An axiomatic design approach in development of nanofluid coolants

Available online at www.sciencedirect.com

Applied Thermal Engineering 29 (2009) 75–90 www.elsevier.com/locate/apthermeng

An axiomatic design approach in development of nanofluid coolants In Cheol Bang a,*, Gyunyoung Heo b b

a Energy Sciences, Global Edge Institute, Tokyo Institute of Technology, 2-12-1-S6-13 O-okayama, Meguro-ku, Tokyo 152-8550, Japan Department of Nuclear Engineering, Kyung Hee University, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyunggi-do 446-701, Republic of Korea

Received 4 September 2007; accepted 4 February 2008 Available online 12 February 2008

Abstract The experimental data for nanofluids in thermal-fluid systems have shown that the new fluids promise to become advanced heat transfer fluids in terms of thermal performance. While enhancing thermal characteristics, the solid–liquid mixtures present an unavoidable disadvantage in terms of pumping cost for economic operation of thermal-fluid systems. In addition, there is a lack of agreement between experimental data provided in the literature. The present work found that there would be no comprehensible design strategy in developing nanofluids. In this work, the Axiomatic Design (AD) theory is applied to systemize the design of nanofluids in order to bring its practical use forward. According to the Independence Axiom of the AD theory, the excessive couplings between the functional requirements and the parameters of a nanofluid system prevent from meeting the functional goals of the entire system. At a parametric level, the design of a nanofluid system is inherently coupled due to the characteristics of thermal-fluid system; the design parameters physically affect each other sharing sub-level parameters for nanoparticles with making a feedback loop. Even though parts of the nanofluids are naturally coupled, it is possible to reduce and/or eliminate the degree of coupling by help of AD principles. From the perspective of AD, this implies that we are able to ascertain which nanofluid system is feasible in the light of functional achievement. This study contributes to establishment of the standard communication protocol in the nanofluid research. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Nanofluid; Heat transfer; Axiomatic design; Coolant; Nanoparticle

1. Introduction Nanofluids introduce a unique approach for treating more effective heat removal in thermal-fluid systems. In general, current thermal-fluid systems strive to achieve high thermal performance in an effort to maximize economics and safety. One way to achieve this purpose is by adding nanoparticles to the coolant of the system in order to improve thermal properties of the coolant, itself. It has been shown that a nanofluid consisting of metal or metal oxides nanometer-sized particles dispersed in a pure fluid such as water and ethylene glycol has a higher effective thermal conductivity than that of the pure fluid [1–3]. However, what is lacking for the practical use of nanofluids in a wide range of applications is an agreement or reproducibility between

*

Corresponding author. Tel./fax: +81 3 5734 3836. E-mail address: [email protected] (I.C. Bang).

1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.02.004

experimental data [4]. As the reason, we can find that this issue of nanofluids resembles similar problems of materials design. As Suh shown in Fig. 1a on materials development, many nanofluids researchers tend to view the nanofluid field as a highly coupled ‘‘tetrahedron” whose four vertices (performance, properties, structure, and processes) are interconnected to each other as shown in Fig. 1b [5]. The present design study has shown big merits in systemizing the nanofluid work and reducing a lot of trial-and-error efforts [5]. Furthermore, adding nanoparticles into a base liquid has shown not only an increase of effective thermal conductivity as a thermal characteristic advantage but also an increase of effective viscosity as an important drawback. For example, when the amount of particles is small, the heat transfer increase that is acquired may be small. On the other hand, too many particles may result in large shear stresses and pumping power requirement as a result. It is considered as an issue of competition or optimization [6]. This type of issues have existed even in developments of traditional heat

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I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

Performance

Properties

Nanofluid Performance

Processing

Nanofluid Physical Properties

Structure

Nanofluid Preparation Processing

Nanofluid dispersion structure

Fig. 1. The traditional tetragonal views of the general materials world and similar NF world [5].

