Thermal Conductivity of Nanofluids

Siw, Sin ChienUniversity of Pittsburgh

ENERGETICSME 3007

Oct 27, 2008

Outline

1. Introduction

2. Objective

3. Experimental results

4. Simulation results

5. Discussion and Comments

6. Conclusion

Introduction“ Nanofluid” is the name conceived to describe a fluid in which

nanometer-sized particles are suspended [Choi 2008].

knanoparticles > kbase fluids

X. Q. Wang & A.S. Mujumbar [2007]

Introduction-Why?

• Early days, researchers - heat transfer performance of fluid - changing flow geometry - boundary conditions - enhancing thermal conductivity of the fluid-dispersion of particles

• Base fluid can be enhanced by suspending micro/larger size solid particles. - large particles (micron size) ~ higher density , settling down - induced additional flow resistance ~ possible erosion - - basic concept of dispersing solid particles in fluids to enhance thermal conductivity can be traced back to Maxwell in the 19th Century. - - confined to mm-sized particles. - major challenge is the rapid settling of these particles in fluids.

• Nanoparticles stay suspended much longer than micro-particles and, if below a threshold level and/or enhanced with surfactants/stabilizers, remain in suspension almost indefinitely. - surface area per unit volume of nanoparticles is much larger (million times) than - surface area per unit volume of nanoparticles is much larger (million times) than that of microparticles (the number of surface atoms per unit of interior atoms of that of microparticles (the number of surface atoms per unit of interior atoms of nanoparticles, is very large). nanoparticles, is very large).

Criteria Microparticles NanoparticlesStability Settle Stable (remain in

suspension almost indefinitely)

Surface/volume ratio 1 1000 times larger than that of microparticles

Conductivity Low High

Clog in microchannel? Yes No

Erosion? Yes No

Pumping Power Large Small

Introduction

Table 1 : Comparison of the Old and New [Sarit K. Das et. a.l. 2008]

Introduction

• Unprecedented growth in electronics, communication and computing technologies - Increasing power , decreasing size, higher heat capacity ~ demand for suitable for next generation of flow and heat transfer (innovative cooling technology)

• Conventional method to increase heat flux rates: - extended surfaces such as fins and micro-channels - increasing flow rates increases pumping power

• However, current design solutions already push available technology to its limits.

• NEW Technologies and new, advanced fluids with potential to improve flow & thermal characteristics are of critical importance

• Nanofluids are promising solution to meet and enhance the challenges

Introduction

Thermal ConductivityEnhancement

Particle volume concentration

Base fluid material

Particle SizeParticle material

Temperature

pH

Objectives

1. Explore the experimental and simulation results of thermal conductivity enhancement reported by researcher in the recent years.

2. Compare the experimental and simulation results.

3. Identify the current issues in nanofluids.

Experiment – Preparation of nanofluids

• 2 techniques - The single step method The single step simultaneously makes and disperses the nanoparticles directly into a base fluid; best for metallic nanofluids. - Nanoparticles agglomeration is minimized (Pros) - Only suitable for low vapor pressure fluid (Cons)

- The two-step method (widely used) Nanoparticles was first produced and dispersed into the base fluids.

- Good for oxides nanoparticles (Pros)- Not suitable for metallic nanoparticles (Cons)

Figure 2: ZrO2 in water that produced

with Two Step method

Experiment – Preparation of nanofluids

Figure 3: Cu nanoparticles in ethylene

glycol produced with One Step method

Experimental Results – Effect of Particle Size

Figure 4 Effect of particle size for Al2O3 in water [Chon C.H. et. al. (2006)]

Figure 5 Effect of particle size for Al2O3 in ethylene glycol [H.U. Kang et. Al. (2006)]

- smaller particles, higher thermal conductivity - effective surface area increase as particle size decrease- increment due to Brownian motion- exponential increment as size getting smaller

Experimental Results – Effect of Particle Shape

Figure 6 Effect of particle shape for SiC in water Figure 7 Effect of particle shape for SiC in water

- cylinder shape nanoparticles ~ extended profile/geometry that can transport heat rapidly over significant distance.

