Introduction to Nanofluids

Transcription

1 Chapter 1 Introduction to Nanoluids 1.1 Introduction Thermal properties o liquids play a decisive role in heating as well as cooling applications in industrial processes. Thermal conductivity o a liquid is an important physical property that decides its heat transer perormance. Conventional heat transer luids have inherently poor thermal conductivity which maes them inadequate or ultra high cooling applications. Scientists have tried to enhance the inherently poor thermal conductivity o these conventional heat transer luids using solid additives ollowing the classical eective medium theory (Maxwell, 1873) or eective properties o mixtures. Fine tuning o the dimensions o these solid suspensions to millimeter and micrometer ranges or getting better heat transer perormance have ailed because o the drawbacs such as still low thermal conductivity, particle sedimentation, corrosion o components o machines, particle clogging, excessive pressure drop etc. Downscaling o particle sizes continued in the search or new types o luid suspensions having enhanced thermal properties as well as heat transer perormance. All physical mechanisms have a critical scale below which the properties o a material changes totally. Modern nanotechnology oers physical and chemical routes to prepare nanometer sized particles or nanostructured materials engineered on the atomic or molecular scales with enhanced thermo-physical properties compared to their respective bul orms. Choi (1995) and other

2 Chapter-1 researchers (Masuda et al., 1993; Lee et al., 1999) have shown that it is possible to brea down the limits o conventional solid particle suspensions by conceiving the concept o nanoparticle-luid suspensions. These nanoparticle-luid suspensions are termed nanoluids, obtained by dispersing nanometer sized particles in a conventional base luid lie water, oil, ethylene glycol etc. Nanoparticles o materials such as metallic oxides (Al 2 O 3, CuO), nitride ceramics (AlN, SiN), carbide ceramics (SiC, TiC), metals (Cu, Ag, Au), semiconductors (TiO 2, SiC), single, double or multi walled carbon nanotubes (SWCNT, DWCNT, MWCNT), alloyed nanoparticles (Al 70 Cu 30 ) etc. have been used or the preparation o nanoluids. These nanoluids have been ound to possess an enhanced thermal conductivity (Shyam et al., 2008; Choi et al., 2001; Eastman et al., 2001) as well as improved heat transer perormance (Xuan et al., 2003; Yu et al., 2003; Vassalo et al., 2004; Artus, 1996) at low concentrations o nanoparticles. Even at very low volume ractions (< 0.1%) o the suspended particles, an attractive enhancement up to 40% in thermal conductivity has been reported on these nanotechnology based luids (Wang et al., 1999) and the percentage o enhancement is ound to increase with temperature (Das et al., 2003) as well as concentration o nanoparticles (Shyam et al., 2008). The eective thermal conductivity o these nanoluids are usually expressed as a normalized thermal conductivity value obtained by dividing the overall thermal conductivity o the nanoluid by the base luid thermal conductivity or sometimes as a percentage o the eective value with respect to the base luid value Properties o nanoluids It may be noted that particle size is an important physical parameter in nanoluids because it can be used to tailor the nanoluid thermal properties as well as the suspension stability o nanoparticles. Researchers in nanoluids have 2 Department o Instrumentation, CUSAT

3 Introduction been trying to exploit the unique properties o nano particles to develop stable as well as highly conducting heat transer luids. The ey building blocs o nanoluids are nanoparticles; so research on nanoluids got accelerated because o the development o nanotechnology in general and availability o nanoparticles in particular. Compared to micrometer sized particles, nanoparticles possess high surace area to volume ratio due to the occupancy o large number o atoms on the boundaries, which mae them highly stable in suspensions. Thus the nano suspensions show high thermal conductivity possibly due to enhanced convection between the solid particle and liquid suraces. Since the properties lie the thermal conductivity o the nano sized materials are typically an order o magnitude higher than those o the base luids, nanoluids show enhancement in their eective thermal properties. Due to the lower dimensions, the dispersed nanoparticles can behave lie a base luid molecule in a suspension, which helps us to reduce problems lie particle clogging, sedimentation etc. ound with micro particle suspensions. The combination o these two eatures; extra high stability and high conductivity o the dispersed nanospecies mae them highly preerable or designing heat transer luids. The stable suspensions o small quantities o nanoparticles will possibly help us to design lighter, high perormance thermal management systems. Cooling is indispensable or maintaining the desired perormance and reliability o a wide variety o industrial products such as computers, power electronic circuits, car engines, high power lasers, X-ray generators etc. With the unprecedented increase in heat loads and heat luxes caused by more power in miniaturized products, high tech industries such as microelectronics, transportation, manuacturing, metrology and deense ace cooling as one o the top technical challenges. For example, the electronics industry has provided Department o Instrumentation, CUSAT 3

4 Chapter-1 computers with aster speeds, smaller sizes and expanded eatures, leading to ever increasing heat loads, heat luxes and localized hot spots at the chip and pacage levels. Such thermal problems are also ound in power electronics, optoelectronic devices etc. So the enhanced heat transer characteristics o nanoluids may oer the development o high perormance, compact, cost eective liquid cooling systems. 1.2 Nanoluid thermal conductivity research: A review Practical applications o nanoluids discussed above are decided by the thermophysical characteristics o nanoluids. In the last decade, signiicant amounts o experimental as well as theoretical research were done to investigate the thermophysical behavior o nanoluids. All these studies reveal the act that micro structural characteristics o nanoluids have a signiicant role in deciding the eective thermal conductivity o nanoluids. There are many reviews on nanoluid thermal conductivity research (Wang et al., 2007; Murshed et al., 2008a; Choi et al., 2009; Wen et al., 2009). In all reviews on nanoluid thermal conductivity, both theoretical models as well as experimental results have been discussed. By closely analyzing the experimental results and theoretical models ollowed by previous authors we get a good picture o the conlicting reports on the eective thermal conductivity o nanoluids and the mechanisms supporting these reports. Experimental wor done by a good number o research groups worldwide has revealed that nano luids exhibit thermal properties superior to base luid or conventional micrometer sized particle-luid suspensions. Choi et al. (2001) and Eastman et al. (2001) have shown that copper and carbon nanotube (CNT) nano luid suspensions possess much higher thermal conductivities compared to those o base luids and that CNT nanoluids have showed a non linear relationship between thermal conductivity and concentration at low volume ractions o CNTs (Choi et al., 2001). 4 Department o Instrumentation, CUSAT

