Ratios of nanofluids’ thermal conductivity enhancement with different influence factors.
Nanofluids exhibit novel properties including significant heat transfer properties that make them potentially useful in internal combustion engine cooling. However, although there is a substantial number of mechanisms proposed, modeling works related to their enhanced thermal conductivity, systematic mechanisms, or models that are suitable for nanofluids are still lacked. With molecular dynamics simulations, thermal conductivities of nanofluids with various nanoparticles have been calculated. Influence rule of various factors for thermal conductivity of nanofluids has been studied. Through defining the ratio of thermal conductivity enhancement by nanoparticle volume fraction, Κ, the impacts of nanoparticle properties for thermal conductivity are further evaluated. Furthermore, the ratio of energetic atoms in nanoparticles, E, is proposed to be an effective criterion for judging the impact of nanoparticles for the thermal conductivity of nanofluids. Mechanisms of heat conduction enhancement are investigated by MD simulations. Altered microstructure and movements of nanoparticles in the base fluid are proposed to be the main reasons for thermal conductivity enhancement in nanofluids. Both the static and dynamic mechanisms for heat conduction enhancement in nanofluids have been considered to establish a prediction model for thermal conductivity. The prediction results of the present model are in good agreement with experimental results.
- internal combustion engine
- heat transfer
In recent years, nanofluids (NFs) have received much attention due to their strengthening heat transfer properties, which possess important application in heat transfer. The concept of nanofluids was first proposed by Choi in 1995, which indicates the fluids containing nanometer‐sized particles, called nanoparticles (NPs) . These fluids are engineered colloidal suspensions of nanoparticles in a base fluid. Numerous experimental studies discovered that nanofluids exhibit thermal properties superior to those of base fluid or conventional solid‐liquid suspensions. Most of the thermal properties of nanofluids measured greatly exceed the values predicted by classical macroscopic theories and models. Nanofluids possess significantly increased thermal conductivity and improved convective heat transfer coefficient. Therefore, they are potentially useful in many enhanced heat transfer application, including engine cooling, vehicle thermal management, and power battery. Researchers are working to explain the significant high thermal properties of nanofluids [2–4]. However, although there is a substantial number of mechanisms proposed, and modeling works related to their enhanced thermal conductivity, systematic mechanisms, or models that are suitable for nanofluids are still lacked.
Regarding the excellent thermal properties of nanofluids, researchers are interested in the application of nanofluids in internal combustion engine, and began the study of applying nanofluids in internal combustion engine. In 1999, Wambsganss in Argonne national laboratory proposed the idea of applying nanofluids in car engine to improve the vehicle thermal management performance . Choi indicates in a report that in Argonne national laboratory a research program of enhanced heat transfer by nanofluids is launched aiming at the cooling and heat transfer problems in the heavy‐duty engine . The results show that due to the excellent heat transfer performance of nanofluids, the size and weight of the engine can be reduced by 10%. Choi pointed out that the application of nanofluids in engine is one of the best methods of improving heat transfer performance of the cooling system. Saripella et al. studied the heat transfer performance of nanocoolant (nanofluids) in Volvo truck engine, and the results indicate that with nanofluids the temperatures of combustion chamber components and coolant are lowered . Lockwood et al. in Valvoline Company reported the application of nanofluids in the cooling for internal combustion engine . The experiments found that adding 1% vol. carbon nanotube in engine oil could increase the thermal conductivity by 150%. Wallner et al. in Delphi Company found that applying nanofluids can efficiently improve the efficiency of internal combustion engine and decrease the size and weight of the cooling system . Huminic et al. studied the performance of nanofluids in a car radiator with a numerical method and found that the convective heat transfer performance is distinctly better than that of single‐phase fluids . Furthermore, the heat transfer properties of nanofluids are influenced by many factors, including the volume concentrations, temperatures, and fluid velocities. Vajjha et al. reported their research on the flow and heat transfer properties of Al2O3 and CuO nanofluids when applying them in the car radiator . Their results reveal that nanofluids possess improved convective heat transfer properties and the increase rate is increased by increased volume concentrations. Leong et al. found that the heat transfer coefficient and heat transfer rate in the cooling system of internal combustion engine are improved by using nanofluids . Peyghambarzadeh et al. experimentally verified that the application of nanofluids improves heat transfer efficiency of the car radiator by 45% when using Al2O3‐H2O nanofluids .
