20

Chapter 2

LITERATURE REVIEW

2.1 Review on Making Of Nanofluids

Several studies, including the earliest investigations of

nanofluids, used a two-step method in which nanoparticles or

nanotubes are first produced as a dry powder and then

dispersed into a fluid in a second processing step. In contrast,

the one-step method entails the synthesis of nanoparticles

directly in the heat transfer fluid. The two-step and one-step

methods are discussed in more detail in sections 2.1.1 and

2.1.2 respectively.

2.1.1 Two Step Process

The preparation of nanofluids begins by direct mixing of the

base fluid with the nanomaterials. In the first step,

nanomaterials are synthesized and obtained as powders, which

are then introduced to the base fluid in a second step.

Nanoparticles can be produced from several processes [11,12 ]

which can be categorized into one of five general synthetic

methods. These five methods are: (i) transition metal salt

reduction [13,14], (ii) thermal decomposition and photochemical

methods [15], (iii) ligand reduction and displacement from

organometallics [16] (iv) metal vapor synthesis, and (v)

electrochemical synthesis [17]. Transition-metal nanoclusters

are only kinetically stable because the formation of the bulk

metal is its thermodynamic minimum. Therefore, nanoclusters

21

that are freely dissolved in solution must be stabilized in a way

that prevents the nanoclusters from coalescing, because such

agglomeration would eventually lead to the formation of the

thermodynamically favored bulk metal [18].

Bonnemann et al [16] developed a method for the production of

very small (< 2 nm) and stable nanoparticles via chemical

reduction pathways, which might be suitable for application in

nanofluid synthesis. Organoaluminum compounds have been

used for the “reductive stabilization” of mono and bi-metallic

nanoparticles. Triorganoaluminum compounds were employed

as both the reducing agent and colloid stabilizer, which lead to

the formation of an organo-metallic colloidal protecting shell

around the particles [19,20 ]. This “modification” of the Al-

organic protecting shell leaves the particle size stable.

Silver nanoparticles are one of the most widely studied

nanomaterials because they exhibit unusual optical, electronic

and chemical properties, which depend on their size and shape

[21,22,23]. Silver is also one of the most thermally conductive

metals and its use in cooling applications would be interesting.

Besides silver nanoparticles, Xuan et al. [24] have used

commercially obtained Cu nanoparticles to prepare nanofluids

in both water and transformer oil by sonication in the presence

of stabilizers. Similarly, Kim et al. [25] prepared nanofluids

consisting of commercially obtained CuO nanoparticles in

ethylene glycol by sonication without stabilizers. The optimum

22

duration of sonication was found to be 9 hours and the average

nanoparticle size was 60 nm.

The two-step process is commonly used for the synthesis of

carbon nanotube based nanofluids. Single-wall carbon

nanotubes (SWCNTs) and Multi-walled carbon nanotubes

(MWCNTs) are cylindrical allotropes of carbon. SWCNTs consist

of a single cylinder of graphene, while MWCNTs contain multiple

graphene cylinders nesting within each other [26]. The carbon

nanotubes are usually produced by a pyrolysis method and then

suspended in a base fluid with or without the use of a

surfactant.

Some authors suggested that the two-step process works well

only for nanofluids containing oxide nanoparticles dispersed in

de-ionized water as opposed to those containing heavier metallic

nanoparticles [27,28,29]. Since nanopowders can be obtained

commercially in large quantities, some economic advantage

exists in using two-step synthesis methods that rely on the use

of such powders.

2.1.2 One step process

Few methods exist for the preparation of nanofluids through a

one step process. These methods include the thermal

decomposition of an organometallic precursor in the presence of

a stabilizer [30], chemical reduction [31], and polyol synthesis

[32, 33].

23

The polyol method is one of the most well known pathways to

noble metal nanoparticles [34, 35, 36]. In the polyol process, a

metal precursor is dissolved in a liquid polyol (usually ethylene

glycol), after which the experimental conditions are adjusted to

achieve the reduction of the metallic precursor by the polyol,

followed by atomic metal nucleation and metal particle growth

[37].

The „direct-evaporation‟ technique was developed by Choi et al

[28]. It consists of a cylinder containing a fluid which is rotated.

In the middle of the cylinder, a source material is vaporized. The

vapour condenses once it comes into contact with the cooled

liquid (Figure 2.1). The drawbacks of this technique however,

are that the use of low vapour pressure liquids are essential and

only limited quantities can be produced.

Various single-step chemical synthesis techniques can also be

employed to produce nanofluids. For example, Brust and co-

workers [36] developed a technique for producing metallic

nanoparticles in various solvents by the reduction of metal salts

to produce colloidal suspensions for a wide range of applications,

including studies of thermal transport. Excellent control of size

and very narrow size distributions can be obtained by using

such methods [2].

A submerged arc nanoparticle synthesis system (SANSS) was

developed to prepare CuO nanoparticles dispersed uniformly in

a dielectric liquid (deionized water). The method successfully

24

produced a stable nanofluid [37]. In principle, a pure copper rod

is submerged in a dielectric liquid in a vacuum chamber. A

suitable electric power source is used to produce an arc between

6000 - 12000 °C which melts and vaporizes the metal rod in the

region where the arc is generated. At the same time, the

deionized water is also vaporized by the arc. The vaporized

metal undergoes nucleation, growth and condensation resulting

in nanoparticles dispersed in deionized water. Nanofluids

containing CuO particles of size 49.1 ± 38.9 nm were obtained

[37].

Cooling System

Liquid

Resistively Heated Crucible

Figure 2.1 One-step nanofluid production system (Choi

et.al. [28])

2.2 Review on Thermophysical Properties of Nanofluids

The thermal conductivity measurement of nanofluids was the

main focus in the early stages of nanofluid research.

Considering the application of heat transfer fluids, heat transfer

coefficients of nanofluids in flow condition is also very

25

important. The important properties other than thermal

conductivity that affect the heat transfer coefficients are density,

heat capacity and viscosity of dispersions (see Fig.2.2 to Fig.

2.5). Since the nanoparticle concentration in nanofluids usually

are very low (<1 vol%), the particle effect on the density and heat

capacity of the dispersions is not significant. However, due to

the small particle size, the nanoparticle effect on the viscosity of

the dispersions might be remarkable, especially for nanotube or

other high or low aspect ratio nanoparticle dispersions. Some of

the properties of nanoparticles & base fluids are listed in Table

2.1 useful for assessing the nanofluid properties.

Table.2.1 Thermophysical properties of Nanoparticle & base

fluids

Property Water Ethylene

glycol

Cu Al2O3 CuO Ti O2

C ( J/kg K

( kg/m3) k (W/m K) α (m2/s)

4179

997.1 0.605

1.47

2415

1111 0.252

93

385

8933 400

1163

765

3970 40

1317

535.6

6500 20

57.45

686.2

4250 8.9538

30.7

2.3 Density

The density of a nanofluid can be calculated by using mass

balance as

pfnf ρ)ρ(1ρ (2.1)

For typical nanofluids with nanoparticles at a value of volume

fraction less than 1%, a change of less than 5% in the fluid

density is expected (see Fig.2.2)

26

2.4 Specific Heat

The specific heat of a nanofluid can be calculated by using

energy balance as

nf

ppf

nf

CC

f)-1(C (2.2)

Using these equations, one can predict that small decreases in

specific heat will typically result when solid particles are

dispersed in liquids. For example, adding 3 vol% Al2O3 to water

would be predicted to decrease the specific heat by

approximately 8% compared with that of water alone (see

Fig.2.3). The simple equations above may need to be modified if

nanoparticles are found to exhibit a size dependent specific heat.

2.5 Viscosity

The rheological and aggregation behaviors of spherical

nanoparticles in liquid suspensions have been studied quite

extensively (Meitz, Yen et al. [38]). They suggested at very low

volume fraction (the shear viscosity of a hard sphere

suspension can be predicted by Einstein formula

)5.21(fnf (2.3)

This equation was extended by Brinkman [39] as

5.2fnf)1(

1

(2.4)

The experimental results for the viscosity of copper nanofluids

from Xuan‟s group [24] showed good agreement with this model.

27

Batchelor [40] gave another formula to calculate the viscosity of

particle suspensions (<=0.01)

2

f

nf 2.65.21

(2.5)

However, most of the work was focused on concentrated

nanoparticle dispersions. Das sk et al. [41] conducted

experiments on 1~4 vol% Al2O3 nanoparticles (38nm) in water

dispersions. They reported nanofluids showed Newtonian

behavior and viscosities were higher than water. They also

suggested for many of the spherical nanoparticles dispersions,

the volume fractions of nanoparticle seems low enough to apply

Einstein or Batchelors equations to predict the increase of the

viscosity in dispersions.

The data reported by Chang et al.[42] in CuO nanofluids also

indicted that the viscosity of nanofluids increased with decrease

of particle size due to large specific area and electrostatic forces.