5 Introduction Initial wor on nanoluids was ocused on thermal conductivity measurements as a unction o concentration, temperature, and particle size. Measurements o the thermal conductivity o nanoluids started with oxide nanoparticles (Masuda et al., 1993; Lee et al., 1999) using transient hot wire (THW) method. Nanoluids did not attract much attention until Eastman et al. (2001) showed or the irst time that copper nanoluids, have more dramatic increases than those o oxide nanoluids produced by a two step method. Similarly Choi et al. (2001) perormed thermal conductivity measurement o MWCNTs (Multi walled Carbon nano tubes) dispersed into a host luid, synthetic poly (α-olein) oil, by a two step method and measured the eective thermal conductivity o carbon nanotube-oil suspensions. They discovered that nanoluids have an anomalously large increase in thermal conductivity, up to 150% or approximately 1 vol % o nanotubes, which is by ar the highest thermal conductivity ever achieved in a liquid. This measured increase in thermal conductivity o nanotube based nanoluids is an order o magnitude higher than that predicted using existing theories (Maxwell, 1873; Hamilton and Crosser, 1962). The results o Choi et al. (2001) show another anomaly that the measured thermal conductivity is non linear with nanotube loadings, while all theoretical models predict a linear relationship. This non linear relationship is not expected in conventional luid suspensions o microsized particles at such low concentrations. Soon, some other distinctive eatures such as strong temperature dependent thermal conductivity (Das et al., 2003) and strong particle size dependent thermal conductivity (Chon et al., 2005) were discovered during the thermal conductivity measurement o nanoluids. Although experimental wor on convection and boiling heat transer in nanoluids are very limited compared to experimental studies on conduction in nanoluids, discoveries such as a two old increase in the laminar convection Department o Instrumentation, CUSAT 5

6 Chapter-1 heat transer coeicient (Faulner et al., 2004) and a three-old increase in the critical heat lux in pool boiling (You et al., 2003) were reported. The potential impact o these discoveries on heat transer application is signiicant. Thereore, nanoluids promise to bring about a signiicant improvement in cooling technologies. As a consequence o these discoveries, research and development on nanoluids have drawn considerable attention rom industry and academia over the past several years. Most o the experimental studies on eective thermal conductivities o nanoluids have been done by using a transient hot wire (THW) method, as this is one o the most accurate methods to measure the thermal conductivities o luids. Another method generally employed is the steady state method. All the experimental results obtained by these methods have shown that the thermal conductivity o nanoluids depend on many actors such as particle volume raction, particle material, particle size, particle shape, base luid properties and temperature. More detailed descriptions about the eect o these parameters on eective thermal conductivity o nanoluids are discussed below Eect o particle volume raction Particle volume raction is a parameter that has been investigated in almost all o the experimental studies and most o the results are generally in agreement qualitatively. Most o the research reports show an increase in thermal conductivity with an increase in particle volume raction and the relation ound is, in general, linear. There are many studies in literature on the eect o particle volume raction on the thermal conductivity o nanoluids. Masuda et al. (1993) measured the thermal conductivity o water based nanoluids consisting o Al 2 O 3 (13nm), SiO 2 (12nm) and TiO 2 (27nm) nanoparticles, the numbers in the parenthesis indicating the average diameter o 6 Department o Instrumentation, CUSAT

7 Introduction the suspended nanoparticles. An enhancement up to 32.4% was observed in the eective thermal conductivity o nanoluids or a volume raction about 4.3% o Al 2 O 3 nanoparticles. Lee et al. (1999) studied the room temperature thermal conductivity o water as well as ethylene glycol (EG) based nanoluids consisting o Al 2 O 3 (38.5nm) and CuO (23.6nm) nanoparticles. In this study a high enhancement o about 20 % in the thermal conductivity was observed or 4% volume raction o CuO in CuO/EG nanoluid. Later Wang et al. (1999) repeated the measurement on the same type o nanoluids based on EG and water with Al 2 O 3 (28nm) as well as CuO (23nm) as inclusions. The measurements carried out by these groups showed that or water and ethylene glycol-based nanoluids, thermal conductivity ratio showed a linear relationship with particle volume raction and the lines representing this relation were ound to be coincident. Measurements on other nanoluid systems such as TiO 2 in deionized water (Chopar et al., 2008) and multi walled carbon nanotube (MWCNT) in oil (Choi et al., 2001) show a non linear relation between the eective thermal conductivity and particle volume raction which indicate the interactions between the particles in the system Eect o particle material Most o the studies show that particle material is an important parameter that aects the thermal conductivity o nanoluids. For example, Lee et al. (1999) considered the thermal conductivity o nanoluids with Al 2 O 3 and CuO nanoparticles mentioned in the previous section. They ound that nanoluids with CuO nanoparticles showed better enhancement compared to the nanoluids prepared by suspending Al 2 O 3 nanoparticles in the same base luid. It may be noted that as a material Al 2 O 3 has higher thermal conductivity than CuO. Department o Instrumentation, CUSAT 7

