DEVELOPMENT OF TWO-PHASE MODEL FOR ESTIMATION OF HEAT TRANSFER AUGMENTATION BY NANO-FLUIDS

7/30/2019 DEVELOPMENT OF TWO-PHASE MODEL FOR ESTIMATION OF HEAT TRANSFER AUGMENTATION BY NANO-FLUIDS

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A p r o j e ct r e p o r t o n

DEVELOPMENT OF TWO-PHASE MODEL FOR

ESTIMATION OF HEAT TRANSFER AUGMENTATION BY

NANO-FLUIDS

GUI DED BY

Dr. JYOTIRMAY BANERJEE

SUBMI TTED BY

Adnan Rajkotwala (U07ME 654)

Harshit Gupta (U07ME 627)

Mohit Gupta (U07ME 644)

Prabir Bhattacharjee (U07ME 649)Vineet Maheshwari (U07ME 679)

DEPARTMENT OF MECHANI CAL ENGI NEERI NG

SARDAR VALLABHBHAI NATI ONAL I NSTI TUTE OF TECHNOLOGY

I CHCHHANATH, SURAT-39 5 00 7, GUJARAT, I NDI A


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CERTI FI CATE

This is to certify that the project report titled DEVELOPMENT

OF TWO-PHASE MODEL FOR ESTIMATION OF HEAT

TRANSFER AUGMENTATION BY NANO-FLUIDS submitted by

Mr. Adnan Rajkotwala, Mr. Harshit Gupta, Mr. Mohit Gupta,

Mr. Prabir Bhattacharjee and Mr. Vineet Maheshwari, in

fulfilment of the requirement for the award of the degree of

BACHELOR OF TECHNOLOGY IN MECHANICAL

ENGINEERING of the Sardar Vallabhbhai National Institute

of Technology, Surat is a record of their own work carried

out under my supervision and guidance. The matter

embodied in the dissertation has not been submitted

elsewhere for the award of any other degree or diploma.

GUIDED BY:

Dr. J. BANERJEE

Mechanical Engineering Department

SVNIT, Surat -39500


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APPROVAL SHEET

This is to approve that aforementioned students have successfully

completed and submitted their project report in fulfilment of the

requirement for the award of the degree of BACHELOR OF TECHNOLOGY

IN MECHANICAL ENGINEERING of the Sardar Vallabhbhai National

Institute of Technology, Surat.

Examiner 1 : _______________________

Examiner 2 :_______________________

Examiner 3 :_______________________

Project Guide :________________________


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ACKNOWLEDGEMENT

We feel it as a great privilege in expressing our deepest and most sincere

gratitude to our supervisor, Dr. Jyotirmay Banerjee for his valuable

suggestions and guidance during the project work period, without which

this work would not have been accomplished. We would like to thank all

the professors and other non-teaching staffs for their kind help in carrying

out this work. We also thank the Chemical Engineering Department and

Applied Science Department for their cooperation. Last but not the least,

we would like to thank the world-wide researchers working in the fields of

Nanofluids and Heat Transfer who have done pioneering work in these

fields on which the project work is based. We are honoured to be provided

with this excellent opportunity. We also thank Mr. M. K. Rathore for his

kind cooperation and help.

Our experience while the project work was amazing. It is one of those

which we will certainly never forget. It was a great opportunity to

research on a topic in which we had interest through academic and other

readings but had never got a chance to do. The project work has no doubt

helped me explore in greater depths the fields of Nanofluids and Heat

Transfer. It has further strengthened our bondage to the field.


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ABSTRACT

Nanofluids are colloids of a base fluid and nanoparticles, whose sizeis usually of the order of 1-100nm. Nanofluids have been reported toexhibit appreciable heat transfer characteristics. The reason for thisenhancement was credited to the higher thermal conductivity of themetallic nanoparticles. In the initial models that were proposed for heattransfer in nanofluids, traditional correlations like Dittus-Boeltier wereextended simply by taking the volume fraction of the nanoparticles intoaccount. These models however failed to validate the experimentalobservations. Therefore new approaches have been investigated by theresearchers since the last decade. Our work involves experimentalinvestigation of heat transfer in nanofluids and development of numericalsimulation to verify the results. The nanofluid we chose to use is nano

copper particles and water as base fluid.

An experimental setup was prepared to study the heataugmentation effects on pure water and nanofluids. The flow takes placein a rectangular cavity with insulated side walls, which makes it a case ofbuoyancy driven flow or natural convection. Copper nanoparticles wereprocured and nanofluid was prepared to study the heat transfer effects. .The effects of surfactants on the settling time of the nanofluids, wasundertaken. Further a model of the experimental setup on solid-works hasbeen prepared. The experimental readings are analyzed and comparedwith the results obtained by numerical simulation. A two phase model isalso developed to validate the readings obtained by our experiments.


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TABLE OF CONTENT

1. INTRODUCTION1.1

LITERATURE REVIEW1.2 APPLICATION OF NANOPARTICLES IN INDUSTRIES

1.3 OUR MOTIVATION2. NANOFLUID PREPARATION,CHARACTERISATION AND

MATHEMATICAL MODELLING

2.1 PREPARATION OF NANOFLUID2.1.1ONE STEP METHOD2.1.2TWO STEP METHOD

2.2 FACTORS AFFECTING THERMAL CONDUCTIVITY2.2.1STABILIZERS2.2.2PH OF NANOFLUID2.2.3CONDUCTIVITY OF BASE FLUID2.2.4SIZE OF THE PARTICLE2.2.5SHAPE OF THE PARTICLE2.2.6PARTICLE VOLUME FRACTION

2.3 CHARACTERIZATION OF NANOFLUID2.4 MATHEMATICAL MODELING OF THE PROCESS

2.4.1HOMOGENEOUS FLOW MODELS2.4.2DISPERSION MODELS2.4.3TWO FLUID MODEL2.4.4NON DIMENSIONALISATION OF THE TERMS

3. EXPERIMENTAL INVESTIGATIONS OF HEAT TRANSFERCHARACTERISTICS OF NANOFLUIDS

3.1 INTRODUCTION3.2 OBJECTIVES3.3 APPARATUS

3.3.1COMPONENTS3.4 SELECTION OF MATERIALS

3.4.1POLYMETHYL METHACRYLATE (PLEXI GLASS)3.4.2HEATING SYSTEM

3.4.2.1 PID CONTOLLER THEORY3.4.2.2 PROPORTIONAL TERM3.4.2.3 DROOP3.4.2.4 INTEGRAL TERM3.4.2.5 DERIVATIVE TERM3.4.2.6 LOOP TUNING3.4.2.7 SHORTCOMINGS OF PID CONTROLLER


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3.5 COOLING SYSTEM3.6 RESISTIVE THERMAL DEVICES3.7 6 CHANNEL DATA ACQUISITION SYSTEM3.8 MEASUREMENT APPROACH3.9 PREPARING THE NANOFLUID3.10 PROCEDURE3.11 RESULTS3.12 CONCLUSIONS

4. NUMERICAL SIMULATION OF SINGLE PHASE MODEL4.1 INTRODUCTION4.2 PROBLEM DEFINITION4.3 NUMERICAL METHOD

4.3.1STREAM FUNCTION VORTICITY METHOD4.3.2DISCRETIZATION TECHNIQUE4.3.3GSSOR4.3.4CODE DEVELOPMENT

4.4 MATHEMATICAL MODEL4.4.1MODELS FOR CALCULATING PROPERTIES OF NANOFLUID4.4.2GOVERNING EQUATION FOR FLOW AND HEAT TRANSFER4.4.3NON-DIMENSIONAL FORM OF GOVERNING EQUATION

4.5 RESULTS AND DISCUSSIONS4.5.1INFLUENCE OF SOLID VOLUME FRACTION4.5.2INFLUENCE OF THE RAYLEIGH NUMBER4.5.3VARIATION OF THE NUSSELT NUMBER

4.6 CONCLUSION5. CLOSURE

5.1 CONCLUSION5.2 FUTURE SCOPE

5.2.1INVESTIGATION OF THERMAL CONDUCTIVITYENHANCEMENT BY NANOPARTICLES USING THIN

CYLINDER METHOD

5.2.1.1 INTODUCTION5.2.1.2 EXPERIMENTAL SETUP AND METHODS

5.2.2MAGNETIC NANOPARTICLES5.2.3MULTIPHASE MODEL

REFERENCES


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1.INTRODUCTON1.1 LITERATURE REVIEW

Heat transfer has always been one of the key areas in research, more so withthe advancement of science and technology. Effective thermal management is

presently one of the most vital challenges in many technologies because of the

constant demands for faster speeds and continuous reduction in device

dimensions. Recent technological advances in manufacturing have led to the

miniaturisation of many devices with various applications. The functionality and

reliability of such a system depends invariably on the efficacy of its heat transfer

units.

