- Email: [email protected]
The effects of nanofluid on thermophysical properties and heat transfer characteristics of a plate heat exchanger
International Communications in Heat and Mass Transfer 44 (2013) 58–63
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
The effects of nanofluid on thermophysical properties and heat transfer characteristics of a plate heat exchanger☆ F.S. Javadi a,⁎, S. Sadeghipour a, R. Saidur a, b, G. BoroumandJazi a, B. Rahmati a, M.M. Elias a, M.R. Sohel a a b
Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R&D UM, University of Malaya, 59990 Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Available online 9 April 2013 Keywords: Plate heat exchanger Nanofluid Thermal conductivity Heat transfer rate Pressure drop Entropy generation
a b s t r a c t Improving heat exchanger's performance by increasing the overall heat transfer as well as minimising pressure drop is one of the promising fields of research to focus on. Nanofluids with higher thermal conductivity and better thermophysical properties can be applied in heat exchanger to increase the heat transfer rate. In the present study SiO2, TiO2 and Al2O3 are applied in a plate heat exchanger and the effects on thermophysical properties and heat transfer characteristics are compared with the base fluid. Since it is desired to minimize the pressure drop, the influence of nanofluid application on pressure drop and entropy generation is investigated. It is concluded that the thermal conductivity, heat transfer coefficient and heat transfer rate of the fluid increase by adding the nanoparticles and TiO2 and Al2O3 result in higher thermophysical properties in comparison with SiO2. The highest overall heat transfer coefficient was achieved by Al2O3 nanofluid, which was 308.69 W/m2.K in 0.2% nanoparticle concentration. The related heat transfer rate was improved around 30% compared to SiO2 nanofluid. In terms of pressure drop, SiO2 shows the lowest pressure drop, and it was around 50% smaller than the pressure drop in case of using TiO2 and Al2O3. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Heat exchangers are devices to provide heat transfer between two or more fluid streams at different temperatures. By progressing the technology and increasing the price of energy, greater emphasis must be placed on improving heat exchanger performances by increasing overall heat transfer as well as minimising pressure drop [1]. Plate-fin heat exchangers with various applications such as air conditioners, petrochemical processes, gas liquefiers, oil and gas processing, automobile radiators, waste heat recovery, aeronautical and cryogenic systems are one of the most common heat exchangers in industry. Plate fin is a compact type of heat exchanger that is consisted of number of plates or parting sheets and fins which can be in different shapes such as wavy, plain, offset strip, perforated, pin, and louvered. Several benefits such as compact size, high heat transfer performance and large capacity made them become more popular in industrial applications. Shown in Fig. 1 is a schematic of a plate fin heat exchanger (PFHE) [2]. The main advantages of PFHEs over compacting structures are high thermal effectiveness, high overall heat transfer area, low weight, and multi-stream operation. Despite the high performance of PFHE, which has made it popular, temperature and pressure limitation, difficulties in passage cleaning, blocking the small flow passage, ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (F.S. Javadi). 0735-1933/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2013.03.017
and hardships of repairing the failure or leaking passages are the main disadvantages [3,4]. Aluminium with high thermal conductivity, low density and high strength at low temperature is preferred to be used as the plate heat exchanger material in cryogenic and aerospace applications. In case of brazed aluminium PFHE, the maximum design pressure should not exceed 9 MPa. In high temperature applications (up to 5000 K), aluminium alloys lose their mechanical strength, therefore stainless steel, nickel and copper alloys are used [2]. Among the researches that have been conducted on PFHEs, the following can be pointed out as some of the recent studies in this field; average heat transfer coefficient determination [5], plate fin and elliptic tubes analyses [6,7], calculation of the local and overall heat transfer coefficient [8], dimension optimization calculation [9], the geometrical effect of various plates and corrugated fins [10], improving correlations of Colburn and friction factors [11], numerical studies of plate fin [12] and rectangular heat exchanger [13]. Enhancing the heat removal ability of cooling fluids by designing fluids that are more conducting would result in a higher heat transfer rate and better heat exchanger performance. Heat transfer and thermal conductivity of fluids enhanced by using micro sized particles with a basefluid. However, problems such as sedimentation, agglomeration, erosion and high-pressure drop of the new fluids encouraged scientists to use nanoparticles instead of micro sized particles. Nanofluids as heat conducting fluids, in which nano-sized particles are suspended in liquid, have been intensively studied in order to improve heat transfer characteristics and thermophysical properties of basefluid. Numerous research
F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
59
Fig. 1. Schematic of plate fin heat exchanger [2].
papers devoted in this field show remarkable growth in heat transfer improvement as well as other fundamental properties of the fluid [1,14–18]. The present study focuses on nanofluid application in plate heat exchangers. Since increasing the heat transfer rate and minimising the pressure drop are considered as the main objectives of improving heat exchangers performance, the effect of nanofluid on these parameters is investigated. Variation of fluid thermal conductivity, pressure drop, entropy generation and heat transfer coefficient of the flow is compared for three different nanofluids.