8 Chapter-1 Authors explain this behavior as due to the ormation clusters o Al 2 O 3 nanoparticles in the luid. Chopar et al. (2008) made room temperature measurements in water and EG based nanoluids consisting o Ag 2 Al as well as Ag 2 Cu nanoparticles and it was ound that the suspensions o Ag 2 Al nanoparticles showed enhancement in thermal conductivity slightly more than Ag 2 Cu nanoparticle suspensions. This was explained as due to the higher thermal conductivity o Ag 2 Al nanoparticles. Also, the suspensions o carbon nanotubes in dierent luids were ound to possess a surprising enhancement upto about 160% (Choi et al., 2001) in the eective thermal conductivity value Eect o base luid According to the conventional eective medium theory (Maxwell, 1873), as the base luid thermal conductivity decreases, the eective thermal conductivity o a nanoluid increases. Most o the experimental reports agree with the theoretical values given by this conventional mean ield model. As per Wang et al. s (1999) results on the thermal conductivity o suspensions o Al 2 O 3 and CuO nanoparticles in several base luids such as water, ethylene glycol, vacuum pump oil and engine oil, the highest thermal conductivity ratio was observed when ethylene glycol was used as the base luid. EG has comparatively low thermal conductivity compared to other base luids. Engine oil showed somewhat lower thermal conductivity ratios than Ethylene Glycol. Water and pump oil showed even smaller ratios respectively. However, CuO/EG as well as CuO/water nanoluids showed exactly same thermal conductivity enhancements at the same volume raction o the nanoparticles. The experimental studies reported by Xie et al. (2002b) also supported the values given by the mean ield theory. 8 Department o Instrumentation, CUSAT

9 Introduction Chopar et al. (2008) contradicted the above results based on mean ield theory statement by reporting higher thermal conductivity enhancement or nanoluids with a base luid o higher thermal conductivity. The theoretical analysis made by Hasselmann and Johnson (1987) have shown that the eective thermal conductivity o luid-particle mixtures were nearly independent o base luid thermal conductivity Eect o particle size The advent o nanoluids oers the processing o nanoparticles o various sizes in the range o nm. It has been ound that the particle sizes o nanoparticles have a signiicant role in deciding the eective thermal conductivity o nanoluids. There are many studies reported in literature regarding the dependence o nanoparticle size on eective thermal conductivity o nanoluids. Chopar et al. (2006) studied the eect o the size o dispersed nanoparticles or Al 70 Cu 30 /EG nanoluids by varying the size o Al 70 Cu 30 nanoparticles in the range rom 9 nm to 83 nm. In another study on water and EG based nanoluids consisting o Al 2 Cu and Ag 2 Al nanoparticles, Chopar et al. (2008) also investigated the eect o particle size on eective thermal conductivity o nanoluids. In all these cases it has been ound that the eective thermal conductivity o a nanoluid increases with decreasing nanoparticle size. Also, the results o Eastman et al. (2001) and Lee et al. (1999) support this conclusion drawn by Chopar et al. (2008) on the particle size eect on the eective thermal conductivity o nanoluids. In another study o the eect o particle size on the thermal conductivity o nanoluids, reported by Bec et al. (2009) in water as well as EG based nanoluids consisting o Al 2 O 3 nanoparticles, the normalized thermal conductivity o nanoluids vary in such a way that it decreases with decreasing Department o Instrumentation, CUSAT 9

10 Chapter-1 the nanoparticle size. Thus conlicting reports have appeared in literature on the dependence o particle size on the thermal conductivity o nanoluids Eect o particle shape For experimentation, spherical as well as cylindrical shaped nanoparticles are commonly used or nanoluid synthesis. The cylindrical particles have larger aspect ratio (length to diameter ratio) than spherical particles. The wide dierences in the dimensions o these particles do inluence the enhancement in eective thermal properties o nanoluids. Xie et al. (2002a) measured the thermal conductivity o water as well as EG based nanoluids consisting o both cylindrical as well as spherical SiC nanoparticles. It was observed that in water based nanoluids, the cylindrical suspensions had higher thermal conductivity enhancement o about 22.9% than the spherical particles or the same volume raction (4.2%). Also the theoretical values based on Hamilton-Crosser model (1962) are ound to be in good agreement with this comparatively higher enhancement or cylindrical particle suspensions. Another experimental study reported by Murshed et al. (2005) in water based nanoluids consisting o spherical as well as rod shaped TiO 2 nanoparticles showed a comparatively higher enhancement or rod shaped particles (32.8%) than spherical particles (29.7%) at a volume raction o 5%. In addition to these experimental results a general observation is that nanotube suspensions show a higher enhancement than the spherical particle suspension due to rapid heat transer along a larger distance through a cylindrical particle since it has a length o the order o a micrometer. However, the cylindrical particle suspension need higher pumping power due to its enhanced viscosity (Timoeeva et al., 2009) which limits its usage, possible application as a heat transer luid. 10 Department o Instrumentation, CUSAT