Wang et al [43] measured the viscosities of Al2O3 in water

nanoparticle dispersions which were created by different

dispersing methods. An increase between 20% and 30% was

reported to 3vol%. They indicated that the particle concentration,

size and particle shape, the aggregation structure of

28

Figure 2.2 Effect Nanofluids density with volume fraction

29

Figure 2.3 Effect of Nanofluids specific heat with volume fraction

30

Figure 2.4 Effect of Nanofluids Prandtl number with volume fraction

31

Figure. 2.5 Effect of Nanofluids thermal diffusivity with volume fraction

32

nanoparticles will also affect the rheological behaviors of particle

dispersions. They also gave a correlations as follows for Al2O3 +

water & EG and found to be nearer to experimental data as

shown in Fig.2.6.

For Al2O3 + water

13.7123 2 nf (2.6)

For Al2O3 + Ethylene Glycol

10.19-306 2 nf (2.7)

However, Pak & Cho [44] reported a three times higher viscosity

for Al2O3 (13nm) + water nanofluids that of water. The authors

suggested different dispersing techniques which can lead to

different particle or agglomerate size may be the reasons for this

large discrepancy. They also gave correlations for

For Al2O3 + water

)9.53311.391( 2

fnf (2.8)

For TiO2 + water

)2.10845.51( 2

fnf (2.9)

Chen et.al.[45] also gave correlation for the viscosity of TiO2 +

Ethylene glycol as follows

For TiO2 + Ethylene glycol

2)6.106.101( fnf (2.10)

33

For Cu + water

)72.468645.3995.0( 2 fnf (2.11)

Tseng and Li [46] correlation for viscosity of TiO2 + water as

follows

98.35

fnf e47.13 (2.12)

Kulkarni et.al.[ 47] presented the correlation for the viscosity of

CuO + water as follows

BT

Anf

1ln (2.13)

3.10781585720587 2 A

8715.2548.5312.107 2 B

In the present work the above equations are used wherever

necessary and found to be nearer to experimental data available

in the literature.

2.6 Thermal Conductivity of Nanofluids

In this section the measurement of thermal conductivity of the

nanofluids is reviewed and important factors are discussed. The

possible mechanisms are explained for the high thermal

conductivity of nanofluids is presented in the following sections.

34

Figure 2.6 Effect of Nanofluids viscosity with volume fraction

35

2.6.1 Metallic nanoparticle dispersions

Choi et.al [48] pioneered the work in the nanofluids by dispersing

nanometer sized particles into liquids. They suggested that

compared with the suspension of larger particles, nanoparticles

can be kept in dispersions for much longer time. Because

nanoparticles are so small, they may act like macromolecules in

solution, dramatically reducing erosion and clogging and their

larger surface areas improve heat transfer. After that, numerous

experimental results have been reported and this concept has been

proved.

Enhanced thermal conductivities have been reported for metal

nanoparticle dispersions by different research groups. The metals

applied in dispersion are gold, sliver, copper, iron and aluminum.

Eastman et.al [49] reported that copper nanoparticles dramatically

increased the thermal conductivity of base fluid, ethylene glycol

(EG). The effective thermal conductivity of nanofluids with 0.3vol%

of copper nanoparticle (~10 nm) was 40% higher than that of pure

EG when thioglycolic acid was used as dispersing agent. The

nanoparticle dispersion without dispersant in it had a much lower

increase ratio (~ 5%) compared to an acid containing dispersion

with same particle loading (0.3 vol%). They also suggested Aging of

the dispersion can decrease the effective thermal conductivity of

36

the nanofluids. The authors suggested that particle size is an

important factor for the effective thermal conductivity of nanofluids.

Another work on copper nanoparticle in EG dispersions was done

by Asseal et.al [50]. The nanoparticle applied in their work had a

mean diameter of 10 nm, but containing agglomerates with sizes

greater than 50 nm. With 0.5 vol% of copper nanoparticles, the

effective thermal conductivity of EG increased 3.5%. They

suggested result is much lower than the one in Eastman‟s work

which may be caused by the agglomerates in the dispersions.

Li and Xuan [51] studied the particle size effect on copper

nanoparticle in water dispersions. They found that the dispersion

containing smaller particles (20 nm) had a higher thermal

conductivity than that containing bigger particle (100 nm). For

example, by adding 2 vol% of 20 nm copper nanoparticles, the

effective thermal conductivity of the base fluid increased 23% while

the increase was around 15% for the case when 100 nm particle

were used. They suggested that larger surface area of smaller

particles may help for heat transfer occurring at the interface. They

also measured the thermal conductivity of Al2O3 nanoparticle

dispersion and compared it with that of copper nanofluids. They

found the thermal conductivity of 2 vol% Al2O3 nanofluids only had

a 6.3% increase compared with water while copper nanofluid

showed a 23% increase. It indicated that the thermal property of

37

the particle is one of the essential factors for the properties of

nanofluids.

Naked gold nanoparticle in the 10~20 nm range and monolayer

protected gold nanoparticle were prepared and dispersed in water

and toluene by Patel et.al [52]. The naked nanoparticle dispersion

showed thermal conductivity enhancement of 5%~21% in the

temperature range from 30~600C at very low loading (0.00026

vol%) while the dispersion containing nanoparticle with a thiolate

covering showed 7% ~ 14% for a loading of 0.011 vol%. It is

surprising that the particle volume fraction of particle in this work

is one or more order magnitude lower than other cases mentioned

above, and the differences of the thermal conductivities of two

nanofluids at different temperatures may suggested surface action

can have a significant effect on the behavior of the nanofluids.

They also measured thermal conductivity of sliver nanoparticle in

the 60~80 nm range and compared with those of small gold

nanoparticle dispersions. It showed that even with higher particle

loading, the thermal conductivity of the larger particle dispersion

was still comparatively lower than small particle dispersions. This

result was consisted with other studies of the particle size effect.

Hong et.al [53] studied the thermal conductivity of iron

nanoparticle in EG dispersions. The mean diameter of the

nanoparticles was 10 nm, however, they existed in the dispersion

38

as clusters due to the absent of dispersing agent. The authors

observed that the thermal conductivity of Fe nanofluids was

increased nonlinearly up to 18% as volume fraction of the

nanoparticle was increased up to 0.55 vol%. Compared with copper

nanofluids reported by Eastman et.al [49], higher increase ratios of

thermal conductivities for Fe nanofluids indicated the dispersion of

high thermal conductivity materials is not always effective for

improving the thermal properties of nanofluids. The authors

suggested that the size of nanoparticle clusters or the

microstructure in the dispersion is an important factor for

improving the thermal conductivity of fluids.

2.6.2 Nonmetallic nanoparticle dispersions

Compared with metal nanoparticle dispersions, experimental work

started earlier for oxide nanoparticle dispersions. Al2O3 and CuO

are most common candidates being applied for nanofluids research.

Masuda et.al [27] reported a 30% thermal conductivity increase of

water by adding 4.3 vol% of Al2O3 (average diameter ~13 nm)

nanoparticles. However, in the research done by Lee et.al [54] the

same amount (4.3 vol%) of Al2O3 (average diameter ~ 38 nm)

nanoparticles only lead to 10% thermal conductivity increase of

water. It is another example to show the importance of particle size

on thermal conductivity of nanofluids. In addition to the smaller

size of particle, the nanofluids prepared by the Masuda [27] group

39

contained chemical dispersant which was supposed to modify the

surface of nanoparticles while there was no such chemical added

in Lee‟s work. This result is consisting with the one observed in

Eastman‟s [49] work on the metallic nanoparticle dispersions.

Lee et.al [54] also studied another three systems, Al2O3 in EG, CuO

in water, CuO in EG. The Cuo particles they used in their work

were smaller than Al2O3 nanoparticles, which had an average

diameter of 24 nm. They found that in low volume fraction range

(upto 5 vol%), the thermal conductivity increase ratios moved

almost linearly with particle loading, but with different rates for

each system. It indicates thermal conductivity depends on both

dispersed particle and base fluids. For the systems using the same

base fluid, knf /kf in CuO nanoparticle was always higher than that

of Al2O3 nanofluids which may be caused by the smaller size of

CuO particles. The thermal conductivity increase ratios of EG

nanofluids were always higher than those of water based

nanofluids. It suggested that the increase ratio was dependent on

the thermal conductivity of the base fluids. There is another very

interesting study of thermal conductivities of Al2O3 nanoparticle

dispersions. Xie et.al [55] used a series of different alumina

nanoparticles with different particle size, specific area and

crystalline phase and dispersion them into distilled water, EG and

pump oil. The experimental results showed that adding

40

nanoparticles into base fluids led to increased thermal

conductivities much higher than calculated from conventional

models. The enhanced ratio of thermal conductivity increased with

particle loading. They found that the increase ratio of thermal

conductivity decreased with increase of pH value of aqueous

dispersions. For the dispersions containing the same nanoparticle,

the enhancement ratio of the thermal conductivity was reduced

with the thermal conductivity of the base fluid. This result was

consistent with Lee‟s results [54]. For the dispersions based on the

same base fluid, the thermal conductivity increase ratio was

dependent on specific surface area or particle size of the

nanoparticles. There was an optimal specific surface area 25 m2g-1

(corresponding particle size 60 nm) which gave highest increase

ratio for the thermal conductivity of nanofluids. The particle

smaller or larger than 60 nm gave lower thermal conductivities.