Re ¼
GD μ
ð2Þ
The heat transfer and flow friction characteristics of a PFHE are expressed by Colburn factor j and friction factor f, which are defined by the following relations according to the basic characteristics of the surface: −0:286
F ¼ 0:32Re
2. Methodology −0:42
J ¼ 0:18Re 2.1. Geometry configuration General geometry of a PFHE is shown in Fig. 2. In order to calculate the heat transfer characteristics of PFHE, following equations have been used in this study [2]. Initial mass velocity can be obtained by Eq. (1) and Reynolds number is then obtained using the mass flux and other known variables, Eq. (2): G¼
mff Aff
ð1Þ
−0:221 −0:185 −0:023 h l t s s s
−0:288 −0:184 −0:05 h l t s s s
ð3Þ
ð4Þ
With known surface geometries and Colburn data, heat transfer coefficient and Prandtl number are calculated by Eqs. (5) and (6), respectively.
h¼
jcp l Prð2=3Þ
Pr ¼
Cp μ k
Fig. 2. Geometry of a typical offset strip fin surface [2].
ð5Þ
ð6Þ
60
F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
The overall efficiency of heat exchanger can be calculated by Eq. (7): Af N ¼ 1− 1−nf As nf ¼
ð7Þ
tanhðmlÞ ml
nc wc 1 nh wh Nh hh
þ
aA0 1 þ K w Aw Nc hc
ð9Þ
The core pressure drop with the major contribution in the total pressure drop can be approximated as follows: p¼
Properties
SiO2
TiO2
Al2O3
ρ(kg/m3) Cp(J/kg.K) k(W/m.K)
2220 745 1.38
4157 710 8.4
3970 765 36
ð8Þ
An overall thermal resistance is then found based on known surface geometries and other known values as stated by Eq. (9). 1 ¼ Uo
Table 2 Thermophysical properties of the nanoparticles.
4FLG2 2ρDeq
Where subscripts n and f refer to nanoparticle and base fluid, respectively. Nanofluids dynamic viscosity is calculated using Eq. (13) μ nf ¼
knf
2.2. Nanofluid In the present study, three different kinds of nanoparticles with different volume concentrations in basefluid; liquid nitrogen; are investigated analytically. Aluminium Oxide (Al2O3), Titanium Oxide (TiO2) and Silicon Oxide (SiO2) are the considered nanoparticles in this study. The thermophysical properties of Al2O3, TiO2, and SiO2 nanoparticles are given in Table 2. Heat capacity of base fluid is 1043 J/kg.K and Prandtl number of hot and cold fluid is 0.74767 and 0.75, respectively. Thermophysical properties of the nanofluids can be determined using general formulas derived for a two-phase mixture [1,19,20]. Density of nanofluids can be computed by Eq. (11): ρnf ¼ ϕρp þ ð1−ρÞρf
ð11Þ
ð13Þ
Thermal conductivity of nanofluids is calculated by the correlation recommended by Maxwell (Eq. (14)) [21].
ð10Þ
All the calculations were done in bulk temperature, which is equal to the average of the inlet and outlet temperatures of each hot and cold fluid. Inlet and outlet temperatures are 310 K and 124.26 K for hot fluid and 99.719 K and 301.54 K for cold fluid, respectively. The mass flow rate is 0.0822 kg/s and 0.07791 kg/s for hot and cold fluid, respectively. Inlet pressures are 0.8 and 0.115 MPa for hot and cold fluid. Density at average temperature also equals to 1.583 and 1.711 kg/m 3 for hot and cold fluids, respectively. Fin material is aluminium with 150 W/m.K thermal conductivity. Other geometry data of the heat exchanger are summarized in Table 1.
1 μf ð1−ϕÞ2:5
3 2 kp þ 2kf þ 2ϕ kp −kf 4 5kf ¼ kp þ 2kf −ϕ kp −kf
ð14Þ
This formula is based on the volume fraction of nanoparticle ϕ, and the thermal conductivity of the particle kp and base fluid kf. The following equation can be applied to calculate the volume concentration of nanoparticles in the base fluid: mn
ϕ¼
Vn ρn ¼ V n þ V f mn þ mf ρn
ð15Þ
ρf
The thermodynamic term of entropy generation is used to measure the useless energy in a system that is not able to produce work. Based on Eqs. (16) and (17), total entropy generation is a function of fluid regime and geometry of application, which is produced due to fluid friction and heat transfer [22]. 0
Sgen ¼
2 _ 3f q Dh 2m þ 2 2 _ 4T b;av mC p St ρ T b;av Dh A
S_ gen ¼ S_ gen
T b;av ¼
Heat:Transfer
þ S_ gen
T in −T out ln TT in
Fluid:Friction
ð16Þ
ð17Þ
ð18Þ
out
Where ρp and ρf refer to the density of nanoparticle and based fluid, respectively. The specific heat of nanofluids can be calculated in terms of the density: C p;nf ¼
3.1. Mass flow rate
ϕðρcp Þn þ ð1−ϕÞðρcp Þf
ð12Þ
ϕρn þ ð1−ϕÞρf
Table 1 Specification of the plate fin heat exchanger.
w (width) (mm) No. of layers Area between plates (m2) A = (w × b × n) (m2) Aff (free flow area) (m2)
3. Result and discussion
Hot fluid
Cold fluid
0.115 5 54,625 × 10−7 54,625 × 10−7 38,196 × 10−7
0.115 4 437 × 10−5 437 × 10−5 305 × 10−5
Mass flux is dependent on the mass flow rate, which is 0.278 kg/s at 0.2% volume fraction and 2.079 kg/s at 2% of volume fraction for SiO2–Nanofluid. The mass flow rate for TiO2 and Al2O3–Nanofluids is about 0.456 kg/s and 0.439 kg/s in 0.2% volume fraction and 3.861 kg/s and 3.691 kg/s at 2% volume fraction, respectively. This means that mass flux is lower for dispersing SiO2. On the other hand, SiO2–Nanofluid has the density of 6.107 and 45.676 kg/m 3 at 0.2% and 2% of volume fraction, respectively, while this amount for TiO2 and Al2O3–Nanofluid is 10.021 and 9.647 kg/m 3 at the volume concentration of 0.2% and 84.816 and 81.076 kg/m 3 at volume concentration of 2%, respectively.