11 Introduction Eect o temperature The temperature o a two component mixture, such as a nanoluid, depends on the temperature o the solid component as well as that o the host media. In a nanoluid the increase in temperature enhances the collision between the nano particles (Brownian motion) and the ormation o nanoparticle aggregates (Li et al., 2008a), which result in a drastic change in the thermal conductivity o nanoluids. Masuda et al. (1993) measured the thermal conductivity o water-based nanoluids consisting o Al 2 O 3, SiO 2, and TiO 2 nanoparticles at dierent temperatures. It was ound that thermal conductivity ratio decreased with increasing temperature. But the experimental results o others have been contradictory to this result. The temperature dependence o the thermal conductivity o Al 2 O 3 /water and CuO/water nanoluids, measured by Das et al. (2003), have shown that or 1 vol.% Al 2 O 3 /water nanoluid, thermal conductivity enhanced rom 2% at 21 0 C to 10.8% at 51 0 C. Temperature dependence o 4 vol. % Al 2 O 3 nanoluid was much more signiicant, an increase rom 9.4% to 24.3% at 51 0 C. The investigations o Li et al. (2006) in CuO/water as well as Al 2 O 3 /water reveal that the dependence o thermal conductivity ratio on particle volume raction get more pronounced with increasing temperature. In spite o these experimental results, the theoretical results based on Hamilton-Crosser model (1962) do not support the argument o any signiicant variation in thermal conductivity with temperature. Researchers have explained the enhancement in thermal conductivity with temperature in terms o the Brownian motion o particles since it increases the micro convection in nanoparticle suspensions. Department o Instrumentation, CUSAT 11

12 Chapter Eect o sonication time The ultrasonic vibration technique is the most commonly used technique or producing highly stable, uniormly dispersed nano suspensions by two step process. It has been ound that the duration o the application o the ultrasonic vibration has a signiicant eect on the thermal conductivity o nanoluids (Hong et al., 2006) since it helps to reduce the clustering o nanoparticles Eect o the preparation method ollowed The enhanced heat transer characteristics o nanoluids depend on the details o their microstructural properties lie the component properties, nanoparticle volume raction, particle geometry, particle dimension, particle distribution, particle motion, particle interacial eects as well as the uniormity o dispersion o nanoparticles in host phase. So, the nanoluids employed in experimental research need to be well characterized with respect to particle size, size distribution, shape and clustering o the particles so as to render the results most widely applicable. As per the application, either a low or high molecular weight luid can be used as the host luid or nanoluid synthesis. The dispersion o nanoparticles in a base luid has been done either by a two step method or by a single step method. In either case, a well-mixed and uniormly dispersed nanoluid is needed or successul reproduction o properties and interpretation o experimental data. As the name implies the two step method involves two stages, irst stage is the processing o nanoparticles ollowing a standard physical or chemical method and in the second step proceeds to disperse a desired volume raction o nanoparticles uniormly in the base luid. Techniques such as high shear and ultrasound vibration are used to create uniorm, stable luid-particle suspensions. The main drawbac o this technique 12 Department o Instrumentation, CUSAT

13 Introduction is that the particles will remain in an aggregated state even ater the dispersion in host luids. The single-step method provides a procedure or the simultaneous preparation and dispersion o nanoparticles in the base luid. Most o the metallic oxide nanoparticle suspensions are prepared by the two step method (Kwa et al., 2005). The two step method wors well or oxide nanoparticles as well, but it is not as eective or metallic nanoparticles such as copper. Zhu et al. (2004) developed a one step chemical method or producing stable Cu-in ethylene glycol nanoluids and have shown that the single step technique is preerable over the two step method or preparing nanoluids containing highly thermal conducting metals. 1.3 Experimental methods As mentioned above, thermal conductivity is the most important parameter that decides the heat transer perormance o a nanoluid. Thus, researchers have tried to achieve higher enhancements in eective thermal conductivity o nanoluids by varying the nano particle volume raction, nano particle size, nano particle shape, temperature, the host luid type as well as the ultra sonication time required or preparing nanoluids. For all these measurements researchers have ollowed either a two step or a single step method or the preparation o nanoluids. They have employed experimental techniques such as the transient hot wire method (Hong et al., 2005; Bec et al., 2009) and the steady state method (Amrollahi et al., 2008) or the measurement o the thermal conductivity o nanoluids. Other methods such as temperature oscillation method (Das et al., 2003) and hot strip method (Vadasz et al., 1987) are seldom used or thermal conductivity measurements. In all these methods the basic principles o measurement are the same, but dier in instrumentation Department o Instrumentation, CUSAT 13

14 Chapter-1 and measurement techniques ollowed. The salient eatures o each o these measurement techniques outlined below The Transient hotwire technique The transient hot wire (THW) method to measure the thermal conductivity o nanoluids has got established itsel as an accurate, reliable and robust technique. The method consists o determining the thermal conductivity o a selected material/luid by observing the rate at which the temperature o a very thin platinum wire o diameter (5-80 µm) increases with time ater a step voltage has been applied to it. The platinum wire is embedded vertically in the luid, which serves as a heat source as well as a thermometer. The temperature o the platinum wire is established by measuring its electrical resistance using a Wheatstone s bridge, which is related to the temperature through a well-nown relationship (Bentley et al., 1984). I i is the current ollowing through the platinum wire and V is the corresponding voltage drop across it, then the heat generated per unit length o the platinum wire is given by, q l * = iv (1.1) l I T 1 and T 2 are the temperatures recorded at two times t 1 and t 2 respectively, the temperature dierence (T 1 -T 2 ) can be used to estimate the thermal conductivity using the relationship, iv t 2 = ln 4 π( T2 T1) l t1 (1.2) 14 Department o Instrumentation, CUSAT