transfer enhancement technologies which have been evaluated for the heat transfer performance under consideration of the competition between heat and flow performances. Therefore, there is the necessity for systematic design approach of nanofluids in order to bring nanofluid’s practical use forward. The lack of an agreement between experimental data acquired by different groups can be due to different preparation method, different suspension state, and different size or agglomeration of nanoparticles, as well as different shape of particles. In addition to considering general preparation methods of nanofluids, additional factors should be considered depending on a uniqueness of each application area. For example, nuclear industry should consider coolant activity by neutron radiation. In case of electronics application, a dielectric constant should be considered while the magnetic field effect on particles should be considered for high magnetic field environment of application. We presume that the ‘object-oriented design’ of the nanofluids should be necessary on the basis of the research achievements previously done. Given the top functional requirements that a nanofluid should meet, the object-oriented design enables us to have insights about not only what the must-have items are but also how we take the items, which is useful when we adopt an innovative concept that we have not dealt with before. The object-oriented design is akin of top–down thinking processes that organize objects and means while minimizing individuals’ subjectivity. Here we will illustrate an object-oriented design of nanofluids to give a systematic philosophy of developing such new coolant using Axiomatic Design (AD), which is one of the object-oriented design methodologies. We are therefore able to have the standard communication protocol on designing nanofluids. The design product developed by the present nanofluid theories and design axioms of the AD theory ensures achieving high thermal performance in an effort to maximize economics and safety. 2. Nanofluid coolant 2.1. Brief description of nanofluid as a coolant of a thermalfluid system It is necessary to remind the features of nanofluids required as a coolant in a thermal-fluid system. Because of small dimensions of nanoparticles, it has been consid-

ered that nanofluids may be easily fluidized and consequently, can behave like a fluid. This means nanofluids are considered as a conventional homogeneous singlephase fluid with assumptions of a uniform distribution of nanoparticles, negligible motion slip, and thermal equilibrium conditions [7]. The general consideration of such fluid in a thermal-fluid system is on forced convection heat transfer of uniformly heated tube under laminar or turbulent flow. A promising coolant of a thermal-fluid system should meet the requirements of both heat removal capability and pumping power limitation. To identify what kind of parameters as a desirable coolant are important, heat transfer backgrounds are reminded. The heat removal capability can be expressed as _ p DT ¼ qA ¼ hAðT w  T f Þ ¼ pkNuLðT w  T f Þ Q_ ¼ mC

ð1Þ

Similarly the pumping power is Dp 8m_ 3 L ¼f 2 2 5 W_ ¼ V_ Dp ¼ m_ q pqD m n Nu ¼ CRe Pr ; f ¼ CRea

ð2Þ ð3Þ

In Nu number, C, m, and n are often independent of the nature of the fluid and dependent of the geometry of a system. The nature of fluid is expressed with different Prandtl numbers. Nu ¼ CRem Prn quD cp l m Re ¼ ; Pr ¼ ¼ ; l k a

a¼

k qcp

ð4Þ

Above equations show that convection heat transfer and pumping power for general application depends on coupling of coolant’s thermo-physical properties (q, l, cp and k) if everything else is same [7]. Because nanofluids technology is to change such properties differently from other heat transfer enhancement methods in terms of system geometry, we should consider the nanofluids properties. The effective thermo-physical properties can be considered as follows. Basically, it is noted that the equations for other properties except viscosity are based on simple approximation of linear variation between two components depending on fraction. Density : qnf ¼ ð1  /Þqbf þ /qnp

ð5Þ

Specific heat : ðqcp Þnf ¼ ð1  /Þðqcp Þbf þ /ðqcp Þnp

ð6Þ

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

Thermal conductivity : k nf ¼ ð1  /Þk bf þ /k np ðlinear variationÞ

ð7Þ

Dynamic viscosity : lnf ¼ lbf ð1 þ 2:5/Þ½22

ð8Þ

Additionally, thermal diffusivity which measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy and Prandtl number to show whether fluid is heat conduction dominant or convection dominant can be checked in terms of the nature of coolant. Fluids of large a will respond quickly to changes in their thermal environment, while fluids of small a will respond more sluggishly, taking longer to reach a new equilibrium condition [8].   k ð1  /Þk bf þ /k np ¼ ð9Þ anf ¼ qcp nf ð1  /Þðqcp Þbf þ /ðqcp Þnp The Pandtl number can be used for a measure of the relative effectiveness of momentum and energy transport by diffusion in the velocity and thermal boundary layers. c l  m p ¼ Prnf ¼ k nf a nf   ð1  /Þðqcp Þbf þ /ðqcp Þnp ðlbf ð1 þ 2:5/ÞÞ ð10Þ ¼ ðð1  /Þqbf þ /qnp Þðð1  /Þk bf þ /k np Þ Fig. 2 shows the trend of water-based nanofluid properties by using the above-referred relations and the physical properties of materials as shown in Table 1. Nanofluids can be considered as fluids which show quicker response to the thermal environment and have relatively different growth of the velocity and thermal boundary layers compared to base fluids. For predicting the thermal conductivity of a nanofluid, Hamilton and Crosser’s model has been well known and it can consider the shape of particles differently from simple linear variation [9]. k nf ¼