- High aspect ratio nanoparticles may aligned parallel to the temperature gradient ~ enhance keff

cylindrical shape

cylindrical shape

Experimental Results – Effect of Temperature

Figure 8 Effect of temperature for Al2O3 in water

- temperature increment reduce the viscosity of the nanofluids – promote Brownian motion

- same volume fractions, highest thermal conductivity ~ highest temperature.

- ~ 7% - 10% increment for temp. range from 28oC – 35oC.

Figure 9 Effect of temperature for Al2O3 in water

Experimental Results – Effect of Temperature

Figure 10 Effect temperature for MWCNT in water Figure 11 Effect temperature for MWCNT in water

- temperature increment reduce the viscosity of the nanofluids

- Inconsistency; At 0.4% volume fraction – different keff

1.261.62

Experimental Results-Volume fraction

Figure 12 Particle volume fraction effect of Ag in water [ H.U. Kang et. al. (2006) ]

Figure 13 Particle volume fraction effect of Si in water [ H.U. Kang et. al. (2006) ]

- Silver nanoparticle (~8-15nm) ; Silica nanoparticle (~15-20nm)

- keff increase with volume fraction

Maxwell was one of the first to analytically investigate conduction through Maxwell was one of the first to analytically investigate conduction through suspended particles.suspended particles.

This equation and other equations for thermal conductivity e.g., Hamilton and This equation and other equations for thermal conductivity e.g., Hamilton and Crosser, Crosser, and and Rayleigh predict thermal conductivity reasonably well for dilute Rayleigh predict thermal conductivity reasonably well for dilute mixtures of relatively large particles in fluids.mixtures of relatively large particles in fluids.

When we go to the nanoscale we have to consider some effects that When we go to the nanoscale we have to consider some effects that dodo not not exist in large scalesexist in large scales. T. To improve the predictions we consider:o improve the predictions we consider: 1- Effect of nanoparticle-matrix interfacial layer1- Effect of nanoparticle-matrix interfacial layer 2- Effect of nanoparticle Brownian motion2- Effect of nanoparticle Brownian motion 3- Effect of nanoparticle cluster/aggregate3- Effect of nanoparticle cluster/aggregate

Simulation Results

Simulation Results – Jang and Choi (2007)

- Investigate the effects of various parameters

1. ratio of the thermal conductivity of the nanoparticles to the base fluid

2. volume fraction

3. nanoparticle size

4. temperature effect

Model of Nanofluid Thermal Conductivity – 4 modes

1st mode ~ Base Fluid Molecules

2nd mode ~ Nanoparticles

3rd mode ~ Collisions of Nanoparticles with Each Other

4th mode ~ Nanoconvection

Simulation Results – Jang and Choi

1st Mode - Base Fluid Molecules ~ derived based kinetic theory

f = volume fraction

kBF = thermal conductivity of the base fluid molecules

Ĉv = heat capacity per unit volume

= mean speed of molecules

l = mean free path

T = temperature

~ collisions of base fluid molecules with each other – indicate the heat transfer by thermal conductivity

C

dZ

dTfk

dZ

dTfCClJ BFBFBFVBFU )1()1(

3

1,

Simulation Results – Jang and Choi

2nd Mode – Thermal Diffusion of Nanoparticles

knano = thermal conductivity of nanoparticle

= mean speed of free electron

lnano = mean free path of heat carriers in nanoparticles

~ diffusion of nanoparticles

~ knano, thermal conductivity of nanoparticles using Chen’s correlation

dZ

dTfk

dZ

dTvClJ nanofnanoVnanoU

,3

1

v

fdZ

dTkJ nanoU

β = Kapitza resistance per unit area ~ 0.01

Simulation Results – Jang and Choi

3rd Mode – Nanoconvection

- collisions between base fluid molecules and nanoparticles by thermally induced fluctuations - assume linear temperature profile in thermal boundary layer

h = heat transfer coefficient

δT = thermal boundary layer

f = volume fraction

dZ

dTfh

TTfhTThJ T

T

BFnanoTBFnanoU

~

)()(

Simulation Results – Jang and Choi

4th Mode – Collisions of Nanoparticle with Each Other

dz

dTfCCJu TnanoVnano

,3

1

)10(~3

1 5,

OfCC TnanoVnano

~ Brownian motion (minimal effect among all modes)

