To study the effect of metallic and non metallic solids in base fluids. To formulate mathematical equations in order to understand the changes in thermal conductivity, convective heat transfer coefficient, viscosity and density of nanofluids, with temperature and composition.
This project is designed to study the variations in properties of nanofluids. The discussed properties are thermal conductivity, convective heat transfer coefficient, viscosity and density. Various models have been proposed for calculating these properties, and all the models are case specific. Research continues to formulate the best possible model. This project illustrates the interpretation of these models and tries to find out the scope and limitations of these models
Fluids with suspended nanoparticles are called nanofluids, a term that was coined by Choi in 1995 of the Argonne National Laboratory, U.S.A. [1]. Nanoparticles are suspended in the base fluid to increase the thermal conductivity of the resulting nanofluid. Nanoparticles have a significant effect on the flow geometry, boundary conditions, viscosity and density of nanofluids. Though nanoparticles increase the rate of convective heat transfer, yet there is a downside to their usage. The stability of the suspension, additional flow resistance and the possibility of corrosion are just some of the factors that restrict the progressive use of nanofluids. It cannot be denied that nanoparticles have proved out to be the solution of many challenges faced in the field of heat transfer; the inception of smaller and miniature heat transfer systems is just one such example.
Production of Nanoparticles
Nanoparticles are made out of various materials either by chemical processes or physical processes. Few of the physical techniques that are used include inert - gas - condensation & mechanical grinding technique [2]. Processes that are currently being used for making metal nanoparticles include inert- gas- condensation technique, micro emulsions, spray pyrolysis mechanical milling, chemical vapor deposition, thermal spraying & chemical precipitation. Nanoparticles are most widely used in their powdered form [3]. When in powdered form, nanoparticles dispersed in aqueous or organic base liquids form nanofluids. So far, nanofluids of varying qualities have been produced. Low cost & large scale production, of well dispersed nanofluids, is required on a commercial basis [4].
There are broadly two ways of producing nanofluids: single step method and the two-step method. An approach developed by Akoh et al. [5] called the single-step direct evaporation and is called the VEROS (Vacuum Evaporation onto a Running Oil Substrate) approach. The basic idea of this technique was the production of nanoparticles; however there was one hitch in this method which was that it was difficult to separate particles from the fluids. And we required was to produce dry nanoparticles. A modified VEROS technique was proposed by Wagener et al [6] in which high pressurised magnetron sputtering is used for preparing suspensions that contain metal nanoparticles like Fe, Cu, Ag etc. A further modified VEROS method was developed by Eastman et al. [4]. In this method using direct condensation with a flowing low-vapour-pressure liquid we are directly able to condense Cu vapour. On the other side the two-step method is more dependent on the commercial availability of nanopowders, only then can the nanoparticles be synthesised. In this technique, the particle production is done first, and then only are they dispersed in the base fluids. In order to reduce the agglomeration & achieve an enhanced dispersivity ultrasonic equipment is used.
Properties of Nanofluids
Thermal Conductivity of Nanofluids
There is a remarkable increase in the thermal conductivity of nanofluids due to the suspension of nanoparticles having high thermal conductivity in the base fluid of low thermal conductivity. Many models have been developed to explain the increase and various experiments have been carried out to compare experimental data with the analytical models. Further research & study is required for the development of a sophisticated theory in order to understand thermal conductivity of nanofluids. However, there are some empirical correlations to calculate effectively and efficiently the thermal conductivity of two-phase mixtures.
In theory, ratio of thermal conductivity enhancement is explained as the ratio of the nanofluid's thermal conductivity to that of the base fluid (Keff/K1). Researchers used the classical research of Maxwell on conduction through heterogeneous media, to develop their thermal conductivity studies. For a two-phase mixture consisting a continuous phase and a discontinuous one, the effective thermal conductivity has been given by Maxwell [7] and the effective thermal conductivity Keff can be given by
where K1 and K2 are the thermal conductivities of the liquid and particle respectively and Φ is the fraction of particle volume. Maxwell successfully derived his model on the basis of the assumption that the discontinuous phase has a spherical shape and the conductivity of nanofluids depends on that of the spherical particles, the base fluid and the particle volume fraction.