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61
3.2. Thermal conductivity Fig. 3 shows the comparison between the thermal conductivity of nanofluids with different nanoparticle volume fraction. The thermal conductivity of TiO2 and Al2O3–Nanofluids are almost the same and it is more than thermal conductivity of SiO2 nanofluid. In fact, the graph shows that thermal conductivity increases by increasing the nanoparticle volume fraction in basefluid. Al2O3 has the highest effect on thermal conductivity improvement of base fluid in comparison with the other investigated nanoparticles. 3.3. Heat transfer coefficient Heat transfer coefficient will be enhanced with increasing thermal conductivity by increasing the particle volume fraction. For instance, SiO2–Nanofluid at 0.2% of volume fraction has a mass flow rate equal to 0.27 kg/s and 923.44 W/m 2.K heat transfer coefficient, but at 2% has a mass flow rate of 2.08 kg/s with 2943.98 W/m 2.K. On the other hand, TiO2 and Al2O3 with the same mass flow rate—around 0.45 kg/s for 0.2% volume fraction—have higher heat transfer coefficients, 1257 and 1260 W/m 2.K, respectively. Fig. 4 shows the heat transfer coefficient of different types of nanofluid in different volume fractions. It illustrates the heat transfer coefficient enhancement by increasing nanoparticle volume fraction. According to the calculation, SiO2–Nanofluid has the lowest heat transfer coefficient. TiO2 and Al2O3 nanoparticles have more influence on heat transfer coefficient increment. If the nanofluid is prepared based on nanoparticle volume fraction, the mass flow rate increases because of extra density imposed by nanoparticle. Therefore, a part of the enhancement in heat transfer comes from the added mass and the rest is due to the effect of nanoparticles.
Fig. 4. The heat transfer coefficient of nanofluids.
heat transfer rate is obtained for TiO2 and Al2O3 nanofluids whereas the SiO2 shows the lowest heat transfer rate. TiO2 and Al2O3 nanofluids have almost the same heat transfer rate. This is because of the fact that, TiO2–Nanofluid has the higher density and the Al2O3 has the higher specific heat. Therefore, they have almost similar effect on the rate of heat transfer. Heat transfer rate for TiO2 and Al2O3 nanofluids is 30% greater than the SiO2–Nanofluid at 2% volume concentration.
3.4. Overall heat transfer coefficient The overall heat transfer coefficient is increased by increasing the particle volume fraction. It can be clearly seen from Fig. 5, that adding Al2O3 nanoparticles to the basefluid gives higher overall heat transfer coefficient with the highest value of about 308.69 W/m 2.K at 2% volume fraction. 3.5. Heat transfer rate Heat transfer rate for all nanofluids increases with increasing the volume fraction of nanoparticles. From Fig. 6, it is seen that the highest
Fig. 3. Thermal conductivity of nanofluids in different volume fractions.
3.6. Prandtl number Comparing the Prandtl number of different investigated nanofluids, a significant difference has been observed between the TiO2–Nanofluid and the others. Fig. 7 indicates that Prandtl number decreases with increasing the volume concentration of the nanoparticle. The maximum Prandtl number which is occurred at 0.2% volume concentration is equal to 0.415, 0.406 and 0.382 for SiO2, Al2O3 and TiO2 nanofluids, respectively.
Fig. 5. The overall heat transfer coefficient of nanofluids.
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F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
Fig. 6. Heat transfer rate of plate fin heat exchanger with different nanofluids. Fig. 8. Pressure drop per unit length for different nanofluids.
3.7. Pressure drop From the obtained results (Fig. 8), it can be seen that the lowest pressure drop occurs by applying SiO2 nanoparticle, while using TiO2 and Al2O3 nanoparticles result in remarkably higher pressure drops. It is clear that the fall in pressure is proportional to the volume concentration of nanofluid. Higher pressure drop is obtained with higher volume concentration. Therefore, SiO2 nanoparticles with volume concentration of 0.2%, result in the lowest pressure drop of near 0.06 MPa/m. However, there is a slight difference between the pressure drops of nanofluids using TiO2 and Al2O3. The difference between the two is more significant in higher concentrations where TiO2 results in higher pressure drop. According to Eq. (10), the pressure drop has a direct relation with the friction factor and the square of mass flux and reverse relation with density. Friction factor itself as stated by Eqs. (2) and (3) is proportional to Reynolds number and then mass flux. Due to the noticeable difference between the density of liquid nitrogen containing SiO2 and the other two, the effect of density on
pressure drop is higher than mass flux, and lower pressure drop can be found for SiO2–Nanofluid. Comparison of the pressure drop in the case of basefluid and using different studied nanoparticles having volume fractions of 0.2% is shown in Table 3. It is clear that pressure drop is much higher by using nanoparticles in the base fluid even at the lowest concentration. 3.8. Entropy generation Eq. (16) shows that the entropy generation is changed by altering the thermophysical properties of the fluid and the geometry. Since the geometry is fixed, using nanofluid can change the entropy generation by changing the thermal properties of the fluid. According to Fig. 9, it is observed that the entropy generation ratio is increased with nanoparticle volume fraction. This ratio at 0.2% volume concentration is almost the same for the three nanofluids, between 6 and 8.5. At 2% volume concentration, SiO2–Nanofluid has the lowest entropy generation ratio of about 25, while this amount for TiO2 and Al2O3 nanofluids is about 40 and 38.7, respectively.