A very popular method to achieve adequate heat transfer in systems is to use a

heat transfer fluid in a closed thermodynamic cycle. A heat transfer fluid is afluid medium which is used in a system to add or remove heat in a controlled

manner. Commonly used such fluids like water, ethylene glycol, ammonia, CFCs,

mineral oils were widely used in commercial and industrial applications like

power generation, chemical plants, refrigeration and air conditioning. However

they failed to impress with their performance, when it came to high heat transfer

requirements, primarily because of poor thermal conductivities, which implied

the use of bulky heat exchangers and high pumping power. Over the past

decade, a new dimension has been provided by nano technology, which enables

the use of materials in their nano form i.e., of the size of 1 100 nm. As such,

metals, which are known to exhibit very high thermal conductivities, were mixed

with the conventional heat transfer fluids, to obtain a new heat transfer medium

called nanofluids.

Nanofluid is a suspension of nano particles, whose size is usually of the order of

1 100 nm, in a base fluid. The term nanofluid was first coined by Choi[1] , who

also showed that such a fluid can have significantly better heat transfer

characteristics than the base fluid. After that, several researchers performed

experiments on nanofluids by taking Cu, Al, Cu0, Al2O, Au, Ag, TiO2 and other

metallic nanoparticles, having high thermal conductivities in a base fluid likewater, mineral oils or ethylene glycol, which were conventionally used as

coolants for general purpose heat transfer equipment. The heat transfer

equipments employing nanofluids or heat transfer fluids, to be more general,

essentially have three types of convection processes, namely natural or free

convection, forced convection and mixed convection. Research in nanofluid is

also categorised according to the above mentioned classification, because each

phenomenon is, in itself, quite intensive both experimentally as well as

numerically.

It has been experimentally found that the thermal conductivity of nanofluids is

higher than its base fluid for same flow properties and it increases with increase


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in nano-particle concentration and decreasing particle size. Also for given flow

Reynolds number and particle size the convective heat transfer coefficient

increases with particle concentration in both laminar and turbulent regimes[2].

Further it was observed that for 3% volume fraction of nano-particles, the

increase in thermal conductivity was around 20%, as reported by Masuda et

al[3]. However similar experiments performed by Lee et al[4] showed an

increase of 8% and those by Wang et al[5], showed an increase of 12%.

The maximum increase was however around 40% for a volume fraction of 0.3%

as reported by Eastman et al[6].

Nevertheless there were speculations that the effective thermal conductivity may

also sometimes decrease, as opposed to the conventional belief. This was

supported by the experimental results of Li et al[7]. Also the results by Putra et

al[8], and Wen et al[9], which reported similar trends of decreasing thermalconductivity.

There was an unusual rise in thermal heat transfer coefficient as well, which,

however was still largely unexplained. Based on these observations, several

hypothesis were proposed, for modelling of convection phenomena in nanofluids.

Buongiorno[10], in his paper suggested seven mechanisms: inertia, Brownian

diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage, and

gravity settling. However, after an order of magnitude analysis, it was concluded

that Brownian diffusion and thermophoresis were the only two potential

candidates which can account for these observations. However there were noinstances where both the natural and forced convection experiments were

performed using the same experimental conditions. So the deterioration in heat

transfer for natural convection is still an area unaccounted for.

1.2 APPLICATION OF NANOFLUIDS IN INDUSTRIESThere has been an increasing need of superior cooling devices in engineering

applications like microelectromechanicaldevices (MEMS), LEDs, radiators,

semiconductor and integrated circuit. The conventional heat rejection methods

like liquid coolants, heat pipes and extended surface (fins) have already reached

their upper limit. Nanofluids in this respect offer a new horizon for the

researchers to explore. Many researchers have reported unusual thermo physical

properties shown by liquids having nano sized metal particles suspended in

them.Choi() was the first person who reported enhanced thermal conductivity in

liquid and metal nanoparticle emulsion. He coined the term nanofluid owing to

the size of metal particles. The idea of adding metal particles into a base fluid is

not a novel concept. It originated more than a century ago when Maxwell tried

adding micro sized solid metal particles to the fluid. It showed detrimental effect

in some cases due to the suppression of turbulence. Moreover the suspensionssettled down as sediment by the passage of time which leads to clogging of

channels and erosion of the container/tubing surface. They also suffered with


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large pressure drop. A high pumping power to maintain the flow was required as

viscosity of the fluid increased. Hence the idea of adding micro sized particles

into the liquid was discarded. However in case of nanofluids, it largely behaves

as a single phase fluid with minimum settling of metal particles. The pressure

drop and increase in viscosity is also found to be small.

1.3 OUR MOTIVATIONThere was however quite some disagreement about the performance of

nanofluids in natural convection in an enclosure, differentially heated at vertical

walls . Some Researchers like Khanafer et al [11] advocate that due to

dispersion of copper nanoparticles into water, the amount of heat transfer

increases significantly with increase in volume fraction at any investigated

Grashof number, while others like putra et al[8] have stressed that nanofluids

loose their effectiveness as heat transfer fluids in case of buoyancy driven flowor natural convection, and have given experimental results showing that in a

horizontal cylinder, differentially heated at the ends, the average nusselt number

of the enclosure, decreased with increasing the nanoparticle volume fraction.

However in the more recent times Corcione [6] have demonstrated that the

notion was wrong and that proper selection of variables can prove that

nanofluids are quite efficient in natural convection cases as well. He argued that

the above mentioned differences were insubstantial because Khanafer et al,

based the nusselt number on the thermal conductivity of the base fluid k f, while

Putra et al defined the nusselt number using the effective thermal conductivity ofthe nanofluid, keff , which brought to ambiguous interpretations of the data. The

present study was influenced by this very proposition, and it attempts to

investigate the behavior of nanofluids in natural convection.

Nanofluids can prove to be beneficial for a wide spectrum of industries ranging

from automotive industries to the energy sector to use in electronic devices as

well as biomedical industries. Roubert et al has reported that the use of

nanofluid as a coolant can cut industrial emissions. For e.g. in U.S, industries

can save up to 1 trillion British thermal Units of energy. In process industries,

suitable water based nanofluid can increase productivity. Michelins NorthAmerica tire processing plants are looking forward to obtain 10% increase in

productivity using commercially produced nanofluid. Donzelli et al highlighted

the use of nanofluid as a heat valve as it can be configured at will to reduce or

improve heat transfer. Hence they are also known as smart fluids. A group of

researchers at MIT are exploring the use of nanofluid in nuclear reactors.

Possible application includes pressurized water reactor (PWR), primary coolant,

standby safety systems, accelerator, targets, plasma directors and so forth.

Experiments on pressurized water reactors have shown promising resultsas it

increases the critical heat flux (CHF) between fuel rods and the water. In

automotive industries, it can replace a large number of automotive liquids likeengine oils, automatic transmission fluids, coolants and lubricants. The use of


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nanofluid can reduce the frontal area of the radiators up to 10%. This would

reduce the aerodynamics drag and consequently save fuel up to 5%. The major

obstacle in miniaturization and increasing compactness of electronic devices is

poor heat rejection. Nanofluids can be used as a liquid coolant in the electronic

devices to become the next generation cooling device. Since nanoparticles are of

the size of biomolecules, in biomedical Industries, they are used to ensure

proper delivery of nano-drug to the target living cells at an optimal temperature

of 37oC. This is done by controlling the heat flux and purging fluid velocity of the

supply. Nanofluids increase the surface tension thereby increasing the contact

angle and wettability. So they can be used in microscale fluidic applications such

as fluidic digital display devices, optical devices, and micro-electromechanical

systems (MEMS). Further, nanofluid can be used to replace water by other

organic liquids like ethyl glycol where temperature range falls beyond boiling

point or freezing point of water. Addition of nanoparticle in ethyl glycol can give

comparable thermal conductivity as of water.