Flux energy by collision of nanoparticles

fkd

dCfkfkk dBF

nano

BFparticleBFeff PrRe)1( 2

1

Effective Thermal Conductivity of Nanofluids

C1=18x106

Simulation Results – Jang and Choi

Figure 13 Effect of diameter of nanoparticle on thermal conductivity of nanofluids [Jang & Choi 2007]

- Size nanoparticles reduced, thermal conductivity increased.

~ Brownian motion is greater, nanoconvection become dominant.

- Maxwell model only valid as the size of the nanoparticles is greater than 30nm.

Simulation Results – Jang and Choi

Figure 14 Experimental data for temperature-dependent conductivity of the prediction from Jang & Choi model as comparison to Maxwell model [Jang & Choi 2007].

- ~3 times increment over a small temperature range (20-50oC).

- Temperature increased, dynamic viscosity decreased

~ nanoconvection remarkably increased with temperature.

Simulation Results – Monte Carlo

- Parameters in M.C. simulation

~ 1. thermal conductivities of base fluid and nanoparticles

2. volume fraction

3. size of nanoparticles & cluster generation effect

4. interfacial resistance

Figure 15 Comparison between simulated effective thermal conductivities with the experimental data (Al2O3-EG) [Yongjin Feng et al. 2008]

- Monte Carlo Simulation

~ As cluster size increased, keff increases rapidly. ~ promote rapid conduction

~ Size of the cluster – too big? Optimum size?

Figure 16 Monte Carlo simulation at different volume fraction as a function of radius of gyration [W. Evans et. al 2008]

Figure 17 Effective thermal conductivity for different aggregated clusters [W. Evans et. al. 2008]

Simulation Results – Monte Carlo

Contradiction

S

0

2)()0(

3

1dttSS

VkTkeff

i

fi

i

fi

fi vhfer

dt

dS

= heat flux

Thermal conductivity computed from integrated heat flux autocorrelation function [C.Nie et.al. (2008)]:-

with

fir

fie

hf

fiv

= position of the fluid molecules

= entropy of the fluid molecules

= velocity of the fluid molecules

= total energy of the fluid molecule including kinetic energy and interaction potential

4

2

296

85

R

Tkk

B

eff

kB = Boltzmann constant

keff = f (Φ, T, 1/R, 1/µ)

- keff enhancement ~ due to Brownian motion is proportional to volume fraction

- Temperature increase causes viscosity of decrease ~ keff increased

~ e.g. @ 300K, using water as base fluid with μ=7.978 × 10−4 Pa.s keff ~ O(10-15W/mK)

Contradiction

Contribution to the keff due to the Brownian motion of nanoparticles :-

Figure 18 Density distribution for water around a nanoparticle of 30nm @ 320K [C.Nie et. al 2008]

- Density distributions around a nanoparticle ~ are nearly the same.

- Low volume concentration of nanoparticles, ~ mean free path of phonon nearly the same.

- Phonon transport speed is related to the speed in the fluid

T

c

1

P

T

1

Contradiction

C = sound speed

ĸT = compressibility of material (can be determine from E.O.S)

It is recognized that the thermal conductivity in fluid and solid components of the nanofluid is related to the type of phonon excited, the phonon mean path, and the phonon transport speed, i.e., the speed of sound in the medium. [J.Che et al, 2000]

s

sc

cs

scs

T nP

n

P

n

Pn

1

- Ps = Pressure contribution from fluid molecules

- Pc = Pressure contribution from the suspended cylinder

- α = free volume fraction

- η = packing factors (e.g. for water ~ 0.466)

- n = number density

- negligible changes in compressibility, ~ very small speed of phonon transport

- Proposed Brownian motion has negligible effect.