4. Conclusions In this paper, the thermal conductivity, heat transfer coefficient, overall heat transfer coefficient, heat transfer rate, overall thermal resistance, pressure drop, and entropy generation of nanofluids have been investigated analytically. Three different types of nanofluid were considered as working fluids flowing through a PFHE. The following conclusions have been obtained: 1. The thermal conductivity of the base fluid increases by adding nanoparticles. The increment of thermal conductivity by adding TiO2 and Al2O3 was almost the same and it was higher than SiO2. 2. It is clearly seen that the heat transfer coefficient of nanofluids boosts up by increasing the volume concentration of nanoparticles. Table 3 Pressure drop per length for base fluid and investigated nanofluids.
Fig. 7. Prandtl number of different nanofluid.
Pressure drop per length (MPa/m)
Basefluid
0.2% TiO2
0.2% Al2O3
0.2% SiO2
0.008
0.085
0.083
0.060
F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
63
References
Fig. 9. Entropy generation of different nanofluids in plate fin heat exchanger.
TiO2 and Al2O3 effects on heat transfer coefficient were higher than SiO2. 3. The Prandtl number decreases with increasing nanoparticle's volume concentration. The maximum Prandtl number which occurred at 0.2% volume concentration is equal to 0.415, 0.406 and 0.382 for SiO2, Al2O3 and TiO2 nanofluids, respectively. 4. Pressure drop increases significantly in case of using nanoparticles in the fluid. This is because of high density of nanoparticles compared to the base fluid. Pressure drop also increases with increasing nanoparticle concentration. This implies that nanofluids incurs penalty of pump power and new designs for the application of nanofluids may be required. 5. Using nanoparticles enhances the entropy generation, which has a climbing trend toward increasing nanoparticle concentration. Comparing to SiO2, at 2% volume concentration, TiO2 and Al2O3 showed 57% and 50% increase in the entropy generation ratio. Acknowledgment The authors would like to acknowledge the Ministry of Higher Education Malaysia (MoHE) for financial support. This work was supported by UM-MoHE High Impact Research Grant Scheme (HIRG) (Project No: UM.C/HIR/MOHE/ENG/40).
[1] G. Huminic, A. Huminic, Application of nanofluids in heat exchangers: a review, Renewable and Sustainable Energy Reviews 16 (8) (2012) 5625–5638. [2] J. Dewatwal, Design of compact plate fin heat exchanger, Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela, 2009. [3] Q. Li, G. Flamant, X. Yuan, P. Neveu, L. Luo, Compact heat exchangers: a review and future applications for a new generation of high temperature solar receivers, Renewable and Sustainable Energy Reviews 15 (9) (2011) 4855–4875. [4] T. Kuppan, Heat Exchanger Design Handbook, Marcel Dekker Inc., New York, Basel, 2000. [5] S.M. Saboya, F.E.M. Saboya, Experiments on elliptic sections in one- and two-row arrangements of plate fin and tube heat exchangers, Experimental Thermal and Fluid Science 24 (1–2) (2001) 67–75. [6] F.J. Schulenberg, Finned elliptical tubes and their application in air-cooled heat exchangers, Journal of Engineering for Industry 88 (2) (1966) 179–186. [7] L.A.O. Rocha, F.E.M. Saboya, J.V.C. Vargas, A comparative study of elliptical and circular sections in one- and two-row tubes and plate fin heat exchangers, International Journal of Heat and Fluid Flow 18 (2) (1997) 247–252. [8] E.C. Rosman, P. Carajilescov, F.E.M. Saboya, Performance of one- and two-row tube and plate fin heat exchangers, Journal of Heat Transfer 106 (3) (1984) 627–632. [9] B. Kundu, P.K. Das, Optimum dimensions of plate fins for fin-tube heat exchangers, International Journal of Heat and Fluid Flow 18 (5) (1997) 530–537. [10] M. Abu Madi, R.A. Johns, M.R. Heikal, Performance characteristics correlation for round tube and plate finned heat exchangers: equations relatives aux performances d'échangeurs de chaleur constitués de tubes ronds et de plaques à ailettes, International Journal of Refrigeration 21 (7) (1998) 507–517. [11] Chi- Chuan Wang, Kuan-Yu Chi, Chun- Jung Chang, Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part II: Correlation, International Communications in Heat and Mass Transfer 43 (2000). [12] J.-Y. Kim, T.-H. Song, Microscopic phenomena and macroscopic evaluation of heat transfer from plate fins/circular tube assembly using naphthalene sublimation technique, International Journal of Heat and Mass Transfer 45 (16) (2002) 3397–3404. [13] H.A. Mohammed, G. Bhaskaran, N.H. Shuaib, R. Saidur, Numerical study of heat transfer enhancement of counter nanofluids flow in rectangular microchannel heat exchanger, Superlattices and Microstructures 50 (3) (2011) 215–233. [14] V. Trisaksri, S. Wongwises, Critical review of heat transfer characteristics of nanofluids, Renewable and Sustainable Energy Reviews 11 (3) (2007) 512–523. [15] K.Y. Leong, R. Saidur, M. Khairulmaini, Z. Michael, A. Kamyar, Heat transfer and entropy analysis of three different types of heat exchangers operated with nanofluids, International Communications in Heat and Mass Transfer 39 (6) (2012) 838–843. [16] H.A. Mohammed, G. Bhaskaran, N.H. Shuaib, R. Saidur, Heat transfer and fluid flow characteristics in microchannels heat exchanger using nanofluids: a review, Renewable and Sustainable Energy Reviews 15 (3) (2011) 1502–1512. [17] K.Y. Leong, R. Saidur, T.M.I. Mahlia, Y.H. Yau, Modeling of shell and tube heat recovery exchanger operated with nanofluid based coolants, International Journal of Heat and Mass Transfer 55 (4) (2012) 808–816. [18] M. Raja, R.M. Arunachalam, S. Suresh, Experimental studies on heat transfer of alumina/water nanofluid in a shell and tube heat exchanger with wire coil insert, International Journal of Mechanical and Materials Engineering (IJMME) 7 (1) (2012) 16–23. [19] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer 43 (19) (2000) 3701–3707. [20] A. Kamyar, R. Saidur, M. Hasanuzzaman, Application of computational fluid dynamics (CFD) for nanofluids, International Journal of Heat and Mass Transfer 55 (15–16) (2012) 4104–4115. [21] J.C. Maxwell, A Treatise on Electricity and Magnetism, UK: Oxford University, UK: Clarendon Press, 1981. [22] V. Bianco, S. Nardini, O. Manca, Enhancement of heat transfer and entropy generation analysis of nanofluids turbulent convection flow in square section tubes, Nanoscale Research Letters 6 (1) (2011) 252.