Hamilton and Crosser [8] improved upon Maxwell's work to study non spherical particles and introduced a new aspect, the shape factor (n) which can be experimentally determined for variety of materials. The goal of the research was to formulate a model which varies as a function of the composition and conductivity of both discontinuous and continuous phases, as well as the particle shape. The model developed by Hamilton and Crosser for a discontinuous phase (particles) dispersed in a continuous phase is given as:
where the empirical shape factor (n) is obtained as n = 3/Ψ where Ψ is the sphericity and is determined as the ratio of the surface areas of a sphere to the volume of the particle. The Hamilton-Crosser model becomes equivalent to the Maxwell model with Ψ = 1 and has been found to show agreement with data for Φ < 30%. The model holds as long as the particles have conductivity greater than that of the continuous phase by a factor of 100 at least. Though these experiments show that the models are good in predicting the thermal conductivity; effects of size of nanoparticles are not included in these.
Yu and Choi [9] modified the model of Maxwell with the assumption that the molecules of base fluid which are close to the nanoparticle's solid surface form layered structures which are solid like. Hence the nanolayer forms a thermal bridge between the solid nanoparticles and the liquid base fluid, and this enhances the effective thermal conductivity.
While calculating Keff, in order to include the nanolayer effect, Yu and Choi considered a spherical nanoparticle with radius (r) surrounded byaa nanolayer of thickness (h). It was also assumed that the conductivity of the liquid (K1) is lower than that of the nanolayer (K layer). When the nanolayer and the nanoparticle are combined, an 'equivalent nanoparticle' with a thermal conductivity (Keq) is introduced. The equivalent thermal conductivity can be obtained using the theory of effective medium [10] as:
where β = h/r, the ratio between the thickness of the nanolayer & the radius of the original particle and Klayer / K2. Then, for the case = 1, Klayer = K2 = Keq. Hence, Yu and Choi adapted Maxwell's equation and developed the following model for effective thermal conductivity:
It should be noted that the effective thermal conductivity of nanofluids varies with the thermal conductivity of base fluid and solid particles, fraction of particle volume, particle shape, nanolayer's thermal conductivity and thickness.
By assuming the nanolayer and the radius of nanoparticles, a comparison can be made of these three important models. The thermal conductivity model was illustrated by Yu and Choi [9] by plotting the values for 1 nm and 2 nm nanolayer thickness. A value between the thermal conductivity of the nanoparticles and that of the base fluid is acceptable as the thermal conductivity of the nanolayer.
Lee et al. [11] and Wang et al. [12] studied the fraction of effective particle volume with 23 and 24 nm CuO particles in water as a base fluid, and found that the thermal conductivity enhancement increases with increased concentration of particle volume linearly; the thermal conductivity ratio increased by approximately 34% at 10% volume fraction.
The effect of the concentration of particle volume in base fluid ethylene glycol with CuO nanoparticles has been studied by Lee et al. [11] & Wang et al. [12]. It has been found that 15% volume concentration of CuO particles results in an increase of 50% in the ratio of thermal conductivity. The magnitude of enhancement with identical testing parameters for Al2O3 in water has been agreed upon by investigators.
Research was also carried out by Wang et al. [12] & Lee et al. [11] by isolating the effect of material property by keeping all the parameters such as base fluid, particle size, and temperature constant. However, the situation changes with the particle material when particles such as Al2O3, CuO, and SiC, with same particle size but higher conductivity are used. Enhancement produced is same as the oxide particles but the volume concentration is much lower. On the other hand, producing nanofluids of metal particles without oxidation of the particles during the production process is very difficult.