- No enhancement effect

Contradiction

Discussion & Comments

- keff of alumina nanofluids ~ 8% to 33%

- There is no clear indication about the enhancement rate

- keff varies in the first 5 days, reproducible keff value is achieved later.

- keff of alumina nanofluids ~ 2% to 17% in 7 days period

- There is no clear indication about the exact enhancement rate

- keff varies in the first 5 days, reproducible keff value is achieved later.

~ Why?

Discussion & Comments

Figure 19 Effect of aging in the water based nanofluids on thermal conductivity [Timofeeva et. al 2007]

Discussion & Comments

- No tools/equipments that is capable to capture any visual data that can clearly explain this behavior as compare to macroscale experimental (e.g. internal flow ~ laminar and turbulent flow) ~ Dynamic Light Scattering (DLS) and Scanning Electron Microscopy (SEM) latest approach used to study the structure of the nanoparticles ~ DLS – limited to low volume fraction nanofluids (Φ<1.0%) ~ SEM – can only be performed after drying the base fluid.

- Lack of agreement between experimental results from different groups

- Lack of theoretical understanding of the mechanisms

Jang and Choi ~ No cluster generation effect Monte Carlo ~ Maximum size of the clusters is preset? Will the size of the cluster keep growing? ~ What if the clusters is too heavy and difficult to suspend? ~ Collisions of nanoparticles is not considered ~ Nanoconvection is not considered

Experimental and Simulation approach ~ Comparison

Remaining Challenges

1. Nanoparticles may form agglomerates and settle rapidly - forming a layer on the surface and reduced the overall heat transfer capacity

2. Larger nanoparticles or agglomerates may clog the narrow cooling channels

3. Pressure drop of the fluid increases considerably - Suitable choice of base fluid and nanoparticles for optimum performance.

4. Brownian motion effect – controversial - may need to be revisited – particularly on the effect of temperature

Discussion & Comments

Some of the reported Application

1. Transportation (2005) ~ CuO nanoparticles in engine transmission oil, claims to lower the transmission temperature at both high and low rotating speed. ~ any corrosive effects?

2. Electronics Cooling (2004) ~ Tsai et al used a water based nanofluid as working medium in a circular heat pipe - CPU and notebook- positive results as compare to deionized water.

3. Defense (2007) ~ Transformer cooling (Navy) – nanofluid to replace the transformer oil.

4. Space (2004) ~ Vassalo et al. reported a magnitude increase in the critical heat flux in pool boiling with nanofluids compared to base fluid alone. - potential for space applications ~ high power density.

5. Nuclear System Cooling (On-going) ~ MIT explore the impact of using nanofluids on the safety, neutronic and economic performance of nuclear systems.

6. Biomedicine (1999) ~ Jordan A. et al. reported that nanofluids can produced high temperature around tumor to kill cancerous cells without affecting healthy cells.

Conclusion

1. Nanofluids development is still considered in the research stage ~ many

factors need to be explore and optimized in both experimental and computational areas. ~ Issues/problems (e.g. nanoparticles agglomeration, settling, erosion potential and etc needs to be addressed) ~ The parameters chosen in the simulation is based on the researchers experience, instinct findings.

2. Heat transfer data are somewhat sparse. ~ no clear trends for application guidelines

3. Results may not be repeatable. ~ keff varies at time period.

4. Different types of base fluids (water, E-G, and etc) and nanoparticles (CuO, Al2O3, CNTs, etc) provide different enhancement ~ Suitable choice of base fluid and nanoparticles for optimum performance.

5. Ability to suspend the nanoparticles for a long period of time? – Clusters?

Thank you