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
The effects of nanofluid on thermophysical properties and heat transfer characteristics of a plate heat exchanger☆ F.S. Javadi a,⁎, S. Sadeghipour a, R. Saidur a, b, G. BoroumandJazi a, B. Rahmati a, M.M. Elias a, M.R. Sohel a a b
Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R&D UM, University of Malaya, 59990 Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Available online 9 April 2013 Keywords: Plate heat exchanger Nanofluid Thermal conductivity Heat transfer rate Pressure drop Entropy generation
a b s t r a c t Improving heat exchanger's performance by increasing the overall heat transfer as well as minimising pressure drop is one of the promising fields of research to focus on. Nanofluids with higher thermal conductivity and better thermophysical properties can be applied in heat exchanger to increase the heat transfer rate. In the present study SiO2, TiO2 and Al2O3 are applied in a plate heat exchanger and the effects on thermophysical properties and heat transfer characteristics are compared with the base fluid. Since it is desired to minimize the pressure drop, the influence of nanofluid application on pressure drop and entropy generation is investigated. It is concluded that the thermal conductivity, heat transfer coefficient and heat transfer rate of the fluid increase by adding the nanoparticles and TiO2 and Al2O3 result in higher thermophysical properties in comparison with SiO2. The highest overall heat transfer coefficient was achieved by Al2O3 nanofluid, which was 308.69 W/m2.K in 0.2% nanoparticle concentration. The related heat transfer rate was improved around 30% compared to SiO2 nanofluid. In terms of pressure drop, SiO2 shows the lowest pressure drop, and it was around 50% smaller than the pressure drop in case of using TiO2 and Al2O3. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Heat exchangers are devices to provide heat transfer between two or more fluid streams at different temperatures. By progressing the technology and increasing the price of energy, greater emphasis must be placed on improving heat exchanger performances by increasing overall heat transfer as well as minimising pressure drop [1]. Plate-fin heat exchangers with various applications such as air conditioners, petrochemical processes, gas liquefiers, oil and gas processing, automobile radiators, waste heat recovery, aeronautical and cryogenic systems are one of the most common heat exchangers in industry. Plate fin is a compact type of heat exchanger that is consisted of number of plates or parting sheets and fins which can be in different shapes such as wavy, plain, offset strip, perforated, pin, and louvered. Several benefits such as compact size, high heat transfer performance and large capacity made them become more popular in industrial applications. Shown in Fig. 1 is a schematic of a plate fin heat exchanger (PFHE) [2]. The main advantages of PFHEs over compacting structures are high thermal effectiveness, high overall heat transfer area, low weight, and multi-stream operation. Despite the high performance of PFHE, which has made it popular, temperature and pressure limitation, difficulties in passage cleaning, blocking the small flow passage, ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (F.S. Javadi). 0735-1933/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2013.03.017
and hardships of repairing the failure or leaking passages are the main disadvantages [3,4]. Aluminium with high thermal conductivity, low density and high strength at low temperature is preferred to be used as the plate heat exchanger material in cryogenic and aerospace applications. In case of brazed aluminium PFHE, the maximum design pressure should not exceed 9 MPa. In high temperature applications (up to 5000 K), aluminium alloys lose their mechanical strength, therefore stainless steel, nickel and copper alloys are used [2]. Among the researches that have been conducted on PFHEs, the following can be pointed out as some of the recent studies in this field; average heat transfer coefficient determination [5], plate fin and elliptic tubes analyses [6,7], calculation of the local and overall heat transfer coefficient [8], dimension optimization calculation [9], the geometrical effect of various plates and corrugated fins [10], improving correlations of Colburn and friction factors [11], numerical studies of plate fin [12] and rectangular heat exchanger [13]. Enhancing the heat removal ability of cooling fluids by designing fluids that are more conducting would result in a higher heat transfer rate and better heat exchanger performance. Heat transfer and thermal conductivity of fluids enhanced by using micro sized particles with a basefluid. However, problems such as sedimentation, agglomeration, erosion and high-pressure drop of the new fluids encouraged scientists to use nanoparticles instead of micro sized particles. Nanofluids as heat conducting fluids, in which nano-sized particles are suspended in liquid, have been intensively studied in order to improve heat transfer characteristics and thermophysical properties of basefluid. Numerous research
F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
59
Fig. 1. Schematic of plate fin heat exchanger [2].