The authors have focused on the application of nanofluids in internal combustion engine (ICE) for heat transfer enhancement. In order to apply nanofluids in ICE, the mechanisms of heat transfer enhancement and the rules of enhanced heat transfer by nanofluids should be clarified first. The original cause of heat transfer enhancement is due to the adding of nanoscale particles. Therefore, we have attempted to use molecular dynamics (MD) simulations to study these microscopic mechanisms . By using MD simulation, we have calculated thermal conductivity of nanofluids via the Green‐Kubo equation and proposed an effective criterion for predicting the enhancement of apparent thermal conductivity. Furthermore, possible mechanisms of heat conduction increase in nanofluids are studied by MD simulation, including: (1) the micromotions of nanoparticles, (2) changed microstructure of base fluid by adding nanoparticles, and (3) the influence of absorption layer of base fluid at the surface of nanoparticles. On the basis of the microscopic mechanisms found by MD simulations, we have also proposed a revised thermal conductivity model, which considered both the static and dynamic mechanisms. The revised model is verified by experimental data, which has been proved to be quite accurate for predicting thermal conductivity of common types of nanofluids.
2. Influence rule and criterion for nanofluids’ thermal conductivity
2.1. Simulation results of thermal conductivity
MD simulation is used to calculate thermal conductivity of nanofluids via the Green‐Kubo equation . A series of influencing factors for the thermal conductivity of nanofluids have been considered, including: nanoparticles’ volume concentrations, sizes, materials, and shapes . In this work, inert liquid Ar is chosen as the base fluid because of the mature and credible potential function. The NP materials include Cu, Ag, Fe, and Au. We have chosen these types of nanoparticles because they are commonly reported in the literatures on nanofluids. The MD simulation results reveal that the thermal conductivity of nanofluids can be obviously increased by adding nanoparticles, as shown in Table 1. However, the contributions of several influencing factors for thermal conductivity of nanofluids are different.
Figure 1 shows the MD simulation results of thermal conductivities for nanofluids containing spherical nanoparticles. In this case, the nanoparticle volume fractions, nanoparticle diameter, and thermal conductivity of nanoparticles are considered. For the influencing factors that have been considered in this work, the influencing rules are regular. The thermal conductivity of nanofluids is increased with increased volume fraction of NPs, decreased NP sizes, and higher thermal conductivity of NPs. For instance, the ratios of thermal conductivity enhancement for Ag, Cu, Fe, and Au nanofluids are 1.41, 1.15, 1.11, and 1.08 sequentially when the other conditions are the same.
To examine the influencing rules for thermal conductivity of nanofluids in depth, the ratio of thermal conductivity enhancement by nanoparticle volume fraction,
The physical significance of
2.2. Criterion for the increased thermal conductivity
It is found that the nanoparticles containing higher atomic potential energy (energetic atoms) are better for thermal conductivity enhancement of nanofluids . The ratio of energetic atoms in a nanoparticle
If we set a standard for delimiting the energetic atoms in a nanoparticle,
3. Proposed mechanisms of heat conduction in nanofluids
3.1. Altered microstructure of nanofluids
In order to analyze the microscopic structure characteristics of nanofluids, number density distribution, radial distribution function (RDF), coordination number, and potentials of mean force (PMF) should be considered .
Number density distribution represents the distribution of liquid atoms around a centered nanoparticle. Figure 7 illustrates the number density distributions of base fluid atoms in different types of nanofluids. It is found that at the positions of 0.25 and 0.5 nm all the curves show the first and second peak values. But for different types of nanoparticles, the first peak values of curves are different. The order of first peak values is of the same order of thermal conductivity of bulk materials of nanoparticles.
RDF represents the probability of finding an atom of a specified type near the central atom. Through RDF, the microscopic structure of fluid could be examined. Figure 8 illustrates the RDF of Cu nanofluids with a 2 nm‐diameter nanoparticle. In the figure, the RDF curve of “Ar‐Ar” represents the chance of finding an Ar atom near the central Ar atom. It could be found that the Ar‐Ar RDF shows typical characteristics of the liquid: “short‐range order and long‐range disorder.” In the figure, the “total” RDF represents the chance of finding an atom of any type near the central atom, which represents the microscopic structure of nanofluid. It is found that the first curvilinear peak in the RDF of nanofluids is larger than that of base fluid, which means the probability of finding an atom is higher than that in a single‐phase base fluid. It could also be found that there are several diminutive curvilinear peaks in the RDF of nanofluids, which is due to the adding of nanoparticles in base fluid. In general, the microscopic structure of nanofluid exerts a mixed up structure characteristics of liquid and solid. Both the liquid characteristic of “short‐range order and long‐range disorder” and the solid characteristic of “long‐range order” have been found in the microscopic structure of nanofluids. Therefore, the microscopic structure of nanofluids is always ordered.