k np þ ðn  1Þk bf  ðn  1Þðk bf  k np Þ/ k np þ ðn  1Þk bf þ ðk bf  k np Þ/

ð11Þ

where n is the empirical shape factor given by n = 3/w, and w is the particle sphericity, defined as the ratio of the surface area of a sphere with volume equal to that of the particle, to the surface area of the particle. Fig. 3 shows the comparisons between the linear variation and Hamilton and Crosser model. There is a large difference. It is noted that for our design study, it is enough to identify the trend of nanofluids properties depending on nanoparticles concentration and morphology regardless of the good prediction capability of a correlation.

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method of stability. In general, nanofluid preparation method is divided into two such as one-step method and two-step method. One-step method means that nanoparticles formed in a base liquid or inherently dispersed into liquid. Two-step method means that nanoparticles prepared separately are mixed into liquid. Especially, our concerns are on stability of suspension. At the beginning of the nanofluid study, nanoparticles seemed not to have any settlement issue due to its small mass or size. However, nanoparticles tend to agglomerate with each other. In particular, Brownian motions of particles accelerate its agglomeration. Therefore, the nanofluid requires the stability increase method with help of colloid science. From a viewpoint of the colloid science, the suspension stability can be increased by the use of a dispersing agent. It is known that in an aqueous environment, the change in solution conditions such as pH can be done and adsorption of a specific ion on the surface of particle bring out an increase in the repulsive charge between particles. However, it is noted that processing at low or high pH can cause corrosion on structural materials of a system [10]. Therefore, it has been reported that frequently, more complex chemicals are used to disperse particles well enough [10]. The stability of dispersions has been described by DLVO theory [11]. The theory provided the quantitative explanation of agglomeration by equating the total interaction potential equation VT term as the summation of the dispersion attraction VA and electrostatic repulsion VR especially for electrostatic stability. VT ¼VRþVA

ð12Þ

To extend into steric stability with polymers, the total interaction can be explained with VT ¼VRþVAþVS

ð13Þ

Fig. 4 shows the potentials depending on interparticle distance between two primary particles. Lots of studies for colloid stability have clearly described that stability of colloidal particles in all liquid can be controlled in principle as in an aqueous media by London dispersion forces and charge. The used chemical stabilizer and effects can be summarized as follows [10]:

2.2. Brief description of nanofluid preparation methods (suspension stability) affecting on nanofluid properties

– chemical stabilizer to produce a strong electrostatic repulsive force; – chemical stabilizer to reduce the van der Waals attractive force; – polymer adsorption to produce steric stabilization; – hydrophilic film adsorption to produce structural hydration forces.

Nanofluid is a colloidal suspension of nanoparticles into a liquid. Fundamentally, the preparation methods are same as colloid’s ones. Preparation of nanofluids is the key issue because it determines the thermo-physical properties due to

Also, in a few cases stabilization can be carried out by a combination of steric and electrostatic stabilization. It is important to note that one of main reasons why there is a lack of agreement between experimental data may be

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I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90 11

1 al2O3

10

SiO2

9

C

Heat capacity ratio

Density ratio

SiO2

0.8

Ag

8

al2O3

0.9

7 6 5 4

C

0.7 0.6 0.5 0.4 0.3

3

0.2

2

0.1

1

Ag

0 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

Volume fraction

0.8

1

0.8

1

121

10000

Einstein'seq

al2O3

Wang etal.

SiO2

101

Ag C

Viscosity ratio

1000

Knf /kbf

0.6

Volume fraction

100

81

61

41

10 21

1

1 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

Volume fraction 100

10000

al2O3-E

SiO2

Ag-W

SiO2-E

Ag-W

Ag-E

C-W

C-E

10

Ag

1000

SiO2-W

al2O3-W

al2O3

C

Prandtl number ratio

Thermal diffusivity ratio

0.6

Volume fraction

100

10

1 0

0.2

0

0.2

0.4

0.6

0.8

1

0.4

0.6

0.8

1

0.1

0.01

0.001

0.0001

1 0

0.2

0.4

0.6

0.8

1

Volume fraction

Volume fraction

Fig. 2. Physical property change of nanofluids.

due to difference of the suspension stabilizing method. The other reasons could be on the morphology such as particle size, distribution, and shape as well as material phase. Through all of the above-mentioned review, we identified what kind of factors are important for the present design work. We can summarize as follows:

U ¼ f ðconcentration of nanoparticles; morphology of nanoparticles; stabilization methodsÞ ð14Þ where, U represents a thermo-physical property of nanofluid.