papers devoted in this field show remarkable growth in heat transfer improvement as well as other fundamental properties of the fluid [1,14–18]. The present study focuses on nanofluid application in plate heat exchangers. Since increasing the heat transfer rate and minimising the pressure drop are considered as the main objectives of improving heat exchangers performance, the effect of nanofluid on these parameters is investigated. Variation of fluid thermal conductivity, pressure drop, entropy generation and heat transfer coefficient of the flow is compared for three different nanofluids.
Re ¼
GD μ
ð2Þ
The heat transfer and flow friction characteristics of a PFHE are expressed by Colburn factor j and friction factor f, which are defined by the following relations according to the basic characteristics of the surface: −0:286
F ¼ 0:32Re
2. Methodology −0:42
J ¼ 0:18Re 2.1. Geometry configuration General geometry of a PFHE is shown in Fig. 2. In order to calculate the heat transfer characteristics of PFHE, following equations have been used in this study [2]. Initial mass velocity can be obtained by Eq. (1) and Reynolds number is then obtained using the mass flux and other known variables, Eq. (2): G¼
mff Aff
ð1Þ
−0:221 −0:185 −0:023 h l t s s s
−0:288 −0:184 −0:05 h l t s s s
ð3Þ
ð4Þ
With known surface geometries and Colburn data, heat transfer coefficient and Prandtl number are calculated by Eqs. (5) and (6), respectively.
h¼
jcp l Prð2=3Þ
Pr ¼
Cp μ k
Fig. 2. Geometry of a typical offset strip fin surface [2].
ð5Þ
ð6Þ
60
F.S. Javadi et al. / International Communications in Heat and Mass Transfer 44 (2013) 58–63
The overall efficiency of heat exchanger can be calculated by Eq. (7): Af N ¼ 1− 1−nf As nf ¼
ð7Þ
tanhðmlÞ ml
nc wc 1 nh wh Nh hh
þ
aA0 1 þ K w Aw Nc hc
ð9Þ
The core pressure drop with the major contribution in the total pressure drop can be approximated as follows: p¼
Properties
SiO2
TiO2
Al2O3
ρ(kg/m3) Cp(J/kg.K) k(W/m.K)
2220 745 1.38
4157 710 8.4
3970 765 36
ð8Þ
An overall thermal resistance is then found based on known surface geometries and other known values as stated by Eq. (9). 1 ¼ Uo
Table 2 Thermophysical properties of the nanoparticles.
4FLG2 2ρDeq
Where subscripts n and f refer to nanoparticle and base fluid, respectively. Nanofluids dynamic viscosity is calculated using Eq. (13) μ nf ¼
knf
2.2. Nanofluid In the present study, three different kinds of nanoparticles with different volume concentrations in basefluid; liquid nitrogen; are investigated analytically. Aluminium Oxide (Al2O3), Titanium Oxide (TiO2) and Silicon Oxide (SiO2) are the considered nanoparticles in this study. The thermophysical properties of Al2O3, TiO2, and SiO2 nanoparticles are given in Table 2. Heat capacity of base fluid is 1043 J/kg.K and Prandtl number of hot and cold fluid is 0.74767 and 0.75, respectively. Thermophysical properties of the nanofluids can be determined using general formulas derived for a two-phase mixture [1,19,20]. Density of nanofluids can be computed by Eq. (11): ρnf ¼ ϕρp þ ð1−ρÞρf
ð11Þ
ð13Þ
Thermal conductivity of nanofluids is calculated by the correlation recommended by Maxwell (Eq. (14)) [21].