Coordinate number indicates the average adjacent atomic number for a certain atom within an interval of
PMF reflects the combining capacity between particles in pairs. The value of PMF could be used to investigate the combining capacity between different particle pairs. Figure 10 shows the PMF curve for Cu‐Ar nanofluids. The contact minimum (CM), separated minimum (SM), and the layer barrier (LB) could easily be found in the PMF curve of nanofluids. But the positions and values of CM, SM, and LB are different for disparate atom pairs. The cis‐trans direction of energy barrier between molecular layers of liquid Ar is different. When an atom is approaching the central particle, then it needs to conquer the energy barrier between the first and second molecular layers. But the atom is harder to leave the central particle. An atom of base fluid needs to conquer greater energy barrier to reenter the base fluid. The PMF of nanofluids is different from that of base fluid. At 0.3 nm, there is a huge energy barrier in the PMF of nanofluids, which indicates the surrounding atom needs to conquer two energy barriers to get close to the central atom. The cis‐trans direction of the first energy barrier is nearly the same, but the cis‐trans direction of the second energy barrier is obviously different. Once a base fluid atom enters the adjacent area of the central atom, then it is very hard to reenter the base fluid because of the large energy barrier.
3.2. Movements of nanoparticles in the base fluid
Through MD simulation, the nanoparticles are observed to move chaotically at high speed in the base fluid. Through MD simulation, the instantaneous velocity and position coordinates of each atom could be obtained . The translational and rotational velocity of nanoparticles could be acquired by defining a group for the Cu atoms within the nanoparticle. With commands provided by LAMMPS the time‐averaged translational and rotational velocity of the atom group could be calculated and output derived. For the case of imposed shearing velocity
Rotation of nanoparticles is also statistically analyzed. For the case of imposed shearing velocity 50 m/s, the angular velocity component along the
4. Modeling thermal conductivity of nanofluids
Jeffrey applied Green's function method and relaxed the requirement of uniform configuration for particles. The formula, which is suitable for predicting suspensions with nonuniformly distributing nanoparticles and relatively large volume concentration, is written as ,
where is a convergent series, which depends on the specific value of thermal conductivity of nanoparticle and base fluid .
Through considering the above‐mentioned mechanisms of thermal conductivity enhancement in nanofluids, a revised model for predicting thermal conductivity of nanofluids that takes into account both the static and dynamic mechanisms is proposed, which is written as:
In the equation,
Compared with existing prediction models for thermal conductivity of nanofluids, the present model takes into account the static and dynamic mechanisms of strengthened heat conduction in nanofluids simultaneously and possesses more definite physics meaning. In addition, parameters used in the current model are more precise that ensures the veracity of prediction result. For instance, the thermal conductivity of nanoparticles
Through comparing the prediction results of the present model and existing experimental data, the present prediction model is proved to be quite effective for predicting thermal conductivity of common nanofluids, as shown in Table 2. For various types of nanofluids (with different materials including: metal, metallic oxide, and nonmetallic oxide, different volume fractions, or different nanoparticle diameters), the present model gives good predictions.
|Present model||Maximum error|
|Teng et al. ||Al2O3/Water||20||0.001–0.005||1.018–1.065||1.010–1.043||2.1%|
|Chon et al. ||Al2O3/Water||13||1||1.081||1.072||0.9%|
|Xie et al. ||Al2O3/EG||25||1.7–5||1.097–1.294||1.103–1.303||0.8%|
|Wang et al. ||Al2O3/EG||28||5–8||1.246–1.404||1.276–1.445||2.9%|
|Eastman et al. ||CuO/EG||35||1–4||1.050–1.227||1.061–1.245||3.7%|
|Lee et al. ||CuO/EG||24||1–4||1.060–1.242||1.047–1.212||3.2%|
|Xuan and Li ||Cu/Water||100||1–5||1.078–1.434||1.090–1.459||3.1%|
|Li et al. ||Cu/Water||20||1–3||1.120–1.289||1.096–1.293||2.1%|
|Eastman et al. ||Cu/EG||10||0.33–0.55||1.041–1.101||1.061–1.122||2%|
|Hwang et al. ||CuO/Water||33||1||1.05||1.08||2.9%|
|Zhang et al. ||SiO2/Water||7||0.5–3||1.016–1.084||1.014–1.088||0.4%|
|Hwang et al. ||SiO2/Water||12||1||1.03||1.03||0|
5. Concluding remarks
Thermal conductivities of nanofluids with various nanoparticles have been calculated through MD simulations. Influence rule of various factors for thermal conductivity of nanofluids has been studied. Through defining the ratio of thermal conductivity enhancement by nanoparticle volume fraction,
Mechanisms of heat conduction enhancement are investigated by MD simulations. Altered microstructure and movements of nanoparticles in the base fluid are proposed to be the main reasons for thermal conductivity enhancement in nanofluids. Number density distribution, radial distribution function (RDF), coordination number, and potentials of mean force (PMF) are used to analyze the microscopic structure characteristics of nanofluids. Through MD simulation, the average translational and rotational velocities of nanoparticles are obtained.