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90 Table 1 Thermophysical properties of materials [8] Materials Metal oxide SiO2 (silica) TiO2 Al2O3 SiC Metal Fe Ni Au Cu Ag C (diamond) Fluids Water Ethylene glycol

K (W/m K) 300 K

q (kg/m3) 300 K

1.38 8.4 36 490 80.2 90.7 317 401 429 2300

cp (J/kg K) 300 K

2220 4157 3970 3160

745 710 765 675

7870 8900 19,300 8933 10,500 3500

447 444 129 385 235 509

1000 1132

4183 2349

0.6 0.258

l (Pa s) 300 K

0.0008513 0.0157

3. Design framework of nanofluids It is likely to overlook the fact that nanofluids should be prepared and classified depending on the object-oriented requirements that end users provide. Furthermore, unless the requirements are interpreted by a standardized protocol between people who have different concerns on nanofluids, it takes a long time to have solid understanding of nanofluid theories proposed and to make a step forward in an effective way because we have no idea of what we do not know, particularly in developing new scientific or engineering paradigm such as the design of nanofluids. This topic, that is, how to systemize the design process to achieve the functional requirements considering the uncertainty involved, is quite an old one in the arena of engineering education. We found that the Axiomatic Design theory had provided engineers with a standardized

79

design framework based on a top–down decomposition process, and schematic techniques to carry out design activities in a well-organized manner. The theories and practices of Axiomatic Design have been actively released and the Axiomatic Design theory has been also used to design new materials and materials-processing techniques [12]. In this context, we tried to interpret the correlations containing the properties of nanofluids and propose the design process of nanofluids using the Axiomatic Design theory. In order to make the integrity of the paper more perfect, the fundamentals of Axiomatic Design will be briefly described. The Axiomatic Design theory has been developed from a thought that design is being done empirically on a trial-anderror basis resulting from so many design mistakes and wasting budget. We feel the same way as there have been many similar mistakes in nanofluids research so far. Axiomatic Design defines the design as an interplay between ‘what we want to achieve’ and ‘how we want to achieve it’. To elaborately characterize the interplay, the AD proposes the design world which is made up of four domains as shown in Fig. 5: the customer domain, the functional domain, the physical domain, and the process domain. The customer domain is characterized by the needs that the customers or end users are looking for. In the functional domain, the customer needs are interpreted in terms of functional requirements (FRs) and constraints (Cs). To satisfy the specified FRs, we conceive design parameters (DPs) in the physical domain. Finally, to produce the product specified in terms of DPs, we develop a process that is characterized by process variables (PVs) in the process domain. In the case of developing materials, the customer domain specifies the desirable performance of materials with users’ voice. Then, in the functional domain, the desired performance in the customer domain is converted into the properties of the materials, which are the FRs. The DPs in the physical domain are the microstructure (or morphology)

10000

1000 al2O3-HC

Knf /kbf

SiO2-HC Ag-HC C-HC

100

al2O3 SiO2 Ag 10

C

1 0

0.2

0.4

0.6

0.8

1

Volume fraction

Fig. 3. Comparisons between linear variation and Hamilton and Crosser model.

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I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

+

FR0 FR1

VR (+VS)

FR11

DP0 FR2

FR12

Zigzagging

DP1

DP11

DP2 DP12

V VMAX

A

B

h

Fig. 6. Zig-zag design process [5].

VA

Fig. 4. Change of the interparticle potentials based on Kuk [11] (h = the separation distance between particle surfaces).

Mapping

{CA}

Customer domain

Mapping

{FR}

Functional domain

Mapping

{DP}

Physical domain

{PV}

Process domain

Fig. 5. Four domains of the design world [5].

which is the means or choice achieving the FRs. Finally, the PVs in the process domain specify how the microstructure determined can be created. It is of great interest to recognize that the design process driven by AD is very similar to that of nanofluid development. For our own purpose, the design process will be focused on the functional domain, the physical domain, and their interplay or mapping. It should be noted that the process domain can be easily considered because we have ideas on manufacturing nanofluids using the one-step or two-step process mentioned in the Section 1. The interplay between two domains is accompanied with top–down zig-zagging decomposition organizing the design hierarchy linking a high-level conceptual design and a lowlevel detailed design. This is illustrated in Fig. 6. We start at the top FR. From the top FR, we go to the physical domain to conceptualize a design and determine its corresponding DP. Then we come back to the functional domain to create FR1 and FR2 at the next level that collectively satisfies the highest level FR. FR1 and FR2 are the sub FRs characterizing the highest level DP. The decomposition process must proceed layer by layer until the design reaches the final stage, creating a design that can be implemented. It is

important to keep in mind that sub FRs should be Mutually Exclusive and Collectively Exhaustive (MECE) at each layer. The mapping process between the domains can be expressed mathematically in terms of the characteristic vectors that define the design goals which are FRs and design solutions which are DPs. fFRg ¼ ½AfDPg