15 Introduction where l is the length o the platinum wire. The advantages o this method are its almost complete elimination o the eects o natural convection and the high speed o measurement compared to other techniques The steady state technique In the steady state method (SSM), a thin layer o the luid with unnown thermal conductivity is subjected to a constant heat lux. The layer has one dimension thicness very small compared to the other dimensions, so that the one-dimensional Fourier equation can be used to deine the heat low in the system. By measuring the temperature on both sides o this layer the thermal conductivity o the liquid can be determined. Many steady state thin layer experimental systems have been developed or the determination o thermal conductivity o luids including nanoluids (Xuan et al., 2000; Belleet and Sengelin 1975; Schroc and Starman 1958). Among them the coaxial cylinders method is probably the best steady state technique or the determination o the thermal conductivity o nanoluids. The major advantages o this method are the simplicity o its design and the short response time o the measuring procedure. By this method the thermal conductivity measurement is possible with an accuracy o ± 0.1%. This method is applicable to electrically conducting liquids as well as toxic and chemically aggressive substances. The apparatus built or measurements based on this technique include two coaxial aluminum cylinders with dierent diameters and lengths. The region between the two cylinders is illed with the liquid o unnown thermal conductivity. Both ends o the system are well insulated, ensuring no heat loss rom the ends. An electrical heater is inserted at the middle o the inner cylinder, itting well in the hole drilled or this purpose. Then the simultaneous recording o the Department o Instrumentation, CUSAT 15

16 Chapter-1 temperature o the layers is possible with the help o temperature sensors having high accuracy positioned on either side o the layer. For a steady state situation the thermal conductivity o the luid can then be evaluated using the equation (Xuan et al., 2000), Ln( R2 R1) = q 2 πl( T T ) 1 2 (1.3) Knowing the thermal conductivity al o aluminium cylinders which is estimated accurately to be 75 W m -1 K -1, the thermal conductivity o the nanoluid can be determined ollowing the equation (Xuan et al., 2000), q= β ( T T ) = β ( T T) (1.4) n ' al 2 1 where β 1 and β 2 are the equipment shape actors, T and T 1 are the temperatures on either side o the layer and the cylinder. 1.4 Theoretical models or thermal conductivity o nanoluids. For the past one and hal decades there has been a great deal o interest in understanding the anomalous enhancement in thermal conductivity observed in several types o nanoluids. This is mainly due to the act that in several experimental results reported in literature, the observed enhancements in thermal conductivity are ar more than those predicted by the well-established mean ield models. Even in the case o the same nanoluid system, enhancements reported by dierent groups have shown wide dierences. The conventional mean iled models such as the Maxwell-Garnett model, Hamilton- Crosser model as well as Bruggemann model were originally derived or solid mixtures and then to relatively large solid particle suspensions. But, these models have been derived rom standard reerence models or eective thermal conductivity o mixtures. Thereore, it is questionable whether these models are 16 Department o Instrumentation, CUSAT

17 Introduction able to predict the eective thermal conductivity o nanoluids. Nevertheless, these models are utilized requently due to their simplicity in the study o nanoluids to compare theoretical and experimental values o thermal conductivity. In the ollowing sections we briely outline the salient eatures o the theoretical models widely used to explain the observed thermal conductivity o nanoluids. More detailed description o these models are presented and discussed in chapter Maxwell-Garnett model Maxwell (1873) developed the irst theoretical model or eective thermal conductivity o two component mixtures considering negligible interacial resistance at the interace between the host phase and inclusions. This model deines the eective thermal conductivity o isotropic, linear, nonparametric mixtures with randomly distributed spherical inclusions. The inclusions are considered to be small compared to volume o the eective medium and are separated by distances greater than their characteristic sizes. Extension o this model to nanoluids expresses the thermal conductivity o nanoluids as an eective value o the thermal conductivities o the inclusions, and the base luid, which taes the orm (Maxwell, 1873) e p ( p ) φv = + 2 ( ) φ p p v (1.5) Here p is given by (Chen et al., 1996) * 3a = 4 a p * b (1.6) where e, p and are the thermal conductivities o the nanoluid, nanoparticles (in bul) and the base luid, respectively and φ v is the volume raction o Department o Instrumentation, CUSAT 17

18 Chapter-1 dispersed particles. It may be noted that the interaction between the particles is neglected in the derivation. As can be seen rom the above expression, the eect o the size and shape o the particles are not included in the analysis. More detailed descriptions o these models are available in literature (Maxwell, 1873; Das et al., 2007) Hamilton-Crosser model Later, Maxwell model was modiied or non-spherical inclusions by Hamilton and Crosser (Hamilton and Crosser, 1962). They expressed the eective thermal conductivity o a binary mixture by the expression, e p + ( n 1) ( n 1) φv( p) = + ( n 1) + φ ( ) p p v p (1.7) 3 where n = is the empirical shape actor, ψ being the sphericity o the dispersed ψ particle. When n=3, Equation (1.7) reduces to the expression or eective thermal conductivity given by the Maxwell-Garnett model (Equation 1.5) Bruggemann model The two models outlined above have not considered the interaction between the inclusion phases. The model developed by Bruggeman, nown as the Bruggeman model (Bruggeman, 1935), includes the interactions among the randomly distributed spherical inclusions in the host phase. For a binary mixture o homogeneous spherical inclusions, the Bruggeman model gives an expression or eective thermal conductivity as, = (3φ 1) + [3(1 φ ) 1)] + (1.8) e v p v 18 Department o Instrumentation, CUSAT

19 Introduction where, = (1.9) (3φv 1) p [3(1 φv) 1)] 2[2 9 φv(1 φv)] p Most o the experimental indings show that thermal conductivities o several nanoluids are ar more than the values predicted by these mean ield models. The mean ield models ailed to explain the ollowing experimental indings, (i) Nonlinear behavior that have appeared in eective thermal conductivity enhancements o nanoluids (Chopar et al., 2006; Li et al., 2000; Kang et al., 2006; Hong et al., 2005; Jana et al., 2007; Shaih et al., 2007; Xie et al., 2002). (ii) Eect o particle size and shape on thermal conductivity enhancements (Xie et al., 2002; Chon et al., 2005; Kim et al., 2007; Li et al., 2007 ;Chen et al., 2008 ;Shima et al., 2009). (iii) Dependence o thermal conductivity enhancement on luid temperature (Chopar et al., 2006; Li et al., 2006; Chon et al., 2005; Wen et al., 2004). So researchers tried to rennovate these conventional mean iled models by including other mechanisms lie Brownian motion o nanoparticles (Jang and Choi, 2004), clustering o nanoparticles (Prasher et al., 2006; Wang et al., 2003), ormation o liquid layer around the nanoparticles (Yu and Choi, 2003; Keblinsi et al., 2002), ballistic phonon transport in nanoparticles (Keblinsi et al., 2002), interacial thermal resistance (Nan et al., 1997; Vladov and Barrat, 2006) etc. The ollowing sections describe eatures o the various models based on these mechanisms. Department o Instrumentation, CUSAT 19