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2.NANOFLUID PREPARATION, CHARACTERISATION ANDMATHEMATICAL MODELLING

2.1 PREPARATION OF NANOFLUIDDispersing the nanoparticles uniformly and suspending them stably in the host

liquid is critical in producing high-quality nanofluids for the study of their

properties and for applications. The key in producing extremely stable nanofluids

is to disperse nanoparticles before they agglomerate. The preparation methods

can be classified as physical process and chemical process. Physical processes

are mechanical grinding and Inert gas condensation technique while chemical

processes are chemical precipitation, chemical vapor deposition, micro

emulsions, spray pyrolysis and thermal spraying. Another classification can be

done on the basis of number of steps of preparation. Many two-step and one-

step physical and chemical processes have been developed for makingnanofluids. These processes can be summarized as follows:

2.1.1 ONE-STEP PROCESSIn a one-step process, synthesis and dispersion of nanoparticles into the fluid

take place simultaneously. The single-step direct evaporation approach was

developed by Akoh et al. and is called the VEROS (Vacuum Evaporation onto a

Running Oil Substrate) technique. However it is difficult to remove dry

nanoparticles from liquid prepared by this method. A modified VEROS process

was proposed by Wagener et al. in which they employed high pressure

magnetron sputtering for the preparation of suspensions with metal

nanoparticles such as silver and iron. Eastman et al. developed a modified

VEROS technique, in which Cu vapor is directly condensed into nanoparticles by

contact with a flowing low-vapor-pressure liquid (EG). Silver-water nanofluids

were produced using one-step optical laser ablation in liquid. A vacuum-SANSS

(submerged arc nanoparticle synthesis system) method has been employed by

Lo et al. to prepare Cu-based nanofluids. Another one-step physical process is

wet grinding technology with bead mills. Zhu et al presented a novel chemical

method for preparing copper nanofluids by reducing CuSO45H2O with

NaH2PO2H2O in ethylene glycol under microwave irradiation. In this method the

amount of NaH2PO2H2O and microwave irradiation can be used to control the

properties of copper produced.

One step method is mostly used for preparing metal nanoparticles without

forming any oxide. An advantage of the one-step technique is that nanoparticle

agglomeration is minimized, while the disadvantage is that only low vapor

pressure fluids are compatible with such a process.


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2.1.2 TWO-STEP PROCESSThe two-step method is extensively used in the synthesis of nanofluids

considering the available commercial nanopowders supplied by several

companies. In a typical two-step process, nanoparticles, nanotubes, or

nanofibers are first produced as a dry powder by physical or chemical methodssuch as inert gas condensation, wire electric explosion technique and chemical

vapor deposition. This step is followed by powder dispersion in the liquid.

Generally, ultrasonic pulses of 100W at 36 3 kHz for a period of six hours are

used to intensively disperse the particles and reduce the agglomeration of

particles. Nanoparticles prepared by this method which are reported in the

literature are Copper oxide (CuO2), TiO2, gold(Au), silver (Ag), silica and carbon

nanotubes. The major problem with two-step processes is aggregation of

nanoparticles. Most researchers purchase nanoparticles in powder form and mix

them with the base fluid. These nanofluids are not stable, although stability can

be enhanced with pH control and/or surfactant addition. Some researchers

purchase commercially available nanofluids. These nanofluids contain impurities

and nanoparticles whose size is different from vendor specifications.

Although the two-step process works fairly well for oxide nanoparticles, it is not

as effective for metallic nanoparticles.

2.2 FACTORS AFFECTING THERMAL PROPERTIES OF NANOFLUID

2.2.1 STABILIZERS

Stabilizers are surfactants which prevent nanoparticle from agglomerating due to

surface charge. Commonly used surfactants in the literature are laureate salt,

oleic acid and Cetyl Trimethyl Ammonium Bromide (CTAB), Sodium dodecyl

sulfate (SDS) etc. Addition of surfactants can change the surface properties of

the metal nanoparticles. Assael et al. experimentally studied the enhancement of

the thermal conductivity of carbon-multiwall nanotubes (C-MWNT)water

suspensions with 0.1 wt% sodium dodecyl sulfate (SDS) as a dispersant. Theyrepeated the similar measurements using hexadecyltrimethyl ammonium

bromide (CTAB). With respect to the surfactants concentration they found that

CTAB is better than SDS for C-MWNTs. Therefore proper selection of surfactant

depending on the properties of solution and the particle is important.

2.2.2 PH OF NANOFLUID

The pH of the solution plays an important role in preventing agglomeration of

particle. Xie et al investigated the effects of the pH value of the alumina

nanoparticle suspension. They found that the increase in the difference betweenthe pH value and isoelectric point of Al2O3, which lies between 7 and 9, resulted

in enhancement of the effective thermal conductivity. Isoelectric point is the pH


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at which a molecule carries no net electrical charge. This ensures the

nanoparticles are well dispersed and the nanofluid is stable because of very large

repulsive forces among the nanoparticles when pH is far from isoelectric point.

The pH of dispersion can be adjusted adding Hydrochloric acid (HCl).

2.2.3 CONDUCTIVITY OF BASE FLUID

Xie et al. [19] examined the effect of the base fluid material on the thermal

conductivity enhancement. The results show increased thermal conductivity

enhancement of the base fluid which has low thermal conductivity. These results

are important for the design of the heat exchange equipment where heat

transfer enhancement is needed.

2.2.4 SIZE OF THE PARTICLE

It plays an important role in the enhancement of heat transfer. As we go on

reducing the size the ratio of surface area to volume increases as the ratio is

inversely proportional to diameter of the particle. With larger surface area more

heat can be transferred. The Brownian motion, which plays a vital role in

explaining the enhancement in heat transfer, is also significant for small

particles. Brownian velocity varies inversely with diameter. 10nm to 15nm size

of the particle is considered as critical size where Brownian motion is more for

fixed particle volume fraction and temperature. This would follow that reducingthe size of the particle will lead to increase in thermal conductivity. However

Beck2008 stated that thermal conductivity does not show monotonic increase or

decrease with particle size. He opposed that that there is a lower limit as well ,

below which due to phonon scattering, the conductivity shows decreasing trends.

Their results indicate that the thermal conductivity enhancement decreases as

the particle size decreases below about 50 nm. There has been much debate

over the relation of particle size and thermal conductivity and no clear solution

has been arrived at until now. Thus it demands increasing number of

experimental work by the researchers.

2.2.5 SHAPE OF THE PARTICLE

The metal nanoparticle may be spherical, disc shaped or rod like depending on

the process of preparation. Murshed et al investigated TiO2 nanoparticles in rod

shape (1040) and spherical shape (15) dispersed in deionized water. Theyobserved that nearly 33% and 30% enhancement of the effective thermal

conductivity occurred for TiO2 particles of

10 40 and

15, respectively. Thus

rod shaped particles show more enhancements.Xie et al. also studied the effectof particle shape on the thermal conductivity enhancement in nanofluid.The

results were compared with respect to the geometric shape of the particle with


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the same material and base fluid. It indicates that increase in aspect ratio of the

particle will show increase in augmentation. Thus rod shaped nanoparticle

(aspect ratio 100), spherical nanoparticles (aspect ratio = 1) and disc-like

nanoparticles (aspect ratio 0.02) will follow decreasing trend of augmentation in

thermal conductivity. The role of the shape of particle is also confirmed by better

approximation of experimental results with Hamilton-Crosser model which is a

modified Maxwell model taking shape into consideration.

2.2.6 PARTICLE VOLUME FRACTION

In forced convection as well as in mixed convection, heat transfer coefficient has

considerable enhancement which increases with addition of the nanoparticle

volume fraction up to 1%. Eastman et al (2001) reported a 40% enhancement in

the effective thermal conductivity of ethylene glycol when 0.3% (v/v) coppernanoparticles were dispersed in the liquid, and Choi et al. (2001) reported a

150% enhancement in the effective thermal conductivity of synthetic oil

containing 1% (v/v) carbon nanotubes. However, above 1% particle volume

fraction, viscosity and resistance to the flow increases. Unlike forced convection,

experimental results show that in natural convection, heat transfer coefficient

decreases with increasing the nanoparticle volume fraction. However, such

established agreement is not developed and there is a striking lack of

experimental data for natural convection.