Wang et al. [12] & Lee et al. [11] also studied the effect of particle size, with spherical particles for a single particle-water combination over a range of 20 nm to 60 nm particle diameter. The general trend observed is that larger particle diameters produce a larger enhancement in thermal conductivity. On the other hand, there are some theories which predict that small particles which are uniformly distributed produce improved heat transfer enhancement. Many researchers have also proposed models and results for certain specific cases e.g. CuO in ethylene glycol, Cu in water etc. Some of these have been explained in the table on the next page.
BASE FLUID
NANOPARTICLES
AVERAGE DIAMETER /CONCENTRATION
METHOD
DISPERSANT
PEAK THERMAL CONDUCTIVITY RATIO
Water
Al2O3
<50 nm ; upto 4.3 vol%
Two Step
Not specified
1.08
Water
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.22
Water
CuO
<50 nm ; upto 3.4 vol %
Two Step
Not specified
1.1
Water
Cu
18 nm ; upto 5.0 vol %
One Step
No Dispersant
1.6
Water
Cu
upto 100nm ; upto 7.6 vol %
Two Step
Laurate salt 9 wt % via Particles
1.76
Water
C-MWNT
50μm, 5μm, 3μm ; 0.6 vol%
Two Step
Sodium Dodecyl Sulfate
1.38
Ethylene Glycol EG
Al2O3
<50 nm ; upto 5.0 vol%
Two Step
Not specified
1.18
Ethylene Glycol EG
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.29
Ethylene Glycol EG
CuO
35nm ; upto 4 vol%
One Step
Not specified
1.21
Ethylene Glycol EG
Cu
10nm ; upto 0.5 vol %
One Step
No Dispersant
1.14
Ethylene Glycol EG
Cu
10nm ; upto 0.5 vol %
One Step
Thioglycolic acid <1 vol%
1.41
Glycerol Gly
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.27
Oil (Pump oil)
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.38
Oil (Trans oil)
Cu
upto 100nm ; upto 7.6 vol %
Two Step
Oleic acid 22 wt% via particles
1.43
Water + (upto 100% vol) Ethylene Glycol
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.29
Water + (upto 100% vol) Glycerol Gly
Al2O3
s = 25 m2g-1; 5.0 vol%
Two Step
No Dispersant
1.27
Oil (500SN)
TiO2
20 nm; 0.757 wt%; 0.84 wt%; 0.92 wt%
Two Step
Sorbitol monostearat of 1.00 wt%
Table : Literature reported results [22]
Convective Heat Transfer of Nanofluids
The convective heat transfer coefficient is a better property in order to understand the fluidics of nanofluids. The reason for this is because in order to design heat exchangers the most important property that needs to be taken into consideration is convective heat transfer coefficient. Physically speaking the properties of the nanofluids are quite varied from those of the base fluid.
Viscosity, specific heat & density also play significant roles in enhancing the coefficient of heat transfer and also exceeding the thermal conductivity results as portrayed by some experiments. Experiments were done by Heris et al. [13], in which he used Al2O3 and CuO as the nanoparticles and water as the base fluid. These experiments were carried out under laminar flow till the flow become turbulent. He was able to find increases as large as 40%, in the convective heat transfer coefficient, with Al2O3 particles as nanoparticles. On the other hand the enhancement in thermal conductivity was even lesser than 15% [13].
Experiments were performed on turbulent flow of nanofluids by Pak and Cho [14]. They used - Al2O3and TiO2 dispersed in water and tested the frictions of the turbulent flow.