20 Chapter Brownian motion o nanoparticles Jang and Choi (2004) modeled the thermal conductivity o nanoluids by considering the eect o Brownian motion o nanoparticles. This model is based on the aspect that energy transport in a nanoluid consist o our modes; heat conduction in the base luid, heat conduction in nanoparticles, collisions between nanoparticles and micro-convection caused by the random motion o the nanoparticles. Among these modes, the random motion o suspended nanoparticles, the so called Brownian motion, transports energy directly by nanoparticles. This model gives a general expression or eective thermal conductivity o nanoluids by combining the our modes o energy transport in nanoluids. Among the our modes o energy transport the irst mode is the collision between base luid molecules, which physically represents the thermal conductivity o the base luid. Assuming that the energy carriers travel reely only over the mean ree path l BF, ater which the base luid molecules collide; the net energy lux J U across a plane at z is given by (Kittel, 1969) 1 ^ dt dt J = l C C (1 ) (1 ) (1 ) U BF V, BF BF v v BF v 3 φ dz φ = dz φ (1.10) ^ C where C V, BF, BF, T are the heat capacity per unit volume, mean speed, and temperature o the base luid molecules, respectively, andφ v and BF are the volume raction o nanoparticles and thermal conductivity o the base luid. The second mode is the thermal diusion in nanoparticles embedded in luids, the net energy lux J U at z plane is given by, 1 ^ dt dt J = l C vφ = φ (1.11) U nano V, nano v nano v 3 dz dz 20 Department o Instrumentation, CUSAT

21 Introduction where nano and v are the thermal conductivity o the suspended nanoparticles and the mean speed o electron or phonon, respectively. The thermal conductivity o suspended nanoparticles involving the Kapitza resistance is given by (Keblinsi et al., 2002), nano = β (1.12) p The third part o motion is the collision between nanoparticles due to Brownian motion. The nanoparticle collision in a luid medium is a very slow process (Keblinsi et al., 2002); the contribution o this mode to thermal conductivity is much smaller than the other modes and can be neglected. The last mode is the thermal interactions o dynamic or dancing nanoparticles with base luid molecules. The random motion o nanoparticles averaged over time is zero. The vigorous and relentless interactions between liquid molecules and nanoparticles at the molecular and nano scales translate into conduction at the macroscopic level, because there is no bul low o matter. Thereore the Brownian motion o nanoparticles in nanoluids produces convection lie eects at the nano scales. So the ourth mode can be expressed as, ( Tnano TBF ) dt JU = h( Tnano TBF) φv = hδtφv hδtφv (1.13) δ dz where h and δ T are heat transer coeicient or low past nanoparticles and thicness o the thermal boundary layer, respectively. T Here h d BF nano 2 2 d Re P r nano Neglecting the eect o the third mode, we can write the expression or eective thermal conductivity o the nanoluid as, Department o Instrumentation, CUSAT 21

22 Chapter-1 e = BF (1 φv ) + nanoφv + φvhδt (1.14) 3d BF δ T = (1.15) P r The proposed model is a unction o not only thermal conductivities o the base luid and nanoparticles, but also depends on the temperature and size o the nanoparticles. So Equation (1.14) can be modiied or eective thermal conductivity o nanoluid as, d = + + C (1.16) * 2 e (1 φv ) p φv 3 1 Re d Pr φv d p C 1 is a proportionality constant, d is the diameter o luid molecules, d p is the diameter o the nanoparticle, P r is the Prandtl number o the base luid, which represent the ratio o the viscous diusion rate to thermal diusion rate o the base media and * p is the thermal conductivity o the particle considering the interacial thermal resistance nown as the Kapitza resistance, β is a constant and Re d is the Reynold s number given by, Re d C RM, p = (1.17) v d where CRM, is the random motion velocity o nanoparticles and v is the inematic viscosity o the base luid. CRM, can be determined using the relation, C RM, D l 0 = (1.18) BF T B where D = 0 3πµ d is the nanoluid diusion coeicient, where B is the p Boltzmann constant, T is the temperature in K and µ is the dynamic viscosity o the base luid. When the dependence o the model on nanoparticle size is 22 Department o Instrumentation, CUSAT