ð10Þ
All the calculations were done in bulk temperature, which is equal to the average of the inlet and outlet temperatures of each hot and cold fluid. Inlet and outlet temperatures are 310 K and 124.26 K for hot fluid and 99.719 K and 301.54 K for cold fluid, respectively. The mass flow rate is 0.0822 kg/s and 0.07791 kg/s for hot and cold fluid, respectively. Inlet pressures are 0.8 and 0.115 MPa for hot and cold fluid. Density at average temperature also equals to 1.583 and 1.711 kg/m 3 for hot and cold fluids, respectively. Fin material is aluminium with 150 W/m.K thermal conductivity. Other geometry data of the heat exchanger are summarized in Table 1.
1 μf ð1−ϕÞ2:5
3 2 kp þ 2kf þ 2ϕ kp −kf 4 5kf ¼ kp þ 2kf −ϕ kp −kf
ð14Þ
This formula is based on the volume fraction of nanoparticle ϕ, and the thermal conductivity of the particle kp and base fluid kf. The following equation can be applied to calculate the volume concentration of nanoparticles in the base fluid: mn
ϕ¼
Vn ρn ¼ V n þ V f mn þ mf ρn
ð15Þ
ρf
The thermodynamic term of entropy generation is used to measure the useless energy in a system that is not able to produce work. Based on Eqs. (16) and (17), total entropy generation is a function of fluid regime and geometry of application, which is produced due to fluid friction and heat transfer [22]. 0
Sgen ¼
2 _ 3f q Dh 2m þ 2 2 _ 4T b;av mC p St ρ T b;av Dh A
S_ gen ¼ S_ gen
T b;av ¼
Heat:Transfer
þ S_ gen
T in −T out ln TT in
Fluid:Friction
ð16Þ
ð17Þ
ð18Þ
out
Where ρp and ρf refer to the density of nanoparticle and based fluid, respectively. The specific heat of nanofluids can be calculated in terms of the density: C p;nf ¼
3.1. Mass flow rate
ϕðρcp Þn þ ð1−ϕÞðρcp Þf
ð12Þ
ϕρn þ ð1−ϕÞρf
Table 1 Specification of the plate fin heat exchanger.
w (width) (mm) No. of layers Area between plates (m2) A = (w × b × n) (m2) Aff (free flow area) (m2)
3. Result and discussion
Hot fluid
Cold fluid
0.115 5 54,625 × 10−7 54,625 × 10−7 38,196 × 10−7
0.115 4 437 × 10−5 437 × 10−5 305 × 10−5
Mass flux is dependent on the mass flow rate, which is 0.278 kg/s at 0.2% volume fraction and 2.079 kg/s at 2% of volume fraction for SiO2–Nanofluid. The mass flow rate for TiO2 and Al2O3–Nanofluids is about 0.456 kg/s and 0.439 kg/s in 0.2% volume fraction and 3.861 kg/s and 3.691 kg/s at 2% volume fraction, respectively. This means that mass flux is lower for dispersing SiO2. On the other hand, SiO2–Nanofluid has the density of 6.107 and 45.676 kg/m 3 at 0.2% and 2% of volume fraction, respectively, while this amount for TiO2 and Al2O3–Nanofluid is 10.021 and 9.647 kg/m 3 at the volume concentration of 0.2% and 84.816 and 81.076 kg/m 3 at volume concentration of 2%, respectively.
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3.2. Thermal conductivity Fig. 3 shows the comparison between the thermal conductivity of nanofluids with different nanoparticle volume fraction. The thermal conductivity of TiO2 and Al2O3–Nanofluids are almost the same and it is more than thermal conductivity of SiO2 nanofluid. In fact, the graph shows that thermal conductivity increases by increasing the nanoparticle volume fraction in basefluid. Al2O3 has the highest effect on thermal conductivity improvement of base fluid in comparison with the other investigated nanoparticles. 3.3. Heat transfer coefficient Heat transfer coefficient will be enhanced with increasing thermal conductivity by increasing the particle volume fraction. For instance, SiO2–Nanofluid at 0.2% of volume fraction has a mass flow rate equal to 0.27 kg/s and 923.44 W/m 2.K heat transfer coefficient, but at 2% has a mass flow rate of 2.08 kg/s with 2943.98 W/m 2.K. On the other hand, TiO2 and Al2O3 with the same mass flow rate—around 0.45 kg/s for 0.2% volume fraction—have higher heat transfer coefficients, 1257 and 1260 W/m 2.K, respectively. Fig. 4 shows the heat transfer coefficient of different types of nanofluid in different volume fractions. It illustrates the heat transfer coefficient enhancement by increasing nanoparticle volume fraction. According to the calculation, SiO2–Nanofluid has the lowest heat transfer coefficient. TiO2 and Al2O3 nanoparticles have more influence on heat transfer coefficient increment. If the nanofluid is prepared based on nanoparticle volume fraction, the mass flow rate increases because of extra density imposed by nanoparticle. Therefore, a part of the enhancement in heat transfer comes from the added mass and the rest is due to the effect of nanoparticles.
Fig. 4. The heat transfer coefficient of nanofluids.
heat transfer rate is obtained for TiO2 and Al2O3 nanofluids whereas the SiO2 shows the lowest heat transfer rate. TiO2 and Al2O3 nanofluids have almost the same heat transfer rate. This is because of the fact that, TiO2–Nanofluid has the higher density and the Al2O3 has the higher specific heat. Therefore, they have almost similar effect on the rate of heat transfer. Heat transfer rate for TiO2 and Al2O3 nanofluids is 30% greater than the SiO2–Nanofluid at 2% volume concentration.