The authors explained this maximum by two factors: interface area

at which heat transfer happened, and reduced intrinsic thermal

conductivity due to the scattering of phonons at particle-particle

boundaries. When the particle size is much larger than mean free

path of phonon (35 nm), the first factor dominated. The thermal

conductivity of the nanofluid increases with decrease of the

particle size. When the particle size is close to mean free path of

phonon, the thermal conductivity of nanofluid may decreases with

41

decrease of particle size. In another work from the same group, the

thermal conductivity of Al2O3 nanoparticle in water dispersion was

reduced adding dispersing agents. This result was contrary to the

work done by Eastman et.al [49] on copper nanofluid.

Wang et.al [43] dispersed Al2O3 and CuO nanoparticles into four

base fluids: distilled water, engine oil, EG and pump oil. They

suggested for both nanoparticles, the thermal conductivities of

water based nanofluids were always lower than those of EG based

nanofluids which proved the results from other groups. However,

compared to Al2O3 nanoparticle dispersions, EG and engine oil

based nanofluids gave the higher increase ratios of thermal

conductivity than water and pump oil based nanofluids. It

indicated that when same particles were dispersed into base fluid,

thermal conductivity of the base fluid was not the only factor to

affect the increase ratio of thermal conductivity of nanofluid.

The temperature effect of thermal conductivity enhancement in

nanofluids has been presented by SK Das et.al [41].They studied

thermal properties of Al2O3 and CuO nanoparticles at different

temperatures. The particle sizes in their work were 38.4 nm for

Al2O3 nanoparticle and 29 nm for CuO nanoparticles. Their

measurement results confirmed that the level of thermal

conductivity increase at room temperature as observed by Lee et.al

[54]. A dramatically increase of thermal conductivity ratios has

42

been observed at high temperatures. A two or four fold increase in

thermal conductivity enhancement was reported over a small

temperature range 20 ~500C. They suggested this makes

nanofluids more attractive as cooling fluids which were likely to

work at higher temperature than room temperature.

Li and Perterson [56] conducted an experimental investigation to

examine the effects of variations in the temperature and volume

fraction on the effective thermal conductivity of CuO and Al2O3

water suspensions. Results demonstrated that nanoparticle

material, diameter, volume fraction and bulk temperature have

significant effects on the thermal conductivity of the nanofluids.

They observed three times enhancement in Al2O3/water

suspension, increase in mean temperature from 27 to 34.7oC. They

presented correlations for Al2O3/ water and CuO/ water nanofluids

462.0)15.273T(0187.0764.0

k

kk

f

fnf

( Al2O3 + water) (2.14)

307.0)15.273T(0179.0761.3

k

kk

f

fnf

(CuO + water) (2.15)

Thermal conductivity of SiC nanoparticle dispersions have been

studied by Xie et.al [57], 26 nm spherical SiC particle and 600 nm

cylindrical particles were dispersed in distilled water and EG. They

found the thermal conductivities of nanofluids are higher than

corresponding base fluids and increase ratio of thermal

conductivity increased linearly with particle volume fraction.

43

Surprisingly, the increase ratio for 26 nm particles in water

dispersions was lower than that of 600nm particle dispersions. The

thermal conductivity increase ratio for same particle dispersions

seemed independent of base fluids.

Beck, M.P et al.[58] conducted experiments on alumina

nanoparticles dispersed in ethylene glycol in temperature range of

2980K to 4110K. They also compared theoretically by taking shape

factor of n=3.4 in Hamilton and Crosser model and found to be in

good agreement with experimental results.

Kim et al.[59] conducted experiments on water and ethylene glycol

based nanofluids containing Al2O3, ZnO,TiO2 nanoparticles and

found variation with volume fraction and size dependence. They

also observed the effect of particle size change by laser ablation for

ZnO nanofluids and reported thermal conductivity is inversely

proportional to the particle size and dependence appears to be

linear.

Hong et al.[60] proposed TiO2, Al2O3, WO3 nanoparticles dispersed

in water and ethylene glycol and found large enhancement than

basefluids. They reported surface to volume ratio of nanoparticle is

a primary factor in determining the thermal conductivity of

nanofluids.

Murshed et al. [61] conducted both experimental and theoretical

study on thermal conductivity and viscosity of nanofluids. They

44

reported both thermal conductivity and viscosity of nanofluids

increase with volume fraction and also found strong dependent on

temperature. They proposed two static mechanisms based models

to predict thermal conductivity of nanofluids having spherical and

cylindrical nanoparticles considering particle size, interfacial layer

and volume fraction showed reasonably good agreement with

experimental data.

2.6.3 Carbon nanotube dispersions

The large intrinsic thermal conductivity of carbon based

nanostructures combined with their low densities compared with

metals, makes them attractive for use in nanofluids. Moreover,

high aspect ratio particle are more effective than low aspect ratio

ones and much more attractive than spherical particles [62]. All of

the reasons above lead to extensive studies on carbon nanotube

dispersions to improve heat transport recently.

The first article on thermal conductivity of nanofluids containing

carbon nanotubes was published by Choi et.al [62]. Multiwalled

carbon nanotubes were dispersed into oil with loading up to 1 vol%

nanotubes. The thermal conductivity of nanofluids containing

nanotubes (MWNTs) was measured at room temperature and

results were compared to the predictions calculated from several

theoretical models. Nanotubes lead to an anomalously large

increase in the thermal conductivity of base fluid (up to a 160%

45

increase with 1 vol% nanotubes), which is by far the highest

thermal conductivity enhancement ever achieved in a liquid. They

suggested the nature of heat conduction in nanotubes dispersion

and an organized structure at the solid-liquid interface might be

responsible for the high thermal conductivity of nanotubes

dispersion. Moreover, the thermal conductivities of all spherical

nanoparticle dispersions showed linear dependence on the solid

loading in the range investigated (1-5 vol%), while thermal

conductivities of MWNT nanofluids showed nonlinear increase with

nanotubes volume fractions at low solid loadings (<1 vol%). Choi et

al [62] suggested it may be caused by the existence of interaction

among nanotubes even at low volume fractions. However, carbon

nanotubes have hydrophobic surface and can not be dispersed into

most of common heat transfer fluids like distill water and EG

without surface treatment and/or existence of dispersants. A

concentrated nitric acid treatment was applied by Xie at.al [63] to

disentangle MWNT aggregates and produce uniform nanotubes

dispersions. The acid treatment introduced oxygen containing

functional groups onto nanotube surfaces, so they could be

dispersed into polar liquids like distilled water and EG without

additional dispersants or surfactants and into non-polar liquids

like decene with oleylamine as surfactant. All the nanotube

dispersions showed substantial increase of thermal conductivity

46

and the thermal conductivity enhancement were much higher than

those calculated from conventional models. For 1 vol% particle

fraction, the thermal conductivity enhancements are 19.6%, 12.7%

and 7% for decene, EG and water. This trend was consistent with

the one showed in alumina dispersions (Lee,choi et.al [54]) that

thermal conductivity enhancement decreased with increase of

thermal conductivity of base fluids. However, thermal conductivity

increase in this work were just moderate by compared with the

results in Choi‟s[62] work which reported 160% increase for 1 vol%

particles. Moreover, the thermal conductivity enhancements

seemed to increase linearly with particle loading at low volume

fraction (upto 1 vol%) while Choi [62] et.al reported a nonlinear

change. The authors suggested those discrepancies would be

attributed to different base fluids and preparation methods of

nanofluids.

Assael et.al [50] dispersed carbon MWNTs into water with the help

of the surfactant, sodium dodecyl sulfate (SDS).The maximum

thermal conductivity enhancement for 0.6 vol% nanotubes

dispersion was 38% compared with pure water. Another attempt to

disperse carbon nanotube into water has been done by Wen et.al

[64]. Instead of SDS they used sodium dodecylbenzene sulfonate

(SDBS) as dispersant in their work. Effects of particle

concentration and temperature on the thermal conductivity of

47

nanofluids were studied. Their results showed that the thermal

conductivity of nanofluids increased with increase of particle

loading, however, the dependence was nonlinear. The

enhancement ratio increased almost linearly when particle fraction

was lower than 0.2 vol% but the dependence tended to level off

above that loading. The increase ratio of 0.46 vol% nanofluid was

around 22% at room temperature which was much lower than that

of nanotube in oil dispersion (50%) with the same particle loading

reported by Choi et.al [62] but much higher than that of nanotube

in water dispersion (4%) made by Xie et.al [63]. The authors

suggested the possible reason may be the different thermal

conductivities of carbon nanotubes and different thermal

resistances at the interface. Thermal conductivity ratios in carbon

MWNT dispersion increased with temperature linearly on 20~300C

range but the dependence leveled off when temperature was higher

than 300C. This tendency was quite different from that in Al2O3 or

CuO nanoparticles dispersions which showed a linear increase

with temperature in 20~500C range. Dispersant failure happened

in MWNT in water dispersions when temperature was higher than

600C and nanofluids became unstable.