23 Introduction considered, it is seen that the thermal conductivity o nanoluid increases with decreasing particle size, since the decreasing particle size increases the eect o Brownian motion. In the derivation o this model, the thicness o the thermal boundary layer around the nanoparticles was taen to be equal to 3d P r where d is the diameter o the base luid molecule. As the volume raction o nanoparticle increases, the eective thermal conductivity o nanoluids tend to increase with Brownian motion o nanoparticles since it depends on the volume raction and temperature. There are many other studies that appeared in literature on the eect o Brownian motion on the thermal conductivity o nanoluids. But, the validity o this mechanism has been questioned by its room temperature dependence on thermal conductivity since this model describe the eective thermal conduction in nanoluids as an overall eect o micro convective heat transport through nanoparticles Eect o clustering o nanoparticles This model is based on the phenomenon o clustering o nanoparticles (Prasher et al., 2006; Wang et al., 2003) in the host media; the ormation o these particle clusters or aggregates o nanoparticles tend to enhance the thermal conductivity o nanoluids. The interconnected particle clusters, which grow as ractal structures, as reported by some authors (Wang et al., 2003), orm easy channels or thermal waves to propagate resulting in an overall enhancement in thermal conductivity and this mechanism o particle clustering increases with concentration o particles in the luid. The theoretical expression or thermal conductivity o nanoluids by particle clustering has been wored out by previous worers (Prasher et al., 2006; Wang et al., 2003). The expression or the eective thermal conductivity o nanoluids with particle clusters taes the orm (Prasher et al., 2006), Department o Instrumentation, CUSAT 23

24 Chapter-1 clust ([ a + 2 ] + 2φ a[ a = ([ a + 2 ] φa[ a ]) ] (1.19) where p is the single nanoparticle thermal conductivity and a is the thermal conductivity o the clustered nanoparticle, given by =. (1.20) a ( 1 φ int ). + φint p where φ a is the cluster volume raction and φ int is the volume raction o the particles in a cluster φ a = φ v φ int Equation (1.19) implies that the eective thermal conductivity o nanoluids increases with increase in cluster size. Evans et al. (2008) proposed that clustering can result in ast transport o heat over relatively large distances since the heat can be conducted much aster by solid particles when compared to the liquid matrix. They investigated the dependence o thermal conductivity o nanoluids on clustering and interacial thermal resistance and have shown that the eective thermal conductivity increases with increasing cluster size. However, as the particle volume raction increases, the nanoluid with clusters show relatively smaller thermal conductivity enhancement. When it comes to interacial resistance, it is ound that the interacial resistance decreases with the enhancement in thermal conductivity, but this decrease diminishes or nanoluids with large clusters. According to previous reports the nanoparticle clusters increase the eective thermal conductivity o nanoluids, but the enhancement due to clustering at higher particle concentrations is questioned by phenomena lie sedimentation o clustered nanoparticles. 24 Department o Instrumentation, CUSAT

25 Introduction Formation o semisolid layer around nanoparticles It has been speculated that (Yu and Choi 2003; Keblinsi et al., 2002) molecules o the base luid orm a semi-solid layer around the nanoparticles by the adsorption o the base luid molecules. This ordered semi-solid layer, which has a higher thermal conductivity than the base luid, increases the eective particle volume raction and hence the eective thermal conductivity o the nanoluid. Thicness o this adsorption layer is given by Langmuir ormula (Li et al., 2008; Yan et al., 1986). t 1 4M = 3 ρ N A 1 3 (1.21) where M is the molecular weight and ρ is the mass density o the luid. N A is the Avagadro s number. As per Langmuir ormula the thicness o the adsorption layer is ound to be o the order o 10-9 m or a liquid lie water. Yu and Choi (2003) modiied the Maxwell (1873) model including the eect o liquid layering around nanoparticles and assumed some possible values or the thermal conductivity o the nanolayer. This model considered the nanoparticle with liquid layer as a single particle and the thermal conductivity o this particle was determined ollowing eective medium theory. This renovated Maxwell model gives the eective thermal conductivity o a nanoluid as e ( )(1 + β) φ = 3 pe pe v 3 pe + 2 ( pe )(1 + β) φv (1.22) Here pe is the thermal conductivity o the layered nanoparticle, given by pe γ β γ γ = (1.23) [2(1 ) + (1 + )(1+ 2 )] 3 (1 γ) (1 β) (1 2 γ) p Department o Instrumentation, CUSAT 25

26 Chapter-1 l where γ = where l is the thermal conductivity o the nanolayer, and β is a p t constant deined as β = r p, where r p is the radius o the particle and t is the thicness o adsorption layer given by Equation (1.21). In addition to this, Yu et al. (2004) modiied the Hamilton-Crosser model (1962) or non spherical particle suspensions by considering the adsorption eect on nanoparticle suraces. Wang et al. (2003) have presented another expression or eective thermal conductivity o nanoluids based on particle clustering and the surace adsorption eects o nanoparticles. According to this model the eective thermal conductivity o clustered particle-luid suspension is given by, cl ( r) n( r) (1 φv) + 3φv e ( ) 2 0 cl + = ( r) n( r) (1 φv) + 3φv ( ) 2 0 cl r + r dr dr (1.24) where n(r) is the radius distribution unction given by, ln( ) 1 rcl rcl nr () = exp rcl 2π lnσ 2π lnσ 2 (1.25) and cl is the equivalent thermal conductivity o the cluster, which can be determined by replacing φ v by φ v in the thermal conductivity expression given by Bruggeman model and cl can be written as, = + + (1.26) * * cl (3φv 1) p [3(1 φv ) 1] 26 Department o Instrumentation, CUSAT

27 Introduction where = (1.27) * 2 2 * 2 2 * * (3φv 1) p [3(1 φv ) 1] 2[2 9 φv (1 φv )] p and φ v is given by, φ * d 3 ( ) v = rcl rp (1.28) Here r cl is the radius o the clustered nanoparticle and r p is the thermal conductivity o the bare nanoparticle and d is the ractal dimension having values in the range While considering the eect o liquid layering the p in the above expression have to be replaced with cp, the thermal conductivity o the layered nanoparticle, and is given by cp = l A 3 ( p + 2 l) + 2 ( p l) 3 ( p + l) A ( p l) (1.29) where l is the thermal conductivity o the adsorption layer and A = 1 t, ( t+ a) rp + t and r p is replaced by (r p +t) and φ v by φv. The main drawbac o the r p above mechanism is that there is no experimental data available on the thicness and thermal conductivity o the adsorbed nanolayers, which raise serious questions about the validity o the model Models based on interacial thermal resistance According to researchers, various mechanisms described above are responsible or enhancement in the eective thermal conductivity o nanoluids, and all the models based on these have been derived without considering the interacial eects at luid-particle boundaries. I these eects are taen into 3 Department o Instrumentation, CUSAT 27