3.4. Overall heat transfer coefficient The overall heat transfer coefficient is increased by increasing the particle volume fraction. It can be clearly seen from Fig. 5, that adding Al2O3 nanoparticles to the basefluid gives higher overall heat transfer coefficient with the highest value of about 308.69 W/m 2.K at 2% volume fraction. 3.5. Heat transfer rate Heat transfer rate for all nanofluids increases with increasing the volume fraction of nanoparticles. From Fig. 6, it is seen that the highest
Fig. 3. Thermal conductivity of nanofluids in different volume fractions.
3.6. Prandtl number Comparing the Prandtl number of different investigated nanofluids, a significant difference has been observed between the TiO2–Nanofluid and the others. Fig. 7 indicates that Prandtl number decreases with increasing the volume concentration of the nanoparticle. The maximum Prandtl number which is occurred at 0.2% volume concentration is equal to 0.415, 0.406 and 0.382 for SiO2, Al2O3 and TiO2 nanofluids, respectively.
Fig. 5. The overall heat transfer coefficient of nanofluids.
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Fig. 6. Heat transfer rate of plate fin heat exchanger with different nanofluids. Fig. 8. Pressure drop per unit length for different nanofluids.
3.7. Pressure drop From the obtained results (Fig. 8), it can be seen that the lowest pressure drop occurs by applying SiO2 nanoparticle, while using TiO2 and Al2O3 nanoparticles result in remarkably higher pressure drops. It is clear that the fall in pressure is proportional to the volume concentration of nanofluid. Higher pressure drop is obtained with higher volume concentration. Therefore, SiO2 nanoparticles with volume concentration of 0.2%, result in the lowest pressure drop of near 0.06 MPa/m. However, there is a slight difference between the pressure drops of nanofluids using TiO2 and Al2O3. The difference between the two is more significant in higher concentrations where TiO2 results in higher pressure drop. According to Eq. (10), the pressure drop has a direct relation with the friction factor and the square of mass flux and reverse relation with density. Friction factor itself as stated by Eqs. (2) and (3) is proportional to Reynolds number and then mass flux. Due to the noticeable difference between the density of liquid nitrogen containing SiO2 and the other two, the effect of density on
pressure drop is higher than mass flux, and lower pressure drop can be found for SiO2–Nanofluid. Comparison of the pressure drop in the case of basefluid and using different studied nanoparticles having volume fractions of 0.2% is shown in Table 3. It is clear that pressure drop is much higher by using nanoparticles in the base fluid even at the lowest concentration. 3.8. Entropy generation Eq. (16) shows that the entropy generation is changed by altering the thermophysical properties of the fluid and the geometry. Since the geometry is fixed, using nanofluid can change the entropy generation by changing the thermal properties of the fluid. According to Fig. 9, it is observed that the entropy generation ratio is increased with nanoparticle volume fraction. This ratio at 0.2% volume concentration is almost the same for the three nanofluids, between 6 and 8.5. At 2% volume concentration, SiO2–Nanofluid has the lowest entropy generation ratio of about 25, while this amount for TiO2 and Al2O3 nanofluids is about 40 and 38.7, respectively.
4. Conclusions In this paper, the thermal conductivity, heat transfer coefficient, overall heat transfer coefficient, heat transfer rate, overall thermal resistance, pressure drop, and entropy generation of nanofluids have been investigated analytically. Three different types of nanofluid were considered as working fluids flowing through a PFHE. The following conclusions have been obtained: 1. The thermal conductivity of the base fluid increases by adding nanoparticles. The increment of thermal conductivity by adding TiO2 and Al2O3 was almost the same and it was higher than SiO2. 2. It is clearly seen that the heat transfer coefficient of nanofluids boosts up by increasing the volume concentration of nanoparticles. Table 3 Pressure drop per length for base fluid and investigated nanofluids.
Fig. 7. Prandtl number of different nanofluid.
Pressure drop per length (MPa/m)
Basefluid
0.2% TiO2
0.2% Al2O3
0.2% SiO2
0.008
0.085
0.083
0.060
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References
Fig. 9. Entropy generation of different nanofluids in plate fin heat exchanger.
TiO2 and Al2O3 effects on heat transfer coefficient were higher than SiO2. 3. The Prandtl number decreases with increasing nanoparticle's volume concentration. The maximum Prandtl number which occurred at 0.2% volume concentration is equal to 0.415, 0.406 and 0.382 for SiO2, Al2O3 and TiO2 nanofluids, respectively. 4. Pressure drop increases significantly in case of using nanoparticles in the fluid. This is because of high density of nanoparticles compared to the base fluid. Pressure drop also increases with increasing nanoparticle concentration. This implies that nanofluids incurs penalty of pump power and new designs for the application of nanofluids may be required. 5. Using nanoparticles enhances the entropy generation, which has a climbing trend toward increasing nanoparticle concentration. Comparing to SiO2, at 2% volume concentration, TiO2 and Al2O3 showed 57% and 50% increase in the entropy generation ratio. Acknowledgment The authors would like to acknowledge the Ministry of Higher Education Malaysia (MoHE) for financial support. This work was supported by UM-MoHE High Impact Research Grant Scheme (HIRG) (Project No: UM.C/HIR/MOHE/ENG/40).
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