2.3 CHARACTERIZATION OF NANOFLUIDS

Good methods for characterizing nanofluids are critical to a correct

understanding of their novel properties. Characterization of nanofluids includes

determination of colloidal stability, particlesize and size distribution,

concentration, and elemental composition as well as measurements of thermo

physical properties. Forsome applications, measurement of the electrical

conductivity of nanofluids is required. Some of the most commonly used tools for

characterization include transmission electron microscopy TEM imaging and

dynamic light scattering DLS. One of the most measured thermo physical

properties is the thermal conductivity of nanofluids. Generally, three methods

are used to measure the thermal conductivity of nanofluids: the transient hot

wire method, the 3-sigma method, and the laser flash method.

2.4 Mathematical Modeling of the process

Over the years researchers have been attempting to develop convective

transport models to describe the behavior of nanofluids. As such two major


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approaches were followed, namely, the homogeneous flow models and the

dispersion models.

2.4.1 HOMOGENEOUS FLOW MODELS:

The models previously used to describe the phenomenon of heat transfer in

nanofluids were all based on the assumption that the mixture behaved as a

single phase component and the traditional heat transfer correlations like Dittus-

Boeltier, were extended to model them. The models, collectively termed as

homogeneous flow model [1, 2] took into account the increase in thermal

conductivity as the main factor responsible for the augmentation in heat

transfer. However it failed to accurately describe the experimental observations.

They mostly underpredicted the heat transfer augmentation that was actually

observed during experiments.

2.4.2 DISPERSION MODELS:

In the later stages, researchers started employing dispersion models [3] in

which thermal dispersion of nanoparticles along with the increase in thermal

conductivity was considered for the augmentation in convective heat transfer

coefficient. In this approach, the effect of nanoparticle/base fluid relative velocity

was treated as a perturbation of energy equation, with the introduction of a

dispersion coefficient, to describe the heat transfer augmentation. But an order

of magnitude analysis[4] proves that even dispersion effect is insignificant in

comparison to the effect of turbulent eddies.

The main reason behind the performance of nanofluids, is attributed to the

phenomenon of slip, caused by the relative velocity By using the slip mechanics

as proposed above we can develop the transport equations for a 2 phase nano

fluid system.

2.4.3 TWO FLUID MODEL

In this model the system will be treated as a 2 component mixture (base fluid +nanoparticles). The governing equations can be formulated considering following

assumptions:

1. The flow is considered to be incompressible flow.

2. No chemical reactions occur during the heat transfer augmentation.

3. Negligible or no external forces are present during the process.

4. Mixture is considered to highly dilute (


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6. The radiative heat transfer is negligible.

7. At local level nanofluid particles and base fluid are considered to be in thermal

equilibrium.

Assumptions (1) to (6) are valid for nanofluids. Assumption (2) is valid becausethe nanoparticles are chosen due to their inertness with the base fluid.

Assumption (3) is justified in light of the relative importance of transport

mechanism of the nanofluids. Assumption (4) is valid for most of the nanofluid

studies published so far, especially with (


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Where, tis time,jp is the diffusion mass flux for the nanoparticles (kg/m2s), and

represents the nanoparticle flux relative to the nanofluid velocity v. If the

external forces are negligible (Assumption (3)),jp can be written as the sum of

only two diffusion terms, i.e., Brownian diffusion and Thermopherosis:

pB pT

The coefficients DB and DT can be calculated as mentioned in the above sections.

Substituting these values the nanoparticle continuity equation becomes:

[B T ] Equation (1.5) states that the nanoparticles can move homogeneously with the

fluid second term of the (left-hand side), but they also possess a slip velocity

relatively to the fluid (right-hand side), which is due to Brownian diffusion and

Thermopherosis.

The momentum equation with negligible external forces is:

[ ] where, P is pressure. Note that Equation(1.6) is identical to the momentum

equation for a pure fluid. The stress tensor, , can be expanded assuming

Newtonian behavior and incompressible flow:

t where, the superscript t indicates the transpose of

v. If the viscosity is

constant, Eq. 2.3.4.10 becomes the usual Navier-Stokes equation. However, strongly depends on for a nanofluid.

The nanofluid energy equation as proposed in the BSL model is:

[ ] Where, Assumptions (1), (2), (3), (4), and (5) were used. c is the nanofluid

specific heat, T is the nanofluid temperature, hp is the specific enthalpy of the

nanoparticle material (J/kg), and q is the energy flux relative to the nanofluidvelocity v. Neglecting radiative heat transfer (Assumption (6)), q can be


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calculated as the sum of the conduction heat flux and the heat flux due to

nanoparticle diffusion (BSL):

Where, k is nanofluid thermal conductivity. Substituting the above equation in

the energy equation keeping in mind that and indicatingthe nanoparticle specific heat by cp we get:

[ ] Where, has been set equal to which follows from Assumption 7. If here

becomes 0 then the equation turns into the familiar single phase energy

equation. Now, putting the value of in the above equation we get, [ ] [B T ]

2.4.4 NON DIMENSIONALISATION OF THE TERMS

The velocity terms are non dimensionalised as:

The temperature terms theta as:

Pressure term as:

The length terms as:


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The volume fraction as:

And time as:

Using Boussinesqs approximation as well

Also the coefficients are defined as

After non-dimensionalising, the equations become:

Continuity equation

Momentum equation


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Nanoparticle continuity equation

Energy equation:


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3. EXPERIMENTAL INVESTIGATIONS OF HEAT TRANSFER

CHARACTERISTICS OF NANOFLUIDS

3.1 INTRODUCTION

Heat transfer has always been one of the key areas in research, more so with

the advancement of science and technology. Effective thermal management is

presently one of the most vital challenges in many technologies because of the

constant demands for faster speeds and continuous reduction in device

dimensions. Recent technological advances in manufacturing have led to the

miniaturisation of many devices with various applications. The functionality and

reliability of such a system depends invariably on the efficacy of its heat transfer

units.

A very popular method to achieve adequate heat transfer in systems is to use a

heat transfer fluid in a closed thermodynamic cycle. A heat transfer fluid is a

fluid medium which is used in a system to add or remove heat in a controlled

manner. Commonly used such fluids like water, ethylene glycol, ammonia, CFCs,

mineral oils were widely used in commercial and industrial applications like

power generation, chemical plants, refrigeration and air conditioning. However

they failed to impress with their performance, when it came to high heat transfer

requirements, primarily because of poor thermal conductivities, which implied

the use of bulky heat exchangers and high pumping power. Over the past

decade, a new dimension has been provided by nano technology, which enables

the use of materials in their nano form i.e., of the size of 1 100 nm. As such,

metals, which are known to exhibit very high thermal conductivities, were mixed

with the conventional heat transfer fluids, to obtain a new heat transfer medium

called nanofluids.

As such, an experiment has been developed to estimate the heat transfer

characteristics of such nanofluids, which is described in this section.

3.2 OBJECTIVES

1. To estimate the heat transfer characteristics of nanofluids and compare itwith that of the pure base fluid (water).

- A heater supplies heat flux to the apparatus (a cuboidal enclosure),using a PID controller to maintain the bottom wall at a constant

temperature, while a forced circulation at the top wall takes away heat

and maintains it at a constant temperature as well. The gradient of

temperature along the vertical axis gives an estimate of the heat

transfer characteristics.


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2. To measure the temperature distribution throughout the nanofluid volumeand compare the results with those obtained using numerical simulation.

- The Data Logger records the temperature distribution throughout thevolume of the nanofluid. A comparison with the numerical simulations

gives an idea of the effectiveness of the models used to simulate

simulate the system.

3. To measure thermal conductivity of a nanofluid and compare the resultwith that of pure fluid.

- The heat transfer augmentation in nanofluids has been attributed tothe increase in thermal conductivity. A circuit consisting of a

wheatstone bridge has been used to measure the thermal conductivity

of nanofluid and compare it with the base fluid. The method used here

is called the Transient Hot Wire method.

3.3 APPARATUS

The experimental setup has already been fabricated by Sensewell Industries,

Vadodara. A schematic layout of the experimental setup has been presented in

fig.3.1.