The single phase flow of a turbulent fluid was first studied by Xuan and Li [15]. They developed the following correlation using the experimental data for heat transfer:
Nunf = hnf d / Knf = 0.0059 (1.0 + 7.6286 Φ0.6886 Ped0.001 ) Renf 0.9238 Prnf 0.4
For laminar flow Xuan and Li [15] provided also a correlation:
Nunf = hnf d / Knf = 0.4328 (1.0 + 11.285 Φ0.754 Ped0.218 ) Renf 0.333 Prnf 0.4
The Peclet number, Pe, describes the effect of thermal dispersion caused by microconvective and microdiffusion of the suspended particles. The particle Peclet number, Reynolds number and the Prandtl number for nanofluid are defined respectively as
Pe d = u m dp / α nf
Re nf = u m d / nf
And
Prnf = nf / α nf
where the thermal diffusivity is given by
The theoretical analysis of heat transfer enhancements due to nanofluids is also an emerging field with significant literature available. In order to understand the practical applications a comprehensive understanding of heat transfer enhancement in forced convection in turbulent and laminar flow with nanofluids is required. Almost all the forced convection flows depend on the Reynolds and Prandtl number, however when considering the case of nanofluids, additional parameters must be taken into consideration. Many researchers think that Brownian motion plays an important role in determining the characteristics of nanofluids. The ultra fine particles create a slip velocity between the fluid medium and solid nano particles.
Researchers have carried out experiments to relate the volume fraction of dispersed nanoparticles and the convective heat transfer of the nanofluid. The two ways to find the heat transfer coefficient of nanofluids in a duct flow are now being mentioned. The first method is more of a conventional approach using the transport and thermal properties in the correlations available for heat transfer coefficients of the pure base fluid. Hence, the below mentioned are the property expressions for nanofluids.
Einstein's formula used for evaluating effective viscosity was introduced by Drew &Passman [24].
Brinkman[18] extended Einstein's equation as :
If ϕ < 0.05, the below mentioned equation for μeff , for spherical particles can be used:
The Maxwell & Hamilton models can be incorporated to give the effective thermal conductivities.
n is the shape factor which is 3 for a sphere & 6 for a cylinder; and Ï• represents the volume fraction.
For example under a constant wall temperature, for a fully developed laminar flow:
Nu T = 3.675
The so far discussed is the first approach. In the second method, the equations governing specific boundary conditions can actually be solved. The well known equations of conservation (energy, momentum & mass) that known for single phase flow can also be used for nanofluids.
Some of the reported results have been tabulated on the next page.
Table : Summary of experiments on convective heat transfer of nanofluids [23]
Investigator
Geometry
Nanofluids
Findings
Forced convective heat transfer:
Lee and Choi
Parallel channels
Unspecified
Reduction in thermal resistance by a factor of 2
Wen and Ding
Tube (D= 4.5, L= 970 mm)
Al2O3/water (27-56 nm)
Laminar, enhancement increases with Reynolds number and particle concentration
Chien et al.
Disk-shaped heat pipe (D= 9,H =2 mm)
Au/water (17 nm)
Significant reduction of thermal resistance
Tsai et al.
Heat pipe (D= 6,L =170 mm)
Au/water (2-35, 15-75 nm)
High potential to take place conventional fluids in heat pipe applications
Ding et al.
Tube (D= 4.5, L= 970 mm)
CNT/water
Significant enhancement of convective heat transfer, which depends on the flow condition, CNT concentration and the pH level
Pak and Cho
Tube
Al2O3(13 nm), TiO2 (27 nm)/water
h withΦ =0.03 vol% was 12% lower than that of pure water for a given average fluid velocity
Yang et al.
Tube (D= 4.57, L= 457 mm)
Graphite nanofluid
The enhancement of his lower than the increase of the effective thermal conductivity
Heris et al.
Annular tube (Din= 1 mm,Dout=32 mm,L =1 m)
Al2O3(20 nm), CuO
(50-60 nm)/water
Enhancement of hwith Φand Pe. Al2O3showed more enhancement than CuO
Natural convective heat transfer:
Putra et al.