The dispersions of carbon nanotube in EG have been prepared by

Cho et.al [65]. Three different methods to make the nanofluids

were applied: 1) Sonication 2) Sonication plus dispersant

48

(ployacrylamide-co-acrylic acid) and 3) Sonication plus acid

treatment. The thermal conductivity ratios were 16%, 14% and

15% for those three cases respectively at same particle volume

fraction (1 vol%). The thermal conductivity ratios for sonication

nanofluids were 16%, 19% and 23% for 1,2,3 vol% nanofluids

which showed a nonlinear tendency similar to the one reported by

Wen et.al [64] in aqueous dispersions.

An enhancement ratio of 12.4% for nanotube in EG dispersion

without the help of dispersant has been reported by Liu et.al [66].

This result is quite close to the results of Choi‟s [62] work. They

also measured the thermal conductivity of nanotube in engine oil

dispersions with N-hydrosuccinimide as dispersant. An increase

ratio of 30% has been claimed for 2 vol% dispersion system which

was much lower than the result reported by Choi et.al [62].

Biercuk et al. [67] measured the effective thermal conductivity of

suspensions of single wall carbon nanotubes (SWNT‟s) and vapor

grown carbon fibers (VGCF) in epoxy using a comparative method.

Results showed 125% and 45% improvements for 1 vol% SWNT‟s

and VGCF, respectively. They found choi et al. [62] on thermal

properties of SWNT‟s epoxy composites showed similar

improvement of the thermal conductivity. They pointed out that

the bonding of nanotubes could be an important factor for thermal

transport characteristics.

49

Jana et al [68] conducted experiments on nanofluids containing

SWNT, Cu, Au, separately and hybrids of them in water.

Enhancement in thermal conductivity of CNT, Cu, Au was

observed whereas hybrid CNT-Au and CNT-Cu did not improve the

thermal conductivity. They also reported Cu nanofluids showed

best results of 74% increase with base fluids and nonlinear

enhancement in CNT nanofluids. However, both Cu and CNT

nanofluids showed drastic decrease of their thermal conductivity

with time due to sedimentation and agglomeration

Based on the above exhaustive review a thermal conductivity of

nanofluids, the inferences drawn and the experimental

enhancement found by different researchers is presented in

Appendix I. It is observed from the table that most of the

experimental work is carried out for water and Ethylene glycol as

basefluids with either Al2O3 or CuO as nanoparticles. The appendix

I can be used as an immediate reference for finding out

enhancement of thermal conductivity for different nanofluids at

different concentrations and different particle sizes. The

observations recorded by earlier researchers in finding

enhancement are also presented for ready reference. The next

section is denoted to review the work carried out by several

researchers in the past to find out the thermal conductivity of

nanofluids theoretically.

50

2.7 Models for Thermal Conductivity of Nanofluids

The thermal conductivity enhancement of nanofluids was higher

than those predicted from conventional models (in Table 2.2) for

larger size particle dispersions as in Fig.2.7. Therefore, different

researchers (Li and Xuan [83]). Keblinski et.al [84]; Xie etal [85])

explored the mechanisms of heat transfer in nanofluids, and

proposed four possible reasons for the contribution of the system:

1. Brownian motion of the particle

2. Molecular-level layering of the liquid at the liquid/solid

interface

3. The nature of the heat transport in nanoparticles

4. The effects of nanoparticles clustering

Figure 2.7 Comparison of the Conventional Models with the

Experimental Data [41].

51

Table 2.2 Convectional models for effective thermal

conductivity of solid-liquid suspensions.

Models Expression

Maxwell (1873) [76]

)1()2(

)1(31

f

nf

k

k

Hamilton & Crosser

[77]

)()1(

)()1()1(

pffp

pffp

f

nf

kkknk

kknknk

k

k

Bruggerman [78]

fpnf k113k13k

fpf

22

p

2kk1922k113k13

Jeffrey

[79] 2

22

2 ...))32(16

)2(9

4

33(31

f

nf

k

k

Where 2

1

; = Kp/Kf

Davis [80] 2)(

)1()2(

)1(31

f

k

k

f

nf

Where f()=2.5 for = 10, and f()=0.5 for =

Lu & Lin

[81] 21

f

nf

k

k; Where

2

1

; = Kp/Kf

Landau – Lifshitz/Looyenga

[82]

31/3

f

3/1

f

3/1

p

f

nf kkkk

k

For better investigation of these mechanisms some of the authors

have even used computational methods. In the following sections

each possible mechanism will be discussed and theoretical work

on thermal conductivity of nanofluids will be reviewed.

2.7.1 Brownian motion of the particles

In 1827, Robert Brown[86] examined the form of Clarkia pulchella

pollen particles immersed in water and observed that many of

these particles were in continual motion that arose from neither

currents in the fluid, nor from its gradual evaporation, but rather

52

that appeared to belong to the particles themselves. This constant

and irregular motion increased as the size of the particle decreased

and continued for the entire time that the particle remained in

suspension. Further observation of this “Brownian motion”

illustrated the irregular energy and momentum exchanges of

molecules caused by the collision between particles and molecules,

and indicated a strong, temperature dependence.

Jang and Choi [87] derived a theoretical model that involves four

modes are shown in Fig. 2.8 such as

Figure 2.8 Modes of Energy transport in Nanofluids

(Jang and Choi [87])

1. Collision between base fluid molecules(kf (1 −)),

2. Thermal diffusion in nanoparticles in fluids(kp ),

3. Collision between nanoparticles due to Brownian

motion(neglected),

4. Thermal interaction of dynamic or “dancing” nanoparticles

with the base fluid molecules (f h δ T).

53

Where h ~ kb / dpRe2 Pr2 and δ ~3dp presents the heat transfer

coefficient for the flow past nanoparticles and the thickness of the

thermal boundary layer, respectively. The advantage of the model

is to include the effects of concentration, temperature, and particle

size. The resulting expression for the effective thermal conductivity

of nanofluids is

. PrRe31 1 pf

p

f

pfnf kd

dCkkk (2.16)

in which subscript f and p represents base fluid and nanoparticles.

D is diameter of particle or molecule. C1 is proportional constant

and Pr is Prandtl number of nanofluids.

Rep is defined as

v

dC p

p Re (2.17)

in which C and v are the random motion velocity of nanoparticles

and dynamic viscosity of the base fluid. This model has been

compared with experimental results from several research groups

(Masuda, Ebata et al.[27]; Lee, Choi et al.[28]; Eastman, Choi et

al.[29] ; Das, Putra et al. [41]). Most of the data fell onto the

predicted curves calculated from model and it seems this model

not only includes the particle volume fraction and temperature

effect on the thermal conductivity of nanofluids, but also predicts

the strong size dependent conductivity. If the hypothesis in this

54

paper is correct, the increased thermal conductivity enhancement

with decrease of the nanoparticles size which happened in most

reports can be related to Brownian motion of the nanoparticles.

Kumar et al. [88] pointed out that since heat transfer is a surface

phenomenon, higher surface area to volume ratio of nanoparticles

can explain the enhancement of thermal conductivity of nanofluids.

A stationary model has been developed based on this theory,

showing that the enhancement in effective thermal conductivity

increased with the reciprocal of nanoparticles diameter. Moreover,

they developed a moving particle model based on Brownian motion

of the nanoparticles at different temperatures was combined with

stationary model to indicate temperate effect on the thermal

conductivity of nanofluids.

Chon et.al [89] developed an empirical correlation for the thermal

conductivity of Al2O3 nanofluids with different particle size (11nm ~

150nm) and temperature (21 ~ 710C) based on Brownian motion of

the nanoparticles.

Bhattacharya et.al [90] developed a technique to compute the

thermal conductivity of nanofluids using Brownian dynamics

simulation in which they omitted the motion of liquid molecules

and their effects on nanoparticles and represented them as

random force and friction terms. In this simulation, the Langevin

equation of motion was used to describe the particle movement

55

and the effect of solvent molecules and was represented by a

combination of random forces and frictional terms. The potential

energy between the two particles was described by an exponential

model as:

d

drBexpA

ij

ij (2.18)

Where d is the particle diameter, A and B are the parameters for

the system, and is the distance between particles j and i. Their

simulation based on interparticle potential predicted the effective

thermal conductivity of nanofluids to a good level of accuracy in

comparison with some experimental data (Eastman, Choi et.al [28];

Wang et.al [43]).