Figure 3.1: Schematic layout of experimental setup.


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It consists of the following components:

Figure 3.2: Experimental Setup


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Figure 3.3: Multiple views of the test apparatus

Figure 3.4: 6-channel Data Acquisition system


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Figure 3.5: PID Controlled Power supplier


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Figure 3.6: Isometric views of the test section

Figure 3.7: Experimental setup


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Figure 3.8: Detailed view of Test Section

3.3.1 COMPONENTS

It consists of the following components:

1. A cuboidal enclosure, whose vertical walls are made of Perspex(plexiglass). The horizontal walls are made of metal e.g., the top wall is of tin

and the bottom wall is made of steel.

2. A resistive heating coil attached to the bottom wall to maintain it at a

constant high temperature.

3. A cooling compartment attached to the top wall to maintain it at a

constant low temperature.

4. Resistive Temperature Detectors (RTDs) to sense the temperature.

5. A Data Logger to record the temperatures.

6. A PID controller to monitor the heating through the resistive coil.

Resistive

Temperature Detectors

Plexiglass (Perspex)

enclosure

Heating coil

Coling water inlet

Cooling water outlet

Resistive

Temperature Detector

Slot for Silver wire

Cooling water compartment


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3.4 SELECTION OF MATERIALS

3.4.1 POLY METHYL METHACRYLATE (PLEXIGLASS)

Poly methyl methacrylate is a transparent thermoplastic which is used to

prepare the vertical section of the experimental setup. It is a lighter,

transparent and cheaper replacement for glass. This material can withstand

temperature as high as 165oC depending on their manufacturing process. But

the material used to produce the setup has a melting point of 80oC, this was

in accordance to the requirement, is affordable and is easy to procure. It is

often preferred because of its moderate properties, easy handling and

processing, and low cost, but behaves in a brittle manner when loaded,

especially under an impact force, and is more prone to scratching compared

to conventional inorganic glass. Though being brittle this material finds varied

applications varying from use in simple experimental and constructionpurposes to acrylic glass was used for submarine periscopes, windshields,

canopies, and gun turrets for airplanes.

PMMA is routinely produced by emulsion polymerization, solution

polymerization and bulk polymerization. Generally radical initiation is used

(including living polymerization methods), but anionic polymerization of

PMMA can also be performed. To produce 1 kg of PMMA, about 2 kg of

petroleum is needed. PMMA produced by radical polymerization (all

commercial PMMA) is and completely amorphous. The glass transition

temperatures of commercial grades of PMMA range from 85 to 165 C; therange is so wide because of the vast number of commercial compositions

which are copolymers with co-monomers other than methyl methacrylate.

To create the current required model several rectangular blocks of 4mm thick

Perspex sheets were glued together; rectangular assembly was prepared

instead of a cylindrical assembly as this assembly is hard to manufacture and

in rectangular cavities it is easier to vary the shape. To do this cyanoacrylate

cement was used, more commonly known as superglue, with heat (welding),

or by using solvents such as di- or trichloromethane to dissolve the plastic at

the joint which then fuses and sets, forming an almost invisible weld.

Scratches may easily be removed by polishing or by heating the surface of

the material. This method was carried out as it is easier to be carried out in a

workshop with the simplest of the tools.

PMMA is a strong and lightweight material. It has a density of 1.171.20

g/cm3, which is less than half that of glass. It also has good impact strength,

higher than both glass and polystyrene. PMMA ignites at 460 C (860 F) and

burns, forming carbon dioxide, water, carbon monoxide and low molecular

weight compounds, including formaldehyde. PMMA transmits up to 92% of

visible light (3 mm thickness).


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PMMA swells and dissolves in many organic solvents; it also has poor

resistance to many other chemicals on account of its easily hydrolysed ester

groups. Nevertheless, its environmental stability is superior to most other

plastics such as polystyrene and polyethylene, and PMMA is therefore often

the material of choice for outdoor applications.

PMMA has maximum water absorption ratio of 0.30.4% by weight. Tensile

strength decreases with increased water absorption. Its coefficient of thermal

expansion is relatively high as (510)105 /K.

The thermal conductivity coefficient (K value) of PERSPEX and glass

3 mm single pane - 5.6 W/m-K for glass 5.2 W/m-K for Perspex

5 mm single pane - 5.5 W/m-K for glass 4.9 W/m-K for Perspex

3.4.2 HEATING SYSTEM

The heater is made of a resistive coil, which then induces heat to a steel plate

that heats the fluid as it is in direct contact with the fluid. Steel is used as it

is a good conductor of heat, it can withstand high operational temperatures

and is easier to obtain. The steel plate is in contact with the heater coil on

the other side which is attached to it and this setup is insulated using glass

wool.

Glass wool is an insulating material made from fiberglass, arranged into a

texture similar to wool. Glass wool is produced in rolls or in slabs, with

different thermal and mechanical properties. Glass wool is a thermal

insulation that consists of intertwined and flexible glass fibres, which causes

it to "package" air, resulting in a low density that can be varied through

compression and binder content. Due to the presence of the binding material

and the presence of air package it provides great insulation to heat and

heat loss is highly avoided. It can be a loose fill material, blown into attics,

or, together with an active binder sprayed on the underside of structures,

sheets and panels that can be used to insulate flat surfaces such as cavity

wall insulation, ceiling tiles, curtain walls as well as ducting. It is also used to

insulate piping and for soundproofing.

PID controller is used to supply heat to the heater. A heating element in a

setup needs to be provided with a control system which consists of a closed

loop feedback mechanism to maintain either a constant temperature or a

constant heat flux condition. The simplest controllers consist of a simple

automatic ON-OFF switch which operates in accordance with the feedback

received from the heating element. Even the most complex heater have the

same mechanisms, these are constant temperature based heating elements.


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This constant switching of power supply creates a constant residual in the

system thus leading to undesirable variation of the temperature values. The

sensed temperature is the process value or process variable (PV). The

desired temperature is called the setpoint (SP). The input to the process (the

water valve position) is called the manipulated variable (MV). The difference

between the temperature measurement and the setpoint is the error (e) and

quantifies whether the water is too hot or too cold and by how much.

Figure 3.9: PID block diagram

The most common type of controller used is a proportionalintegral

derivative controller (PID controller) which is a generic control loop feedbackmechanism (controller). A PID controller calculates an "error" value as the

difference between a measured process variable and a desired setpoint

which is the value of the temperature set by the user. The controller

attempts to minimize the error by adjusting the process control inputs.

These parameter P, I and D can be controlled individually or with

combination to each other as the following combinations P, I, PI, PD or PID.

PI controllers are fairly common, since derivative action is sensitive to

measurement noise, whereas the absence of an integral term may prevent

the system from reaching its target value due to the control action.

While adjusting the process control inputs the controller uses the value of

proportionalintegralderivative coefficients in the equation to dampen the

value of error so as to remove the residual or a constant error in the system

and to achieve a constant temperature from the heating element.

If the details or information of the process is unknown, a PID controller is the

most useful controller. By maintaining the three parameters in the PID

controller algorithm, the controller can provide control action designed for

specific process requirements. The response of the controller can be described

in terms of the responsiveness of the controller to an error, the degree towhich the controller overshoots the setpoint and the degree of system


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oscillation. Though, the use of the PID algorithm for control does not

guarantee optimal control of the system or system stability.

After measuring the temperature (PV), and then calculating the error, the

controller decides when to change the measured value (MV) and by how

much. When the controller first passes the current to the heating element, itmay heat the element only slightly if increase in temperature is desired, or it

may pass a large amount of current if high temperature is desired. This is an

example of a simple proportional control. In the event that the current does

not arrive quickly, the controller may try to speed-up the process by passing

more-and-more current as time goes by. This is an example of an integral

control.

Making a change that is too large when the error is small is equivalent to a

high gain controller and will lead to overshoot. If the controller were to

repeatedly make changes that were too large and repeatedly overshoot thetarget, the output would oscillate around the setpoint in either a constant

growing or decaying sinusoid. If the oscillations increase with time then the

system is unstable, whereas if they decrease the system is stable. If the

oscillations remain at a constant magnitude the system is marginally stable.