Both the static and dynamic mechanisms for heat conduction enhancement in nanofluids have been considered to establish a prediction model for thermal conductivity. The parameters in the model have definite physical meaning and are more precise. The prediction results of the present model are in good agreement with experimental results.
The authors have received funds from the National Natural Science Foundation of China (Grant Nos. 51506038, 51606052), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015EQ003), and China Postdoctoral Science Foundation (Grant Nos. 2016T90284, 2015M571411). We acknowledge the reviewers’ comments and suggestions very much. Many thanks to INTECH Publishing and the editor and staffs who helped us publish this chapter.
Lee S, Choi SUS, Li S, Eastman JA. Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer. 1999; 121(2):280–289. DOI: 10.1115/1.2825978
Wen DS, Ding YL. Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. International Journal of Heat and Mass Transfer. 2004; 47(24):5181–‐5188. DOI: 10.1016/j.ijheatmasstransfer.2004.07.012
Hussein AM, Sharma KV, Bakar RA, Kadirgama K. A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid. Renewable and Sustainable Energy Reviews. 2014; 29:734–743. DOI: 10.1016/j.rser.2013.08.014
Sundar LS, Singh MK. Convective heat transfer and friction factor correlations of nanofluid in a tube and with inserts: A review. Renewable and Sustainable Energy Reviews. 2013; 20:23–35. DOI: 10.1016/j.rser.2012.11.041
Wambsganss MW. Thermal management concepts for higher‐efficiency heavy vehicles. In: SAE Technical Paper ; 1999. Paper number: 1999‐01‐2240. DOI: 10.4271/1999‐01‐2240
Choi SUS. Nanofluids for improved efficiency in cooling systems. In: Heavy Vehicle Systems Review; April 18–20,2006; Chicago. 2006.
Saripella SK, Yu W, Routbort JL, France DM. Effects of nanofluid coolant in a class 8 truck engine. In: SAE Technical Paper; 2007. Paper number: 2007‐01‐2141. DOI: 10.4271/2007‐01‐2141
Lockwood FE, Zhang ZG, Forbus TR, Choi SUS, Yang Y, Grulke EA. The current development of nanofluid research. In: SAE Technical Paper; 2005. Paper number: 2007‐01‐2141. DOI: 10.4271/2007‐01‐2141
Wallner E, Sarma DHR, Myers B, Shah S, Ihms D, Chengalva S, Parker R, Eesley G, Dykstra C. Nanotechnology application in future automobiles. In: SAE Technical Paper; 2010. Paper number: 2010‐01‐1149. DOI: 10.4271/2010‐01‐1149
Huminic G, Huminic A. The cooling performances evaluation of nanofluids in a compact heat exchanger. In: SAE Technical Paper; 2012. Paper number: 2012‐01‐1045. DOI: 10.4271/2012‐01‐1045
Vajjha RS, Das DK, Namburu PK. Numerical study of fluid dynamic and heat transfer performance of Al2O3 and CuO nanofluids in the flat tubes of a radiator. International Journal of Heat and Fluid Flow. 2010; 31(4):613–621. DOI: 10.1016/j.ijheatfluidflow.2010.02.016
Leong KY, Saidur R, Kazi SN, Mamun AH. Performance investigation of an automotive car radiator operated with nanofluid based coolant (Nanofluid as a coolant in a radiator). Applied Thermal Engineering. 2010; 30(17–18):2685–2692. DOI: 10.1016/j.applthermaleng.2010.07.019
Peyghambarzadeh SM, Hashemabadi SH, Jamnani MS, Hoseini SM. Improving the cooling performance of automobile radiator with Al2O3/water nanofluid. Applied Thermal Engineering. 2011; 31(10):1833–1838. DOI: 10.1016/j.applthermaleng.2011.02.029
Allen MP, Tildesley DJ. Computer simulation of liquids. 1st ed. New York: Oxford University Press; 1987. 385 p. DOI: 10.1063/1.2810937