Koo et.al [91] compared the relative effects of nanoparticle motion

mechanisms on the effective thermal conductivity of dilute

nanoparticle dispersions. They found the effect of Brownian motion

was more significant by factor of 106 and 108 than those of

thermophoresis and osmophoresis.

After reviewing the models mentioned above and performing an

order of magnitude analysis, Prasher et al [92] draw a conclusion

that local convention caused by Brownian motion of the

nanoparticle was the mechanism which can be used to explain

thermal conductivity enhancement of nanofluids. Based on a

traditional model (Nan, et al.[93]) for k of solid liquid composite

56

which considers interface resistance, they developed a semi-

empirical model to predict thermal conductivity of nanofluids. By

fitting the experimental data for aqueous Al2O3 and CuO

nanoparticle dispersions ( Masuda, Ebata et al.[27]; Lee, Choi et

al.[28] ; Xie, wang et al. [43]; Das, Putra et al. [41]) with various dp,

and T. They found most of data can be fit by this model, when

A=400000 and m=2.5+ 15% can be applied for water based

nanofluids.

Prasher et al.[94] in their recent experimental investigation, a drop

of dye in pure water diffuses much more slowly than the same

drop of dye in Al2O3/Water nanofluids. It was also determined that

the optimal volume fraction for the diffusion is around 0.5%. These

results would appear to provide significant evidence of the effect of

the Brownian motion on the enhanced thermal conductivity of

nanofluids.

Therefore, Brownian motion seems to be one of the possible

mechanisms to be applied for predicting thermal conductivity

enhancement in nanoparticle dispersions, especially in spherical

nanoparticle dispersions. Most of the important factors affecting

the enhancement of thermal conductivity in nanofluids can be

included in models base on this mechanism, such as particle size,

temperature, thermal conductivity of particle and base fluid and

viscosity of base fluid.

57

2.7.2 Interfacial layering of liquid molecules

Some literature (Nan, Birringer et al.[95]) addressed the effect of

interfacial resistance (Kapitza resistance) on thermal conductivity

of particulate composites due to weak interfacial contact. They set

up a theoretical model to predict thermal conductivity of

composites by including interfacial resistance. According to this

model, the effective thermal conductivity should decrease with

decrease of the nanoparticle size which is contrary to most of the

experiment results for nanofluids.

Yu et al [96] reported that molecules of normal liquids close to a

solid surface can organize into layered solid like structure. This

kind of structure at interface is a governing factor in heat

conduction from solid surface to liquid. Choi et al [28] pointed out

that this mechanism contributed to anomalous thermal

conductivity enhancement in nanotube dispersions. However,

Keblinski et al [84] indicated that the thickness of the interfacial

solid-like layer is too small to dramatically increase of the thermal

conductivity of nanofluids because a typical interfacial width is

only on the order of a atomic distance (1nm). So this mechanism

only can be applied to very small nanoparticles (<10nm).

In order to find the connection between nanolayer at interface and

the thermal conductivity of nanofluids, Yu et al. (Yu, Richter et al.

[96]; Yu and Choi [97]) modified the Maxwell equation for spherical

58

particles and Hamilton-Crosser equation for non-spherical

particles to predict the thermal conductivity of nanofluid by

including the effect of this ordered nanolayer. They applied this

model to fit some experimental data in which smallest

nanoparticles were dispersed (Lee, Choi et al[28]; Eastman, Choi et

al [29] ) and found the model predicted the experimental data well.

However, the model failed to predict the results for Cu nanofluids

with surfactant.

The simulation work done by Xue et al[98] indicated that the

strength of the bonding between liquid and solid is very important

in determining interfacial thermal resistance. Nanofluids with weak

atomic bonding at interface exhibit high thermal resistance and

wetting systems have small interfacial thermal resistance. Adding

dispersant into dispersion systems or surface treatment will

certainly change the atomic bonding at interface and lead to varied

interfacial resistance.

Xue [99,100] developed a novel model which was based on Maxwell

theory and average polarization theory for effective thermal

conductivity of nanofluids by including interface effect between

solid particle and base liquid. He considered solid nanoparticle and

interfacial shell (nanolayer of liquid molecules) as a “complex

nanoparticle” and set up the model based on this concept. The

theoretical results obtained form this model were in good

59

agreement with the experimental data for alumina nanoparticle

dispersions (Xue, Wu et al. [101] )and showed nonlinear volume

fraction dependence for thermal conductivity enhancement in

nanotube dispersions (Choi, Zhang et al. [62]).

Xie et al. (Ren, Xie et al.[102]; Xie, Fujii et al.[103]) investigated

the effect of interfacial layer on the effective thermal conductivity of

nanofluids. A model has been derived from general solution of heat

conduction equation and the equivalent hard sphere fluid model

representing microstructure of particle suspensions. Their

simulation work showed that the thermal conductivity of

nanofluids increased with decrease of the particle size and increase

of nanolayer thickness. The calculating values were in agreement

with some experimental data (Masuda, Ebata et al.[27];Lee, Choi et

al. [28]; Eastman, Choi et al. [29]).

Recently, a new thermal conductivity model for nanofluids was

developed by Yu et al.[104]. This model was based on the

assumption that monosized spherical nanoparticle are uniformly

dispersed in the liquid and are located at the vertexes of a simple

cubic lattice, with each particle surrounded by an organized liquid

layer. A nonlinear dependence of thermal conductivity on particle

concentration was showed by this model and the relationship

changed from convex upward to concave upward. A comparison of

theoretical prediction and experimental data showed that

60

calculation value were much higher than experimental results

which indicate that there is a potential to improve the effective

thermal conductivity of nanofluids.

Generally, the solid like nanolayer at liquid-solid interface can not

be used to explain most of experimental data in which

nanoparticles larger than 10nm were dispersed. However,

interfacial thermal resistance which had been noticed in particle

dispersion, both composites and larger particle in liquid

suspensions, will be a critical factor to affect the thermal

conductivity of nanofluids because of the huge interface area for

those nanosized particles. Inclusion of dispersant or surface

treatment of nanoparticles will dramatically affect the thermal

conductivity of nanofluids by changing the interactions between

solid and liquid surface

2.7.3 Nature of heat transfer in nanoparticles

Keblinski (Keblinski, Phillpot et al. [84) estimated the mean free

path of a phonon in Al2O3 crystal is ~35nm. Phonons can diffuse in

the 10nm particles but have to move ballistically. In order to make

the ballistic phonons initiated in one nanoparticle to persist in the

liquid and reach another nanoparticle, high packing fractions,

soot-like particle assemblies, and Brownian motion of the particles

will be necessary to keep the separation among nanoparticles to be

small enough.

61

However, Xie et al. (Xie, Wang et al. [55]) found in their research

about alumina nanofluids that when the particle size close to the

mean free paths of phonons, the thermal conductivity of nanofluid

may decrease with particle size because the intrinsic thermal

conductivity of nanoparticle was reduced by the scattering of

phonon at particle boundary. However, this result was not in

agreement with most of the experimental results from other groups.

Choi et al.[28] indicated that sudden transition from ballistic heat

conduction in nanotubes to diffusion heat conduction in liquid

would severely limit the contribution of ballistic heat conduction to

overall thermal conductivity of nanotube dispersions. They

suggested that both ballistic heat conduction and layering of liquid

molecules at interface contributed to the high thermal conductivity

of nanotube dispersions.

The nature of heat transfer in nanoparticles or the fast ballistic

heat conduction can not be the mechanism works alone to explain

thermal conductivity enhancement of nanofluids due to the barrier

caused by slow heat diffusion in liquid. Other mechanisms need to

be combined with it to fully understand the enhancement of the

thermal conductivity in nanofluids.

2.7.4 Nanoparticle clusters

Local nanoparticle clustering is another possible mechanism

offered by Keblinski, Phillpot et al [84]. They suggested that the

62

effective volume of a cluster can be much larger than the volume of

the particles which will lead to higher overall thermal conductivity

of nanofluids. Clusters with very low packing factor which is

defined as ratio of the volume of the solid particles in the cluster to

the total volume of cluster, and very larger effective volume might

be one of the reasons for the unexpected thermal conductivity

enhancement of nanofluids. However, the author also pointed out

that the clusters existing in the dispersion may cause the

settlement of particles or creating particle-free regions with high

thermal resistance.

Except for local clusters, the nanoparticles with aspect ratio much

higher or lower than one can reach the percolation threshold at

very low loading. Eq.2.19 shows an empirical formula (Garboczi,

Snyder et al.[105]) developed to predict the percolation threshold,

Pc as function of the particle aspect ratio, Af.