In the interest of achieving a gradual convergence at the desired temperature

(SP), the controller may wish to damp the anticipated future oscillations. So in

order to compensate for this effect, the controller may elect to temper their

adjustments. This can be thought of as a derivative control method.

If a controller starts from a stable state at zero error (PV = SP), then further

changes by the controller will be in response to changes in other measured or

unmeasured inputs to the process that impact on the process, and hence on

the PV. Variables that impact on the process other than the MV are known as

disturbances. Generally controllers are used to reject disturbances and/or

implement setpoint changes. Changes in temperature of the heating element

constitute a disturbance to the temperature control process.

A controller can be used to control any process which has a measurable

output (PV), a known ideal value for that output (SP) and an input to theprocess (MV) that will affect the relevant PV. Controllers are used in industry

to regulate temperature, pressure, flow rate, chemical composition, speed and

practically every other variable for which a measurement exists.


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3.4.2.1 PID CONTROLLER THEORY

The PID control scheme is named after its three correcting terms, whose sum

constitutes the manipulated variable (MV). The proportional, integral, and

derivative terms are summed to calculate the output of the PID controller.

Defining u(t) as the controller output, the final form of the PID algorithm is:

p i d (3.4.2.1)Kp: Proportional gain, a tuning parameter

Ki: Integral gain, a tuning parameter

Kd: Derivative gain, a tuning parameter

e: Error = SPPV

t: Time or instantaneous time (the present)

Pout: Proportional term of output

3.4.2.2 PROPORTIONAL TERM

Figure 3.10: PV vs time, for three values of Kp (Ki and Kd held constant)

The proportional term makes a change to the output that is proportional to

the current error value. The proportional response can be adjusted by

multiplying the error by a constant Kp, called the proportional gain.

The proportional term is given by:

(3.4.2.2)A high proportional gain results in a large change in the output for a given

change in the error. If the proportional gain is too high, the system can

become unstable.[note 3] In contrast, a small gain results in a small output

response to a large input error, and a less responsive or less sensitive


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controller. If the proportional gain is too low, the control action may be too

small when responding to system disturbances. Tuning theory and industrial

practice indicate that the proportional term should contribute the bulk of the

output change.[citation needed]

3.4.2.3 DROOP

A pure proportional controller will not always settle at its target value, but

may retain a steady-state error. Specifically, drift in the absence of control,

such as cooling of a furnace towards room temperature, biases a pure

proportional controller. If the drift is downwards, as in cooling, then the bias

will be below the set point, hence the term "droop".

Droop is proportional to process gain and inversely proportional to

proportional gain. Specifically the steady-state error is given by:

(3.4.2.3)Droop is an inherent defect of purely proportional control. Droop may be

mitigated by adding a compensating bias term (setting the setpoint above the

true desired value), or corrected by adding an integral term.

3.4.2.4 INTEGRAL TERM

Figure3: PV vs time, for three values of Ki (Kp and Kd held constant)

The contribution from the integral term is proportional to both the magnitude

of the error and the duration of the error. The integral in in a PID controller is

the sum of the instantaneous error over time and gives the accumulated


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offset that should have been corrected previously. The accumulated error is

then multiplied by the integral gain (Ki) and added to the controller output.

The integral term is given by:

(3.4.2.4)The integral term accelerates the movement of the process towards setpoint

and eliminates the residual steady-state error that occurs with a pure

proportional controller. However, since the integral term responds to

accumulated errors from the past, it can cause the present value to overshoot

the setpoint value.

3.4.2.5 DERIVATIVE TERM

Figure 3.11: PV vs time, for three values of Kd (Kp and Ki held constant)

The derivative of the process error is calculated by determining the slope of

the error over time and multiplying this rate of change by the derivative gain

Kd. The magnitude of the contribution of the derivative term to the overall

control action is termed the derivative gain, Kd.

The derivative term is given by:

(3.4.2.5)

The derivative term slows the rate of change of the controller output.

Derivative control is used to reduce the magnitude of the overshoot produced


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by the integral component and improve the combined controller-process

stability. However, the derivative term slows the transient response of the

controller. Also, differentiation of a signal amplifies noise and thus this term in

the controller is highly sensitive to noise in the error term, and can cause a

process to become unstable if the noise and the derivative gain are sufficiently

large. Hence an approximation to a differentiator with a limited bandwidth is

more commonly used. Such a circuit is known as a Phase-Lead compensator.

3.4.2.6 LOOP TUNING

Tuning a control loop is the adjustment of its control parameters

(gain/proportional band, integral gain/reset, derivative gain/rate) to the

optimum values for the desired control response. Stability (bounded

oscillation) is a basic requirement, but beyond that, different systems havedifferent behavior, different applications have different requirements, and

requirements may conflict with one another.

There are various tuning methods to make appropriate adjustments that lead

to a perfectly tuned setup with no oscillations and residuals. In our case we

used manual trial and error method which requires no mathematics but lead

to a proper understanding of the tuning method and effects of each and every

coefficient. Other popular methods include Zeigler-Nicholas method, some

software tools or Cohen-Coon model.

3.4.2.7 SHORTCOMINGS OF PID CONTROLLER

While PID controllers are applicable to many control problems, and often

perform satisfactorily without any improvements or even tuning, they can

perform poorly in some applications, and do not in general provide optimal

control. The fundamental difficulty with PID control is that it is a feedback

system, with constant parameters, and no direct knowledge of the process,

and thus overall performance is reactive and a compromise while PID

control is the best controller with no model of the process, better performancecan be obtained by incorporating a model of the process.

The most significant improvement is to incorporate feed-forward control with

knowledge about the system, and using the PID only to control error.

Alternatively, PIDs can be modified in more minor ways, such as by changing

the parameters (either gain scheduling in different use cases or adaptively

modifying them based on performance), improving measurement (higher

sampling rate, precision, and accuracy, and low-pass filtering if necessary), or

cascading multiple PID controllers.

PID controllers, when used alone, can give poor performance when the PID

loop gains must be reduced so that the control system does not overshoot,


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oscillate or hunt about the control setpoint value. They also have difficulties in

the presence of non-linearities, may trade off regulation versus response

time, do not react to changing process behavior (say, the process changes

after it has warmed up), and have lag in responding to large disturbances.

3.5 COOLING SYSTEM

The cooling system is placed at the other end of the cavity from the heater.

The cooling system is a cavity in itself and is connected to a cooling water

supply which maintains the temperature of the other end of the wall. The

cavity is made of tin which is used due to its conductive properties but it also

has considerable thermal resistance which maintains constant and controlled

heat supply.

The water is supplied continuously from a storage system which uses a

submersible pump to give a constant supply of water through inlet and outlet

valve. Resistive Thermal Devices are put at both the inlet and outlet valve of

the cooling system to retrieve the temperature at the same time interval as

that of the test fluid. The temperature variation pattern obtained is in

accordance with the rise of the temperature of the testing fluid. The cooling

fluid heats up as it extracts heat from the test fluid and the temperature

increment follows a parabolic path as clear from the graphical plots between

the inlet and outlet temperature and time.

The variation between the temperature of the upper layers of the fluid and

the cooling plate is due to presence of air gap which acts as a thermal

dielectric and restricts free passage of air. The air gap is present due to

constructional errors in the setup and is avoided as far as its possible by

using a suction system to create vacuum and fill it with the test fluid.

3.6 RESISTIVE THERMAL DEVICES

Resistance thermometers or resistance temperature detectors aretemperature sensing devices that advantage from the predictable change in

electrical resistance of some materials with changing temperature. As they

are almost invariably made of platinum, they are often called platinum

resistance thermometers (PRTs). They are slowly replacing the use of

thermocouples in many industrial applications below 600 C, due to higher

accuracy and repeatability.

Resistance thermometers are constructed in a number of forms and offer

greater stability, accuracy and repeatability in some cases than

thermocouples. While thermocouples use the Seebeck effect to generate a

voltage, resistance thermometers use electrical resistance and require a


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power source to operate. The resistance ideally varies linearly with

temperature.

Resistance thermometers are usually made using platinum, because of its

linear resistance-temperature relationship and its chemical inertness. The

platinum detecting wire needs to be kept free of contamination to remain

stable. A platinum wire or film is supported on a former in such a way that it

gets minimal differential expansion or other strains from its former, yet is

reasonably resistant to vibration.