Cui WZ, Shen ZJ, Yang JG, Wu SH, Bai ML. Influence of nanoparticle properties on the thermal conductivity of nanofluids by molecular dynamics simulation. RSC Advances. 2014; 4(98):55580–55589. DOI: 10.1039/C4RA07736A
Cui WZ, Shen ZJ, Yang JG, Wu SH. Molecular dynamics simulation on the microstructure of absorption layer at the liquid–solid interface in nanofluids. International Communications in Heat and Mass Transfer. 2016; 71:75–85. DOI: 10.1016/j.icheatmasstransfer.2015.12.023
Cui WZ, Shen ZJ, Yang JG, Wu SH. Effect of chaotic movements of nanoparticles for nanofluid heat transfer augmentation by molecular dynamics simulation. Applied Thermal Engineering. 2015; 76:261–271. DOI: 10.1016/j.applthermaleng.2014.11.030
Jeffrey DJ. Conduction through a random suspension of spheres. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1973; 335(1602):355–367. DOI: 10.1098/rspa.1973.0130
Cui WZ, Shen ZJ, Yang JG, Wu SH. A modified prediction model for thermal conductivity of spherical nanoparticle suspensions (nanofluids) by introducing static and dynamic mechanisms. Industrial and Engineering Chemistry Research. 2014; 53(46):18071–18080. DOI: 10.1021/ie503296g
Masuda H，Ebata A，Teramae K，Hishinuma N. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra‐fine particles. Dispersion of Al2O3, SiO2 and TiO2 ultra‐fine particles. Netsu Bussei. 1993; 7(4):227–233. DOI: 10.2963/jjtp.7.227
Teng TP, Hung YH, Teng TC, Mo HE, Hsu HG. The effect of alumina/water nanofluid particle size on thermal conductivity. Applied Thermal Engineering. 2010; 30(14–15):2213–2218. DOI: 10.1016/j.applthermaleng.2010.05.036
Chon CH, Kihm KD, Lee SP, Choi SUS. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3)(Al2O3) thermal conductivity enhancement. Applied Physics Letters. 2005; 87:153107. DOI: 10.1063/1.2093936
Xie HQ, Wang JC, Xi TG, Liu Y, Ai F, Wu QR. Thermal conductivity enhancement of suspensions containing nanosized alumina particles. Journal of Applied Physics. 2002; 91:4568. DOI: 10.1063/1.1454184
Vajjha RS, Das DK. Experimental determination of thermal conductivity of three nanofluids and development of new correlations. International Journal of Heat and Mass Transfer. 2009; 52(21–22):4675–4682. DOI: 10.1016/j.ijheatmasstransfer.2009.06.027
Wang XW, Xu XF, Choi SUS. Thermal conductivity of nanoparticle – fluid mixture. Journal of Thermophysics and Heat Transfer. 1999; 13(4):474–480. DOI: 10.2514/2.6486
Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ. Anomalously increased effective thermal conductivities of ethylene glycol‐based nanofluids containing copper nanoparticles. Applied Physics Letters. 2001; 78(6):718. DOI: 10.1063/1.1341218
Lee S, Choi S, Li S, Eastman J. Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer. 1999; 121(2):280–289. DOI: 10.1115/1.2825978
Xuan YM, Li Q. Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Flow. 2000; 21(1):58–64. DOI: 10.1016/S0142‐727X(99)00067‐3
Li Q, Xuan YM, Yu F. Experimental investigation of submerged single jet impingement using Cu–water nanofluid. Applied Thermal Engineering. 2012; 36:426–433. DOI: 10.1016/j.applthermaleng.2011.10.059
Hwang Y,Park HS, Lee JK, Jung WH. Thermal conductivity and lubrication characteristics of nanofluids. Current Applied Physics. 2006; 6(Supplement 1): e67–e71. DOI: 10.1016/j.cap.2006.01.014
Zhang SB, Luo ZY, Wang T, Shou CH, Ni MJ, Cen KF. Experimental study on the convective heat transfer of CuO‐water nanofluid in a turbulent flow. Journal of Enhanced Heat Transfer. 2010; 17(2):1–14. DOI: 10.1615/JEnhHeatTransf.v17.i2.60