3

f

2

f

5.1

ff

2

ffc

A658.1A763.1A33.12A61.14742.7

AA875.9p

(2.19)

The calculation results from this equation were plotted in Fig 2.9.

When the particles reach the percolation threshold, they can build

up three dimensional network structures in the nanofluids and

change the properties of the base fluids substantially.

63

Figure 2.9 Percolation threshold for particles with different

aspect ratios (Garboczi, Snyder et al.[ [105])

A theoretical model which included Brownian motion and diffusion

limited aggregation was developed by Xuan et al.[83]. The

calculation values of enhancement of thermal conductivity of

nanofluids containing 10nm copper nanoparticles agreed with their

experimental data (Li and Xuan[51]). However, according to this

model, the thermal conductivities enhancement of nanofluids

should decrease with cluster size.

Wang et al.[106] developed another theoretical model to predict the

thermal conductivity of nanofluids with cluster in it. The specific

size effect on thermal conductivity and liquid monolayer adsorbed

on to solid surface were also included in the model.

64

Recently, Gao et.al [107] presented differential effective medium

theory by taking into account both physical and geometrical

anisotropy of the nanofluids to predict the enhanced thermal

conductivity of nanofluids. Interestingly, their simulation results

showed a nonlinear dependence of thermal conductivity

enhancement on volume fraction of nanoparticles which agreed

with the experimental results from Choi et al [28].

Based on the above review on theoretical thermal conductivity

models of nanofluids a summary of different models and equations

by different researchers is presented in Appendix II.

2.8 Convection heat transfer properties of Nanofluids

Increasing the heat transfer coefficient of the heat transfer fluids is

very important for Nanofluids applications. Compared with the

experimental work on thermal conductivity of Nanofluids, there

were fewer papers that discuss the heat transfer coefficients of

Nanofluids in convective flows. Choi [108] pointed out that heat

transfer coefficient should increase with flow rates or with the

thermal conductivities of the fluid, while other properties of the

nanofluid system, such as heat capacity, density and viscosity are

kept same as the base fluid. If a nanofluid can have high thermal

conductivity at low volume fractions, a high heat transfer

coefficient might be obtained without increasing the pumping

power. In heat exchanger design, the length of the exchanger

65

surface affects the local heat transfer coefficient via entrance

effects and other factors. In some cases, using Nanofluids can help

achieve higher exchanger efficiency without increasing its size.

2.8.1 Forced convection heat transfer coefficients for

Nanofluids

Forced convection heat transfer tests and theoretical simulations

have been done for different kinds of Nanofluids including metallic,

metal oxide nanoparticles and carbon nanotubes dispersions in

both laminar and turbulent flow conditions.

Ahuja [109] conducted an experimental investigation of the

effective thermal conductivity of suspensions in laminar flow. In

his investigation, the experimental system was calibrated using tap

water, and the over all accuracy was estimated to be within 10%.

The suspension samples were 88 to 105 micrometers in diameter

and 44 to 53 micrometer diameter polystyrene spherical particles

with a weight fraction of 1.2%, 1.9%, 3.1%, 4.6%, and 8.8% were

placed in a base liquid of aqueous sodium chloride (5.2 wt%) and

aqueous glycerine (20wt%). In this experiment, the effective

thermal conductivity of the suspension in flow was two times

higher than that of the non-flow nanoparticle suspension and

varied with different shear rates, particle concentrations, particle

sizes, tube sizes, and base liquids. The results indicated that the

angular Reynolds number and Peclet number both played an

66

important role in the enhancement of the effective thermal

conductivity of the suspension in a flow situation.

Xuan and Li[110] studied convective heat transfer and flow

charterstics of Cu-water Nanofluids in both laminar and turbulent

flow in circular tube. The heat transfer coefficients of their

nanoparticles suspensions are much higher than that of the base

fluid at the same Reynolds number and increase of the heat

transfer coefficients increased with particle volume fraction. For

example, they reported a 60% heat transfer coefficient increase

compared with that of base fluid by adding 2 vol% nanoparticles.

Increased thermal conductivity and chaotic movement of

nanoparticles were offered as two mechanisms for increased heat

transfer. When the volume fraction of nanoparticles is low, the

friction factor of the fluid is not changed compared with base fluid.

In one of their early reports, they pointed out that same factors

affected convective heat transfer behaviors of Nanofluids like heat

capacity, thermal conductivity of base fluid and nanoparticles, flow

velocity, volume fraction of nanoparticles, viscosity of Nanofluids

and the shape of the nanoparticle [111]. They proposed general

form for the Nusselt number of Nanofluids as

n

c

c

k

kfNu

fp

pp

f

p,,

)(

)(,Pr,Re,

(2.20)

67

Based on the general form, they proposed a formula to correlate

the heat transfer coefficients of Nanofluids as

4.0

f

9238.0

f

001.0

p

ff

6886.0

f PrReD

dPrRe6286.710059.0Nu

(2.21)

The calculated results from these model in turbulent flow showed

good agreement with experimental data they obtained for Cu

nanoparticle.

Lee et al. [112] studied the forced convection heat transfer behavior

of sliver Nanofluids with water; water-EG mixture and water-

ammonia mixtures as base fluids. The tests were done in double

pipe heat exchanger system and heat transfer coefficient of

Nanofluids were 5~13% higher than that of water at same

Reynolds number (laminar region).

Heat transfer behavior of aqueous Al2O3 (13nm) and Ti2O (27nm)

Nanofluids were studied experimentally in turbulent flow in a

circular tibe by Pak and Cho [44]. The viscosities of the Nanofluids

were much higher than that of water, especially for alumina

nanoparticles. The authors found that the Nusselt number of

nanofluid for fully developed turbulent flow increased with increase

of Reynolds number and volume fraction of nanoparticles. However,

when the heat transfer coefficients of Nanofluids and water were

compared at the same average velocity, they found that the heat

transfer coefficient value of 3 vol% Nanofluids was 12% lower than

68

that of water. Suppressed flow turbulence by higher viscosity of

Nanofluids may be the reason for this phenomenon. These results

suggested a proper choice of particle size and volume fraction. A

new correlation for turbulent convection heat transfer of

Nanofluids was established as

5.0

f

8.0

f )(Pr)(Re021.0Nu (2.22)

Wen and Ding [113] reported experimental results for force

convection heat transfer of Al2O3 nanofluids in laminar flow regime.

It showed that addition of nanoparticles increased heat transfer

coefficients of base fluids and the enhancement increased with

Reynolds number and particle loading. Moreover, the enhancement

was significant at the entrance region and decreased with axial

distance. Since the classical model failed to predict the heat

transfer behavior of Nanofluids. The author suggested that

increased thermal conductivity was not the only reason to explain

the enhancement of convective heat transfer. Migration of

nanoparticles [114] was proposed to be another critical mechanism.

Experimental were conducted to study the convective heat transfer

of CuO (50nm) nanofluids in a mini tube by Chen et al. [115]. The

tests were taken in both laminar (Re=200~1500) and transition

(2000~4000) regimes. They found the inclusion of nanoparticle

increase heat transfer. In laminar flow, the enhancement always

increased with increase of Reynolds number. Surprisingly, for

69

transition regime, the enhancement of heat transfer coefficient

decreased with Re in mini tubes with smallest diameter.

A study on the heat transfer of nanotube dispersion was done by

Ding et al[71]. They studied the laminar heat transfer behavior of

aqueous carbon nanotube dispersions in horizontal tube. The

effective thermal conductivity, viscosity and heat transfer

coefficient were collected experimentally. They found that

nanotubes increased the heat transfer of base fluid and the

enhancement increased with Re, particle loading, and axial

distance. A maximum heat transfer enhancement happened in the

position between entrance and outlet. For given particle

concentration, a critical Re number existed above which dramatic

increase of the heat transfer coefficient occurred due to strong

shear thinning of nanofluids at certain shear rate. A maximum

heat transfer coefficient enhancement of 350% was claimed for 0.5

wt% nanotube dispersion when Re was 800. Particle

rearrangement, shear induced enhancement of thermal

conductivity, reduction of thermal boundary due to nanotubes

were suggested as possible mechanisms other than increased

thermal conductivity for increased heat transfer properties.

Heris et al. [116] investigated laminar flow of CuO/water and

Al2O3/water nanofluids through a 1 m annular copper tube with 6

mm inner diameter and with 0.5 mm thickness and 32 mm

70

diameter outer stainless steel tube, where saturated steam was

circulated to create constant wall temperature boundary condition

rather than constant heat flux condition by other researchers.

Comparison of experimental results showed that the heat transfer

coefficient enhanced with increasing volume fraction of

nanoparticles as well as Peclet number while Al2O3/water showed

more enhancement.

Tsai et al. [117] also employed aqueous solutions of various-sized

(2–35 nm and 15–75 nm) gold nanoparticles, which were prepared

by the reduction of HAuCl4 with trisodium citrate and tannic acid.

