anf
/nf ¼
knf knf ¼ ðqC p Þnf ð1 uv ÞðqC p Þf þ uv ðqC p Þp
ð13Þ
Results show that at 0.5 vol.% of c-Al2O3 nanoparticles and at 0.3 vol.% of TiO2 nanoparticles a good agreement exist between the experimental results and the predicted values by Eq. (9) specially at higher Peclet numbers. At 2 vol.% c-Al2O3 nanoparticles and 0.75 vol.% TiO2 nanoparticles the correlation offers Nusselt numbers which are higher than those of experimental data. For example, the deference between the experimental data and the predicted values for 0.5 vol.% of c-Al2O3 nanoparticles at Peclet number 50,800 is 1.4%, while this deference for 2 vol.% c-Al2O3 nanoparticles at Peclet number 48,467 is 77.7%. The differences for 0.3 vol.% of TiO2 nanoparticles at Peclet number 51,190 and for 0.75% of TiO2 nanoparticles at Peclet number 51,422 are 2.9% and 27.0%, respectively. Therefore, the correlation is almost valid for the prediction of Nusselt number at low volume concentrations.
ð10Þ 5. Conclusion
ð11Þ ð12Þ
In the present experimental study heat transfer behavior of c-Al2O3/water and TiO2/water nanofluids in a shell and tube heat exchanger was investigated. The experiments were done for
B. Farajollahi et al. / International Journal of Heat and Mass Transfer 53 (2010) 12–17
a wide range of Peclet numbers, nanoparticle volume concentrations, and for different particle types. The experimental results for both nanofluids indicate that the heat transfer characteristics of nanofluids improve with Peclet number significantly. Addition of nanoparticles to the base fluid enhances the heat transfer performance and results in larger heat transfer coefficient than that of the base fluid at the same Peclet number. Both nanofluids have the different optimum volume concentration in which the heat transfer characteristics show the maximum enhancement. The nanoparticle with less mean diameter (TiO2 nanoparticle) has a lower optimum volume concentration. At different nanoparticle concentrations the heat transfer enhancement of both nanofluids are not the same. TiO2/water and c-Al2O3/water nanofluids possess better heat transfer behavior at the lower and higher volume concentrations, respectively. Competition of thermal conductivity and particle size of both nanoparticles may be the source of these differences for heat transfer performances. For both nanofluids the experimental results are very close to the predicted values of available correlation at the lower nanoparticle volume concentrations. Acknowledgments The authors thank the Petrochemical Research and Technology Company at I.R. Iran for its financial support to the present research project. References [1] X. Wang, X. Xu, S.U.S. Choi, Thermal conductivity of nanoparticle-fluid mixture, J. Thermophys. Heat Transfer 13 (1999) 474–480.
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