Horizontal cylinder
CuO (87.3 nm), Al2O3(131.2 nm) / water
A systematic and significant deterioration in natural convective heat transfer
Wen and Ding
Two horizontal discs(H = 10, D= 240 mm)
TiO2/water (30-40 nm)
Deterioration increases with particle concentrations
Viscosity of Nanofluids
The resistance to flow of a fluid is called the viscosity. Viscosity can also affect the convective heat transfer of the fluid. With an increase in the particle volume fraction, there is also an increase in the viscosity of the nanofluid [16]. Hence optimal concentrations of nanoparticles are required in the nanofluid.
Many models have developed in order to predict the viscosity of nanofluids. The earliest one being developed by Einstein in 1906:
η nf = η bf ( 1 + K H Φ)
where η nf & η bf are the viscosities of the nanofluid and the base fluid respectively. K H represents the shape factor of the particle, and Φ stands for the volume fraction of particles in the nanofluid. However, this model neglects the effects of particle size. But this model does give due consideration to the particle shape and particle concentration. Einstein's equation is only valid if the particle-particle interactions are negligible. At higher particle concentrations, these interactions become important, and the hydrodynamic volume fraction, Φ h, is used:
Φh = Φ [(d+2s)/d] 3
where d is the particle diameter, and s the thickness of the capping layer [17]. Brinkman [18] further studied the Einstein's model to accommodate for moderate particle volume concentrations. The Brinkman model is valid for particle volume fractions less than 4%, & is as follows:
The effects of Brownian motion for spherical particles has been well taken care of by the Batchelor model [19] which is given below:
Various models have been developed to be able to determine the empirical viscosity with due considerations to particulate size. The following viscosity correlations for 36 and 47 nm particles respectively was developed by Nguyen et al. [20]:
Both of these models determine the viscosity by only considering the particle volume fraction & the viscosity of the base fluid.
S. Masoud Hosseini et al [21]. formulated a model based on dimensionless groups and that uses a least-squares regression technique to determine model parameters. The groups were chosen on a basis so that the thickness of capping layer on the nanoparticle ,the hydrodynamic volume fraction of nanoparticles, viscosity of the base fluid, diameter of the nanoparticle, and changes in temperature are all taken into consideration. The following dimensionless groups are thus defined:
Π1= ηnf / ηbf
Π2 = Φh
Î 3 = ( d / 1+ r)
Î 4 = T / To
where η nf is the viscosity of the nanofluid, η bf the viscosity of the base fluid, Φh represents the hydrodynamic volume fraction of solid nanoparticles, d stands for the nanoparticle diameter, r is the thickness of the capping layer, T0 is a reference temperature and T the measured temperature of the nanofluid. One of the dimensionless groups is taken to be a function of the other groups as follows:
The function f1 is expressed as follows:
where m is the factor that depends upon the properties of the system ( i.e. the nanoparticles, base fluid and their interactions) where α, β and γ are empirical constants determined from experimental data. The empirical constants were calculated from a set of experimental data for alumina-water nanofluids [20] using least square regression. According to the least square regression m = 0.72 ; α = -0.485 ; β = 14.94 ; γ = 0.0105. For this particular system a reference temperature of 20˚C and capping layer thickness of r = 1 nm were used.
The model proposed by S. Masoud Hosseini et al.[21] works well with varied temperatures. This model is can be considered more accurate as it takes particle diameter, capping layer thickness and nanofluid temperature into consideration. The model displays a non-linear behaviour between the nanofluid viscosity and hydrodynamic volume fraction.
In order to analyse the flow behaviours and the thermal behaviours the function and role of viscosity must be under stood. The kinematic viscosity can be well estimated at different temperatures and concentrations by using the Redwood viscometer 1, which is shown below.
Figure : Redwood Viscometer 1
In the experiments carried out by L.Syam Sundar [25] the redwood viscometer was used. Out of the total 100 experiments that were carried out only a 0.5% maximum error was obtained. The below mentioned formula is used to calculate the kinematic viscosity:
Kinematic viscosity of the fluid is represented by. A & B are Redwood viscometer constants which have a numerical value of 0.00260 & 1.791 respectively. 't' represents the time taken to collect nanofluid upto 50 c.c.