They found a large decrease of thermal resistance of the heat pipe

with nanofluids as compared with de-ionized water. The thermal

resistance of the circular heat pipe ranged from 0.17 to 0.215 K/W

with different nanoparticle solutions. The reason is that the

included nanoparticles can bombard the vapor during the bubble

formation. Hence, the reduction of thermal resistance was obtained

due to the resulted smaller bubble size. Results indicated the high

potential of nanofluids as working medium to replace the

conventional fluids in heat pipes.

Maiga et al.[118-120] done a series of simulations on convective

heat transfer of Al2O3 in water and EG nanofluids in both laminar

and turbulent regimes. The inclusion of nanoparticles increased

heat transfer in a uniformly heated tube and the enhancement of

71

heat transfer increased with particle volume fraction and Reynolds

number. However, the presence of the nanoparticles caused a

negative effect on the friction which also increased with particle

loading. EG-based nanofluids showed higher enhancement of heat

transfer and stronger adverse effects on wall shear stress than

water based nanofluids. According to the simulation results,

correlations were provided by the authors to compute average

Nusselt number in laminar flow in circular tube.

5.055.0 PrRe086.0Nu for constant wall heat flux (2.23)

36.035.0 PrRe28.0Nu for constant wall temperature (2.24)

S B Maiga et.al [120] considered the turbulent convection and

obtained the Nusselt number by using CFD based K- model

applying genetic algorithm as

35.071.0 PrRe085.0 nfNu (2.25)

In their simulation work, they applied classical formulas to

evaluate the physical properties of nanofluids including thermal

conductivity.

Roy et al. [121] considered the hydrodynamic and thermal fields of

aqueous Al2O3 nanofluids in a radial laminar flow cooling system.

The simulation results indicated that considerable heat transfer

enhancement (two fold increases for 10 vol% nanofluid). However,

wall shear also increased with nanoparticle loading.

72

By taking Brownian motion of nanoparticles into account, Koo and

Kleinstreuer [122] analyzed the laminar flow in microchannels for

CuO in water and EG nanofluids. New formula were developed and

applied to calculate the effective thermal conductivity and viscosity

of nanofluids. The effects of nanoparticle concentration on

microchannel pressure gradient, temperature profile and Nusselt

number were computed. High Pr number base fluid and

nanoparticle with similar dielectric constant with base fluid were

recommended by authors for maximizing the heat transfer property

of nanofluids.

The convective heat transfer coefficient were also calculated from a

thermal lattice Boltzmann model [123] proposed for simulating flow

and energy transport process of nanofluids. The external and

internal forces acting on nanoparticles were considered in the

model.

2.8.2 Natural convection heat transfer for nanofluids

Compared with research effort in forced convection, relatively few

results have been reported for natural convention. Khanafer et al.

[124] developed a natural convection heat transfer model to predict

heat transfer behaviors of nanofluids in a two dimensional

enclosure. The chaotic motion of nanoparticles was considered

through a thermal dispersion model. The simulation results

illustrated that the nanoparticle substantially increased the heat

73

transfer rate of base fluid at any Grashof number and rate

increased with nanoparticle volume fraction.

Putra et al. [125] and wen et al. [126] conducted an experimental

study of the steady state natural convection of two Al2O3 and CuO

nanoparticle suspensions, in distilled water, under different

conditions. However, in the experimental results (for Rayleigh

number 106~109) in horizontal cylinder showed significant

decrease with increase of nanoparticle volume fraction.

2.8.3 Two-Phase Change Heat Transfer Of Nanofluids

Another aspect of the heat transfer performance of nanoparticle

suspensions is the effect of these suspensions on boiling heat

transfer. You and Kim [127] experimentally investigated the

enhancement of the critical heat flux in pool boiling for Al2O3

nanoparticle suspensions. The results indicted that in the nucleate

boiling regime, the boiling heat transfer coefficient was not

influenced by the addition of the Al2O3 nanoparticles. However,

there was a dramatic increase in the critical heat flux (CHF), for

different concentrations of the nanoparticle suspension that

ranged as high as 300% of that for measured for pure water.

In the experimental investigation of Das et al. [128], the boiling

performance of the water was found to deteriorate with the

addition of the nanoparticles, and that a higher wall superheat

existed for the same heat flux. With the increase of the

74

nanoparticle concentration in the suspension, the deterioration

was more apparent. It was observed that the nanoparticles with a

diameter of 20 to 50 nm filled the cavities of an uneven heating

surface and changed the surface characteristics by effectively

making it smoother. They suggested with the increase of

nanoparticle concentration, a layer of sedimentation of the

nanoparticles developed, which deteriorated the boiling

performance even further.

Vassallo et al. [129] and Zhou [130] studied the boiling

characteristic of silica nanoparticles and microparticle suspensions

with diameters of 15 nm, 50 nm, and 3000 nm in boiling

situations, ranging from nucleate boiling to film boiling under

atmospheric pressure. The heat flux was generated in a

horizontally fixed, NiCr wire and the water level was observed to

decrease approximately 6 mm during the experiment. All of the

suspensions expressed no difference in the boiling performance of

water, below the CHF point, but increased the CHF point

dramatically.

Based on the above review on convective heat transfer of

nanofluids, the inferences drawn and the experimental

enhancement found by different researchers is presented in

Appendix III.

75

2.9 Review on Compact Heat Exchanger

2.9.1 Direct Test data

Direct test data for each compact heat exchanger surface is the

relation between Colburn factor (j) and mean friction factor (f)

obtained by Kays and Londan [8], their 24-year project sponsored

by the Naval Research, which cover experimental data of 132

compact heat transfer surfaces including the plate fin surfaces and

tube fin surfaces.

2.9.2 Surface selection

A general method for comparison of compact heat transfer surfaces

has been recently proposed by Cowell [133]. The method provides

compact statement of the relative merits of different heat transfer

surfaces by comparing relative pumping powers and relative

hydraulic diameters. Also, the relation between several factors of

the performance parameters was clarified.

Nunez [134] developed a thermo hydraulic model that represent

the relationship between pressure drop, heat transfer coefficient

and exchanger volume. A simple approach to surface selection was

based on the concept of volume performance index (VPI): the

higher the VPI, the lower the core volume required. Surfaces were

compared on the basis of VPI and envelopes for best utilization

could be achieved by using envelopes for best surface performance

together with the thermo-hydraulic model.

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Taylor [135] and Shah [136] used the traditional approach to

design the plate fin heat exchangers, and traced the pressure drop

as a constraint to see the acceptable pressure drop values for the

specified heat duty.

Hesselgreaves [6] has attempted to provide a treatment that goes

beyond dimensionless design data information. In addition to the

basic design theory, he includes descriptions of industrial CHEs,

specification of a CHE as a part of system using thermodynamic

analysis and broader design considerations for surface size, shape

and weight. Heat transfer and flow friction single phase design

correlations are given for the most commonly used modern heat

transfer surfaces in CHEs, with the emphasis on those surfaces

that are likely to be used in the process industries, and some of

the operational considerations including installation,

commissioning, operation, and maintenance, including fouling and

corrosion.

2.9.3 Entropy Generation

Tagliafico [137] provided a comparative study of entropy generation

of many surface scaled by that of reference configuration (a

parallel-plate channel), considering the irreversibility analyses an

important factor in determining the operating costs of the heat

exchanger. A possibility to combine hydraulic and heat transfer

characteristics is offered by the thermodynamic (second law)

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analysis developed by Bejan [138], from this point of view, the

entropy generation (irreversibility) in the heat exchanger can be

assumed to measure the quality of the performance ( London,

[139]; Sekulic, [140];, Schenone, [141]).

2.9.4 Vortex Generators

Fiebig [142] provided a comprehensive study on the use of vortex

generators in either tube fin or plate fin compact heat exchanger

and showed the recent results from the “Vortices & Heat transfer”

group. He compared the performance of transverse vortex

generators and longitudinal vortex generators, described the

mechanism if heat transfer enhancement due to using vortex

generators and compared the performance of high performance

surfaces (louvered, strip) used in plate type compact heat

exchangers with two types of vortex generators surfaces. The first

vortex characteristic was obtained from Brockmeier [143] and

second is the ISB configuration.

Jacobi and Shah [144] discussed the recent progress of vortex-

induced heat transfer enhancement, the theoretical basis for

passive and active implementation. They also identified the

research needs in the area of vortex-induced heat exchanger

enhancement. Also they provided a full coverage for the application

of vortex generators in compact heat exchangers. They also studied

the behavior of air flow in complex heat exchangers passages with

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a focus of boundary layer development, turbulence, span wise and

stream wise, and wake management. Each of these flow features is

discussed for the plain, wavy, and interrupted passages found in

contemporary heat exchanger design.