28 Chapter-1 account it has been ound that there is a possibility or de-enhancement in eective thermal conductivity o nanoluids. Xuan et al. (2003) and Koo et al. (2004) have modiied the Maxwell-Garnett model in order to arrive at an expression or eective thermal conductivity o nanoluids in this regime. By perorming molecular dynamics simulation Vladov and Barratt (2004) have developed an expression or eective thermal conductivity o nanoluids considering the eects such as interacial thermal resistance (Kapitza resistance) at the nanoparticle-luid interace and Brownian motion heat transer between the particles and luid molecules. The expression or eective thermal conductivity in this regime can be written as, p p ( (1+ 2 α) + 2) + 2 φv ( (1 α) 1) e = p p ( (1+ 2 α) + 2) φv ( (1 α) 1) (1.30) R where α = r p, R being the Kapitza resistance. This model predicts an enhancement in eective thermal conductivity o nanoluids or α >1, and a decrease or α <1.This is because o the eective increase in Kapitza resistance due to scattering o thermal waves at the solid-liquid interaces, which is determined by the value o α. Nan et al. (1997) generalized the Maxwell Garnett model, considering the interacial thermal resistance at the luid-particle boundary which arises due to the scattering o thermal waves at the interaces. According to this model the normalized thermal conductivity o nanoluids having particles shaped as prolate spheroids with principal axes a 11 =a 22 < a 33, tae the orm, 28 Department o Instrumentation, CUSAT

29 Introduction e 3 + φv[2 β11(1 L11) + β33(1 L33 )] = 3 φ (2 β L + β L ) v (1.31) where, 2 p p 1 L11 = cosh p, 2 2 3/2 2( p 1) 2( p 1) L33 = 1 2 L11, p= a33 / a11 ii βii =, c + Lii( ii ) p = ii 1 + γ L / γ ii p = (2 + 1/ pr ) bd / ( a11 / 2) (1.32) Here R bd is the Kapitza interacial thermal resistance Model based on Ballistic phonon transport in nanoparticles In nanoparticles the diusive heat transport is valid i the mean-ree path o phonons is smaller than the characteristic size o the particle under consideration. In a nanoparticle i the diameter is less than the phonon mean ree path, the heat transport is not diusive, but is rather ballistic. This act prevents the application o conventional theories or modeling the thermal conductivity o nanoluids. Keblinsi et al. (2002) noted that ballistic heat transport still cannot explain the anomalous thermal conductivity enhancements, because temperature inside the nanoparticles is nearly constant and this act does not depend on the mode o heat transer Summary o theoretical models The above are the commonly used theoretical models developed by previous authors to interpret the observed thermal conductivity enhancements Department o Instrumentation, CUSAT 29

30 Chapter-1 in nanoluids. In order to get the best itting with experimental results some authors have also tried dierent combinations o the above mechanisms (Xuan et al., 2003; Koo et al., 2004) and deined the eective thermal conduction in nanoluids as a combined eect o two or more mechanisms. But these mechanisms have aced inadequacies to interpret the wide variations in the experimental data reported in literature since there oten exist physically unrealistic situations with these proposed mechanisms. Table I summarizes some o the experimental data o nanoluid thermal conductivity reported by previous authors and their deviations rom the proposed theoretical models based on the Brownian motion o nanoparticles, clustering eects o nanoparticles and other eects. In association to the Brownian motion o nanoparticles, the main question is about the possibility o micro convection o nanoparticles at room temperature. So the temperature dependence o Brownian motion as well as its inluence on clustering o nanoparticles need to be veriied with experimental data. Other models based on mechanisms such as ormation o nanolayer around the nanoparticles also are ound to be limited to resolve the inconsistencies o the experimental results. The main problems that arise with these models are (i) The variation o the thicness o the adsorption layer with nanoparticle size couldn t be predicted. (ii) There is no experimental data available in literature on the thermal conductivity o the adsorbed nanolayer. (iii) The very existence o a semisolid monolayer is questionable. 30 Department o Instrumentation, CUSAT

31 Introduction Table 1 presents a summary o the experimental indings reported by previous authors or various nanoluids and the corresponding mechanisms proposed or each. The wide dierences in the experimental results that have appeared in the case o the same nanoluid system increases the depth o the issues involved. The main reason or the observed controversies may be due to the dierences in the experimental techniques employed, dierences in sample preparation methods, variations in particle sizes etc. Recently, an elaborate inter-laboratory comparison initiated by International Nanoluid Property Benchmar Exercise (INPBE) done by 34 organizations across the world has been published (Buongiorno et al., 2009). This has helped to resolve some o the outstanding issues in this ield. In this exercise dierent research groups have measured thermal conductivity o identical samples o colloidal stable dispersions o nanoparticles using dierent experimental techniques such as transient hot wire technique, steady state technique and optical methods. The samples tested in the INPBE exercise comprised o aqueous and nonaqueos base luids, metal and metallic oxide particles, spherical and cylindrical particles at low and high particle concentrations. The main conclusions drawn rom the exercise are the ollowing. (i) The thermal conductivity o nanoluids increases with increasing particle loading as well as the aspect ratio o the dispersed particles, which is in tune with the classical eective medium theory, originally proposed by Maxwell (1873) Department o Instrumentation, CUSAT 31