5 RTDs are used out of which 3 of them are used for acquisition of

temperature of the test fluid and the other 2 are exploited for the cooling

fluid. The RTDs height can be varied thus temperature at different heights

within various fluids can be retrieved, but they are at constant distance from

each other at all times. The RTDs are connected to an 8 channel data logger

which is also the power supply for the RTDs.

3.7 6-CHANNEL DATA ACQUISITION SYSTEM

Multi-meters though being precise are ineffective when used for data

collection from multiple points and also when a power supply is needed for

the probes like RTDs. Thus, an externally powered data logging system is

used which can collect data from multiple probes at a given instance of time.

These data points collected are more accurate as compared to multi-metersas data acquisition systems sensitivity is higher.

A manually controlled 6-channel data logging system is used to collect the

data from the RTDs. The data was displayed depending on which probe is

under observation which could be changed by turning the knob at the front

end of the data logger. The least count of the data logger is 0.01oC. The data

logger can directly produce the temperature of the sample instead of voltage

characteristic which is received in a multi-meter, thus the time and man

power required for charting calibration characteristics and data interpretation

can be saved by using such systems for data acquisition.


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3.8 MEASUREMENT APPROACH

Nanofluid would be introduced in the Plexiglass enclosure and heated by

means of the heating coil present at the bottom. Heat would be removed

from the top by circulating cold water. Temperature distribution throughout

the nanofluid volume would be determined by moving three Resistive

Temperature Detectors (RTDs) through the length of the enclosure. To

determine thermal conductivity of nanofluid undergoing natural convection, a

thin silver wire of negligible resistance would be introduced through the slot

shown in the picture above. The change in resistance of the silver wire would

give corresponding change in thermal conductivity of surrounding medium

(nanofluid). Data collection from RTDs and control of heating coil energy

consumption would be done by using a common data-logger and controlling

system.

3.9 PREPARING THE NANOFLUIDS

After acquiring the apparatus (shown above), the next task was to prepare

the nano-particle solution. We prepared the copper oxide nanofluid using two

step method. The first step was the production of nanoparticles which was

done with the help of Electric wire explosion technique. The size of the

nanoparticles was reported to be 70nm. In the second step, the copper oxide

nanoparticles were mixed in water and agitated with the help ultrasonic

agitator or sonicator. CTAB was used as a surfactant which was procured

from Applied Sciences and Humanities Departments. We used the sonicatoravailable in the Chemical Engineering Department of SVNIT. The mixture was

agitated at 30KHz for 15 minutes. Settling times for nanofluids of different

concentrations was investigated.

Copper nanoparticles (Quantity: 22 grams) have been procured from

Neo Ecosystems and Software Limited, Dehradun.

Mode of Preparation: WEE (Wire Electrical Explosion)

Diameter: 70 nm

Purity: 99.7 %

Diameter: 70nm

Surface area: 3.88m2/gm

Density: 7.9 g/cc

The nanofluid was prepared by taking specific percentage of nanoparticles by

volume fraction, e.g., for preparing a 1% solution of Cu nanofluid, 99 ml (99

gms) of water was added drop wise from a burette to a test tube containing

7.9 gms (1 cc) of Cu nanoparticles. The mixture was then subject to

ultrasonic agitation at 30kHz for 15 minutes.


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Figure 3.12: SEM photograph of nanoparticles


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Figure 3.13: Nano-particle solution in water (2.5% by volume), prepared by ultra-sonic agitation

at 30 kHz.

Figure 3.14 Nano-particle solution after 4 hours

(Settling begins)


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The observations recorded were:

1. The nanoparticles started settling at the bottom of the test tube, after a

period of 6 hours.

2. the nanoparticles started sticking to the glass walls of the test tube.

In order to take care of these problems, a surfactant CTAB was used. The

surface active agent was influential in controlling the agglomeration of

nanoparticles as well as their sticking to the glass walls. However the settling

time could not be extended.

3.10 PROCEDURE

First, the remaining vital components of the experimental setup, viz. Coolingwater pump, data-logger and controlling system and silver wire would be

procured. Next, necessary circuits for resistance measurement of silver wire

would be fabricated. Then measurements with single fluid (water) will be

carried out followed by the introduction of nanofluids of different

concentrations.

The setup consists of a heater plate at the base which is heated with the

help of a power supply controller based on the PID technology. The PID

controller takes feedback from the heater and then controls the powersupply accordingly to maintain a constant temperature at the plate. The

heater is maintained at a constant temperature of 55oC.

The setup consists of a rectangular vertical section which is made up of Poly

methyl methacrylate. Resistive thermal devices are used for temperature

sensing purposes. In the first case the RTDs are kept at a constant distance

from the heater and from each other, thus their height remains constant.

Using these values obtained at a constant time interval of 2 minutes and a

temperature variation profile with respect to time is generated.

In the second case the RTDs are placed at varied heights from the heater,

with probe 1, probe 2 and probe 3 being at a distance of 5cm, 2cm and 8cm

respectively and at a constant distance from each other. The temperature

variation is collected at constant time interval of 2 minutes and this data is

plotted as well.

The temperature of the cooling fluid placed at the other end of the setup is

also collected at the same time intervals as that of the test fluid. The

temperature of the cooling system also increases continuously following

almost a linear path.


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A drastic temperature difference between the top layer of the fluid under

study and the cooling fluid is observed which can be attributed to the small

air gap which being a bad conductor of heat creates a huge variation of

temperature. This leads to an interesting observation that the variation of

temperature due to presence of air gap can be as high as 10 degree Celsius

even if its thickness is as low as few millimetres.


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3.11 RESULTS

Figure 3.15 :Temperature vs Time graph for constant probe height

Figure 3.16: Temperature deviation vs Time for constant probe height

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38

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42

44

46

48

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 50 60

Temperature(oC)

Time (min)

Temperature vs. Time

probe 1

probe 2

probe 3

average

-0.5

0

0.5

1

1.5

2

2.5

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 50 60

Temperature(oC)

Time (min)

Temperature deviation vs. Time

probe 1

probe 2

probe 3

average


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Figure 3.17: Absolute Temperature vs. Time for constant probe height

Figure 3.18: Absolute Temperature vs. Time for constant probe height

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30

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40

45

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Temperature(oC)

Time (min)

Absolute Temp. Avg.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Temperature(oC)

Time (min)


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Figure 3.19: Temperature vs Time with different probe heights

Figure 3.20: Temperature deviation vs Time with different probe heights

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38

40

42

44

46

48

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Temperature(oC)

Time (min)

Temperature increment vs. Time

probe 1

probe 2

probe 3

average

temperatur

e

0

0.5

1

1.5

2

2.5

3

3.5

4

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Temperaturedeviation(oC)

Time (min)

Temperature deviation vs. Time

probe 1

probe 2

probe 3

Average


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Figure 3.21: Absolute temperatire vs. Time with different probe heights

Figure 3.22: Average Temperature deviation vs Time with different probe heights

25

30

35

40

45

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Temperature(oC)

Time (min)

Absolute temp average vs. Time

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Temperature(oC)

Time (min)

Average temperature deviation vs. Time


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(a)

(b)

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Temperature(oC)

Time (min)

Temperature variation across wall (bottom) vs Time

probe 1 (bottom)

probe 2 (bottom)

probe 3 (bottom)

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Temp

erature(oC)

Time (min)

Temperature variation across wall (middle) vs Time

probe 1 (middle)

probe 2 (middle)

probe 3 (middle)


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(c)

Figure 3.23(a), (b), (c): Transient temperature profile at varying positions across the wall

Figure 3.24: Transient temperature profile at varying heights (probe 2)

0

5

10

15

20

2530

35

40

45

50

0 10 20 30 40 50 60

Temperature

(oC)

Time (min)

Temperature variation across wall (top) vs Time

probe 1 (top)

probe 2 (top)

probe 3 (top)

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Temperature(oC)

Time (min)

Temperature variation across the height (probe 2) vs

Time

Probe 2 bottom

Probe 2 middle

Probe 2 top


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3.12 CONCLUSION

Thus, it is observed that with passage of time, the temperature of the heater

considered constant as set, the temperature of the test fuid increases and

very soon reaches a stable contdition with low deviation in temperature

increment, also at different heights in the same plane in the cavity the

temperature varies due to natural convection and bouyancy effects. This is in

coherence with the natural convection theory and results from numerical

simulation as the fluid stops the mutual heat tranfer after reaching a certain

limiting value of temperature.