2.9.5 Minimum Weight of Compact heat exchanger

Hesselgreaves [145] presented a dimensionless analytical method

of calculating the size and weight parameters of simplified plate fin

heat exchanger core for given thermal duty. The thickness of fin

material and separating plates which constitute the bulk of the

core weight, have lower limits set by pressure containment

capability, but it does not necessarily follow that the minimum fin

thickness gives the minimum core weight. This optimum fin

thickness is shown to be a function of several geometric, material

and performance parameters.

2.10 Thermal Design Procedures

The problem of heat exchanger design is complex and

multidisciplinary (Shah, [9]). The major design considerations for a

new heat exchanger include process/design specifications, thermal

and hydraulic design, mechanical design, manufacturing and cost

considerations, and trade-offs and system-based optimization, as

shown in Fig. 2.10. The thermal and hydraulic design methods are

mainly analytical, and the structural design is analytical to some

extent. Most of the other major design considerations involve

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qualitative and experience based judgments, trade-offs, and

compromises. Therefore, there is no unique solution to designing a

heat exchanger for given process specifications.

Two broad categories of design problem specifications as follows:

Rating

sizing.

The rating problem, also called to as the performance problem, is

analyzed for predicting the performance of an already built

exchanger. The objective here is either to verify vendor‟s

specifications or to determine the performance at off-design

conditions. In this problem, the following quantities are specified:

the exchanger construction type, flow arrangement, overall core

dimensions, and complete details on the material and surface

geometries on both sides including their heat transfer and

pressure drop characteristics, fluid flow rates, inlet temperatures,

and fouling factors. The output is to predict the fluid outlet

temperatures, heat transfer rate, and pressure drop on each side.

The sizing problem, also called as design problem, involves a

design of new heat exchanger for specified performance within

known constraints and minimum objective function. In this

problem, the fluid inlet and outlet temperatures and flow rates are

generally specified as well as the pressure drop on each side. The

output is to select construction type, flow arrangement, materials

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and surfaces on each side, and to determine the core dimensions

to meet the specified heat transfer and pressure drop.

Many theories were developed to describe the design and

performance of compact heat exchangers starting with Bergeles

and Taborek [146], Bergeles [147] Bejan [148], Sparrow and Liu

[149], Shah and Bergeles [150] , kays and London[8], Sekulic [151],

Campell and Rohsenow [152], Smith [153]. More recent texts such

as those of Webb [154] Andrews and Fletcher[155], Kakac and Liu

[156] have also been referred to extensively in the CHE research.

Shah and Sekulic[9] presented the procedures of rating and sizing

using the mean temperature difference of the fluid on each side of

the heat exchanger in order to calculate the fluid on each side of

the heat exchanger in order to calculate the fluid properties

assuming the uniformity of thermo physical properties.

Sekulic [157] offered a very clear methodology for calculating core

dimensions of a compact heat exchanger. Considering the

analytical complexity of implemented calculations, the most

intricate basic flow arrangement situation in a single pass

configuration would be a crossflow in which fluids do not mix

orthogonal to the respective flow directions. Calculations are

executed using an explicit step-by-step routine based on set of

known input data is provided in the problem formulation. The

procedure follows a somewhat modified thermal design (sizing)

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procedure derived from the routine advocated in Shah and Sekulic

[9]. The main purpose of the calculation sequence is to illustrate

the iteration procedures used in commercial software.

Automobile industry is continuously straining to bring out the best

design of automotive vehicle in terms of improving its thermal

performance, optimizing the fuel consumption in addition to better

safety. In this process the cooling incorporated for the engine and

other related systems are found to be vital factors in improving the

thermal performance of the automobile. The heat exchanging

system adopted in

radiators, air conditioning system need to be optimized in terms of

weight, volume, which has a strong impact on the vehicle

aerodynamic characteristics. Normal practice to improve the heat

transfer from a surface is promoting heat transfer from a surface is

promoting turbulence and applying roughness to the surface etc.

However these two methods will create additional problem in terms

of pressure drop, increased drag etc.

In automobile applications use of compact tube fin heat exchanger

is ideal to reach high levels of temperature and pressure with in

severe constraints of dimensions. Different verities of

configurations are adopted to increase the heat transfer area such

as plain, wavy, perforated and louvered fins (Kays et al., [8]).

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Taler [158] proposed two numerical methods for determining

correlations for heat transfer coefficients in cross-flow

compact heat exchangers. In the first method, only the

correlation for the air-side heat transfer coefficient is

determined. The heat transfer coefficient on the tube-side is

calculated using the Gnielinski or Dittus-Boelter correlations.

In the second method, the heat transfer correlations both on

the tube and air-side are determined simultaneously in order

to predict the air-side heat transfer more accurately.

Charyulu et al. [159] developed a numerical model based on ε –

NTU method and analyzed the characteristics of radiator in diesel

engine model TBD 2323 V-12 for different fin configurations and

tube materials. Carluccio et al. [160] presented numerical analysis

of air-oil radiator made of aluminum alloy using CFD and

compared with experimental data. Witry et al. [161] carried the

thermal performance using CFD for a radiator with aluminum

plate and established there dominates in terms of high heat

transfer rates, low pressure drop and smaller size. They have also

established that the coolant flow velocities decreases due to

impingement and erosion/corrosion of the plate. Mahmoudi [162]

conducted experimental and developed theoretical analysis using

2D CFD model for copper based automobile radiator. A detailed

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Figure 2.10 Methodology of Compact Heat Exchanger Design

(Shah,[9])

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knowledge base of parametric study of automobile radiators using

CFD based ε – NTU method is proposed by Oliet et al.[163]. In

radiators which are vital in the control of engine temperature in an

automobile, the common liquid used is water + glycol mixture. This

hot liquid coming from the engine flows in flat tubes while the

atmosphere air drawn in flows in the channels setup by fin

configuration and cools the liquid.

Saripella et.al [164] conducted numerical simulation on Class 8

Truck engine cooling system using Nanofluids. They replaced

standard coolant 50/50 mixture of Ethylene glycol and water with

Nanofluids comprised of CuO nanoparticles suspended in base

fluid of 50/50 mixture of Ethylene glycol and water. They reported

that due to high heat transfer coefficients of nanofluids mainly an

improvement in engine heat rejection was observed.

Bang et al.[165] presented an axiomatic design approach for

innovative nanofluids as coolants by using Colloid science. They

suggested at parametric level the design of nanofluids is inherently

coupled with heat performance and flow performance and

developed a design matrix as a standard communication protocol

in the nanofluids research to practical use.

2.11 Conclusion

The transportation industry as well as many other industries has

specific needs to increase heat transfer rates under a variety of

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constraints. Literature review shows that suspensions containing

nanometer-sized particles (nanofluids) show potential for use as

cooling fluids due to enhanced heat transfer properties. The two-

step method is the most widely used method to prepare nanofluids,

however, agglomeration during drying, storage and redispersion of

the nanoparticles in the base fluid are some of the drawbacks

which makes the one-step method a more attractive route to

nanofluids. A surfactant is generally used to prevent particle

agglomeration during nanoparticle formation and also to ensure

very small nanoparticles are formed. It is also known that

structural differences and defects present in most nanostructures

have a noticeable effect on their physico-chemical properties. The

rheological properties of the nanofluids are rarely investigated.

Nanofluids containing metal nanoparticles were found to be

Newtonian, whereas nanofluids containing metal oxides as well as

carbon nanotubes showed non-Newtonian, shear thinning

behavior. Since the interaction forces between particles usually

decrease during flow conditions, the flow resistance is also

decreased. With no significant interaction forces between the

particles, separation of the particles in the form of sedimentation

may occur and therefore, rheological studies could possibly provide

more information about the stability of the nanofluids and also the

interactions between the particles and fluid molecules.

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The literature review also has shown that the research on

nanofluids thermal conductivity is far enough along to be able to

identify reproducible trends from multiple researchers in many

areas. Some parametric trends, such as particle size, still require

substantiation, and the use of additives has barely been addressed.

However, general trends were identified in thermal conductivity

and heat transfer enhancement in the range of 15-40% with oxide

and metallic nanoparticles in a variety of base fluids. But

comparing results among research groups involve in- accuracies

due to the poor characterization of the nanofluids studied. It is

difficult to measure the nanoparticle size, shape, and distribution

in fluids by laser scattering technique. A more advanced technique

for these measurements is X-ray small angle scattering, which can

potentially yield accurate measurements.

While many theoretical models have been proposed and

simulations have been developed for nanofluid thermal properties,

it is still not possible to specify a nanofluid for a particular

application based on general verified theory. Current theories

generally fail to predict thermal conductivity enhancement and its

temperature dependence from the properties of materials.

To solve these problems a semi empirical approach of experiments

and correlations should be developed for thermal conductivity of

nanofluids and also for both laminar and turbulent heat transfer

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flows so that these correlations can be used in industrial

applications like vehicular transportation industry, power plants

etc.