These values were also plotted by L.Syam Sundar [25] as shown below:
Figure : Kinematic Viscosity Vs Volume Fraction [25]
As the temperature increases, time taken in order to collect 50 c.c. of nanofluid also decreases. Hence, with an increase in temperature, the viscosity of the nanofluid also decreases.
Figure : Kinematic Viscosity Vs Temperature [25]
L.Syam Sundar[25] also commented on the pH of the nanofluids. Upon increasing the volume fraction of nanoparticles the pH of the nanofluids becomes increasingly acidic.
The below mentioned correlation for density is widely used in finding the density of the nanofluid.
In a similar fashion the specific heat can also be calculated
The viscosity can be determined by the Pak & Cho model:
)
Density
Based on the law of mixtures the density of nanofluids can be estimated, at atmospheric temperatures. When nanoparticles are added in the base fluid, the mass of the newly form nanofluid is more than the mass of the base fluid due of the presence of metallic particles of nano sizes, however the volume remains constant. As we know the density is directly proportional to mass, hence we can expect an increase in the density of the nanofluid as compared to the base fluid. For engineering calculations the properties must be measured at different temperatures. For this purpose we take the help of the 'Constant Volume Method'. This method is used for the estimation of density of nano fluid at different temperatures. Firstly, using an electronic weighing machine we estimate the mass of the measuring flask. The mass of the volumetric flask is measured with liquid and without the liquid, using a digital analytic balance of ±0.1 mg resolution. The temperature of the surrounding and the fluid can be measured using a digital thermometer of ±0.1 0C resolution. Assume the mass of the empty measuring flask to be m1. Measure the mass of the flask which contains 50 ml of the nanofluid, and label it as m2. The difference between m2 - m1 gives the net mass of the nanofluid. Using a heater to heat the measuring flask, a thermocouple dipped in the nanofluid can be used to measure the temperature difference. As the temperature is raised, the mass of the flask decreases, and the fluid in the flask shall expand. Label the decreased mass as m0. Now, to measure the density we make use of the increased volume as constant and m0.
In order to understand the properties of the nanofluids the specific heat is parameter that has to be taken into consideration. Only for this particular case we take the mixture of nanopowders & water to be homogeneous. The formula for specific heat of a homogeneous mixture is:
The values from the above mentioned formulae have been experimentally tested by L.Syam Sundar et al[25]. Their results are in good agreement with the values mentioned in literatures. A few graphs shown below, are testimony to the fact.
In the below quoted graphs L.Syam Sundar has taken Al2O3 as the nano particles and water as the base fluid. 0.2%, 0.4% & 0.8% are the different density concentrations at which these experiments have been carried out.
Figure : Density Vs Temperature [25]
Figure : Specific Heat Capacity Vs Volume Fraction [25]
Figure : Specific Heat Capacity Vs Temperature [25]
From these graphs it can be inferred that with an increase in volume fraction the specific heat decreases. This suggests that the nanoparticles help in absorbing the heat being transferred to the nanofluid.
Conclusion
From the reported literature, the following conclusions can be drawn firstly; nanofluids containing small amounts of nanoparticles have substantially higher thermal conductivity than those of base fluids. The thermal conductivity enhancement of nanofluids depends on the particle volume fraction, size and shape of nanoparticles, type of base fluid and nanoparticles and type of particle coating. Secondly, it is still not clear which is the best model to use for the thermal conductivity of nanofluids. Therefore it requires further investigation. Thirdly, the suspended nanoparticles remarkably increased the forced convective heat transfer performance of the base fluid. Lastly, increase in volume fraction of nanoparticles leads to a non-linear increase in the viscosity of the nanofluid. However, the effect of nanoparticles on the density of nanofluids is yet to be investigated.