NOTE: Due to lack of instruments and lack of availability of proper stabilizers

and surfactants, stable nanofluids couldnt be produced in lab. Thus, water

was used as test fluid to study the effects of heat transfer and natural

convection due to heat transfer.


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4. NUMERICAL SIMULATION OF SINGLE PHASE MODEL

4.1 INTRODUCTION

Considering the difficulties in the experimental approach of studying nanofluids,

computational simulation of the nanofluid in different scenarios has become an

important tool. Lots of efforts have been put by various researchers but yet no

standardized equations have been put forward to completely predict the heat

transfer behaviour of the nanofluid. One of the reasons is the ambiguity

regarding the behaviour of nanoparticles in the nanofluid. As discussed in the

literature review, the variation of the thermal conductivity and rheology of the

nanofluid are not clearly understood and modeled. There are two approaches to

study nanofluid: Single phase approach and multiphase approach. Xuan and

Roetzel [4] proposed a single phase homogeneous flow model where the

convective transport equations of pure fluids are directly extended to nanofluids

with the properties of pure fluids replaced by those of nanofluids. Buongiorno

[10] proposed a multiphase or two fluid model in which he proposed on more

equation of particle mass diffusion in addition to standard continuity, momentum

and energy equations. It is not clear yet whether the single phase or multiphase

approach predicts the heat transfer behaviour of nanofluid more successfully.

In this chapter, the details of numerical simulation of buoyancy driven flow for

copper-water nanofluid in a 2D cavity are given. Single phase approach is used.

Nanofluid is considered to be incompressible and steady flow is assumed. Patel

et al. [3] model is used for calculating thermal conductivity of nanofluid. It is

considered to be best option because it explicitly includes the effect of Brownian

motion which is considered to be most important factor for the heat

augmentation in nanofluid in the present times. Nanofluid is considered to be

Newtonian and non-Newtonian and a comparative study has been presented.

Brinkmann model [7] is used to calculate the viscosity for Newtonian fluid and

Ostwald-de Waele model [18] (two parameter power law model) is used for non-

Newtonian behavior of fluid. Governing equations are converted to stream

function vorticity form. Finite difference approach has been used to discretizedthese equations. These discretized equations are solved implicitly by Gauss

Siedel Successive Over Relaxation method.

4.2 PROBLEM DEFINITION

Buoyancy driven flow of nanofluid in a 2D square enclosure is considered for

analysis as shown in fig1. Copper particles of 100 nm diameter are taken as

nanopaticles and water as a base fluid. Nanofluid is assumed to be

incompressible. The side walls of the enclosure are kept at constant temperatureTH (30 C)and TC (20 C) where TC is taken as reference temperature. The top


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and bottom walls are considered to be insulated i.e. non-conducting. The

boundaries have no-slip tangential and zero normal velocity boundary condition.

Nanoparticles are of same shape and size. Density gradients are considered only

in the buoyancy force with the help of Boussinesq approximation.

Insulated

Nanofluid

Y TH h g TC

l

X

Figure 4.1 - Physical model of the problem.

4.3 NUMERICAL METHOD

4.3.1 STREAM FUNCTION VORTICITY METHOD

For the incompressible flow, the density is constant and thus the Navier-Stokes

equation is decoupled with the energy equation. Though we have two equations

and two unknowns i.e. velocity V and pressure P, but there is no direct link for

the pressure between the continuity and momentum equations. To establish a

connection between the two equations, mathematical manipulations are

introduced. One of the simplest methods to solve incompressible flow equations

is stream function vorticity method. The momentum equations are converted to

vorticity equation in such a way that pressure term is removed and continuityequation is satisfied by using definition of vorticity in terms of stream function

(kinematic equation)

Vorticity transport equation:

(4.1)Stream function equation:

(4.2)


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From the stream function values, the velocity field can be calculated. The only

drawback of this method is that it is applicable to only 2D flows as stream

function is defined only for 2D (Though few researchers tried to use it for 3D but

it turned out to be really cumbersome).

4.3.2 DISCRETIZATION TECHNIQUE

Such partial differential equations cannot be solved by standard integration

techniques. So this type of equations is converted into algebraic equations by

different discretization techniques. There are three discretization techniques:

1. Finite Difference approach2. Finite volume approach3. Finite element approach

Finite difference approach has been used here because of its simplicity. It uses

Taylors expansion to give approximation of different differential terms.

4.3.3 GAUSS SIEDEL SUCCESSIVE OVER RELAXATION METHOD

The algebraic equations obtained after discretization are solved by GSSOR. It is

an iterative method. Implicit approach has been used i.e. initial conditions are

assumed for the whole grid. Then from every governing equation, one variable is

calculated for the given grid (in this case 2D cavity) and this goes on till the

difference between the variables in successive steps is lower than a residual

value. A residual of 10-7 is taken.

Convective term in the Navier-Stokes equation is considered to be non-linear

term as coefficient of variable is varying with it. This term makes most of the

numerical methods unstable. To solve this problem, upwinding scheme is used

and all the major variables are properly under-relaxed.

4.3.4 CODE DEVELOPMENT

A code has been developed for the natural convection in the 2D cavity with one

wall heated and other cooled. Standard results for different Rayleigh number are

available in the literature. A comparision of the results obtained with the

developed code is presented in table 1.

Table 4.1: Validation of the results by comparing Nusselt number (Nu) for different Raleigh

number (Ra)

Rayleigh number (Ra) Present De Vahl Davis Khanafer Fusegi

104

2.237 2.243 2.245 2.302

105

4.539 4.519 4.522 4.646

106

8.834 8.799 8.826 9.012


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Also it is required to check whether the grid size used is sufficient or not.

Optimum grid size is the size after which any further increase in size will not

affect the result. Also large grid size is not favourable as it will increase the

computational labour. Grid independence check is done. The solutions obtainedby 151 151 and 181 181 grids have negligible difference. Hence all the

solutions reported here are obtained using uniform grid of size 151 151.

4.4 MATHEMATICAL MODEL

4.4.1 MODELS FOR CALCULATING PROPERTIES OF NANOFLUID

The effective thermo-physical properties were calculated as function of

properties of both constituents and their respective concentrations. Thus, all

equations of conservation were directly extended to nanofluids. The major

properties affecting the flow and heat transfer are viscosity, heat capacity,

density, thermal expansion co-efficient and thermal conductivity. These

properties are calculated for the nanofluids using the suitable models proposed

by different researchers. The effective density (nf) and heat capacity (cp)nf of

the nanofluid in the present work are calculated from the classical formulation

for two phase mixure proposed by in the Xuan and Roetzel []:

(4.3)

() () () (4.4)

Similarly effective thermal expansion coefficient is calculated by

(4.5)

The model proposed by Patel et al. is considered the best option for calculating

the effective thermal conductivity because it includes the effect of micro-

convection in addition to conduction through liquid and conduction through solid

and thus defines the change of thermal conductivity with the change in

temperature. Here, it is assumed that the liquid medium and the nanoparticles

are in local thermal equilibrium at each location, and so the temperature

gradients in liquid and solid phases are the same. Patel et al. has assumed only

one-directional heat transfer in their model. Thus particle movement (by

Brownian motion) in one direction only will be helpful in increasing the heat

transfer.


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(4.6)

Where (4.7)

Here the Peclet number is defined as and the Brownian motion velocitygiven by ; where kb is the Boltzmann constant, f is the dynamicviscosity of the base fluid, dp is the diameter of the nano particle, dfis the size of

the molecules of base fluid and f is the thermal diffusivity of the base fluid.

The variation of viscosity with particle volume fraction is given bybrinkmann model for Newtonian nanofluid. For the non-Newtonian fluid, thevariation of the viscosity does not depend on any direct co-relation but depends

on the shear rates (which are influenced by velocity field) and thus indirectly

incorporate the effect of

Documents

DEVELOPMENT OF TWO-PHASE MODEL FOR ESTIMATION OF HEAT TRANSFER AUGMENTATION BY NANO-FLUIDS