ð15Þ

where [A] is called the design matrix. During the mapping process between the functional and physical domain, the following two axioms provided by AD prevent designers from serious design mistakes and therefore guide them to the better design decisions: Axiom 1: The Independence Axiom. Maintain the independence of the FRs. Axiom 2: The Information Axiom. Minimize the information content of the design. The design matrix helps us to apply the independence axiom in a mathematical manner. To satisfy the independence axiom, the design matrix must be either diagonal or triangular. When the design matrix [A] is diagonal, each of the FRs can be satisfied independently by means of one DP. Such a design is called an uncoupled design. When the matrix is triangular, the independence of FRs can be guaranteed if and only if the DPs are determined in a proper sequence. Such a design is called a decoupled design. Any other form of the design matrix is called a full matrix and results in a coupled design. Therefore, developing designs that create either a diagonal or a triangular design matrix corresponds to the systematic design process for a better decision. Unfortunately, in the real world, most of the designs cannot be uncoupled, and a decoupled design is usually considered satisfactory. In any circumstance, a coupled design is to be avoided. The lessons given by Axiomatic Design are applied to the design of nanofluids as well. It is desirable that the direction of developing a new nanofluid is to establish design hierarchy, to populate the design matrix, to identify couplings, and finally, to propose the way of eliminating such couplings so that nanofluids can show better improved thermal performance without significant economic loss of power dissipation.

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

4. Nanofluid design practices 4.1. Design mind of traditional nanofluids preparation 4.1.1. Requirements of traditional nanofluids preparation There are two classified processes used to produce nanofluids as above-mentioned: the one-step and the two-step method. The one-step methods are generally to produce the nanoparticles in base liquid environments and to achieve the dispersion state. The two-step method is extensively used in the synthesis of nanofluids using the available nanopowders. Nanoparticles are first produced and then dispersed into the base liquids with various stabilization methods [4]. Preparing nanofluids is the first key step in experimental studies with nanofluids which evaluate whether new fluids show an improved thermal performance and how much the properties change. The accurate information of stabilization methods have been too easily overlooked in most of experimental investigations. From the viewpoint of design engineer, this stage controlling not only the stabilization information, but also, nanoparticles parameters such as shape and size is the most important part which must includes design concepts in terms of heat transfer performance. The requirements for nanofluids shown in literatures has been described conceptually regarding only stability of suspension even though nanofluids ultimately pursuit improving thermal performance economically because there has been no enough information available on the detailed effects. For example, Xuan and Li proposed design requirements of preparation of nanofluids as follows [13]: – – – – –

Even suspension. Stable suspension. Durable suspension. Low agglomeration of particles. No chemical change of the fluid.

So far, nanofluids have been processed without any design principles. Namely, numerous trial-error approaches to develop nanofluids have been carried out. The reason why this type of ad hoc design and process in the nanofluid research is a big problem is that this preparation especially for two-steps can be unreliable, costly, and risky. In general, those processes have resulted in unreliable nanofluids and uncertainty in experimental data for nanofluids properties and performances. 4.1.2. Analysis of original nanofluid concept by using axiomatic design In this section, we intend to look over nanofluids studies in the literature in terms of original starting idea of nanofluids concept by using the AD. This is the simple analysis of the current nanofluid design. One of the key messages of AD is that we must think of design in terms of functional requirements. That is, define ‘‘what we want to achieve” before we proceed. If we are thinking functionally of a

81

nanofluid with this design mind, what we want to achieve is to enhance heat transfer or to increase thermal conductivity of a liquid (the original concept of nanofluid). The design problem is very simple because its functional requirement is only one. Based on the AD, when there is only one FR, coupling of functional requirements cannot occur, by definition, as coupling refers to the creation of interdependencies among FRs in the functional domain through improper selection of DPs. So with the one-FR design, the remaining design issue becomes the selection of the right DP. A general Axiomatic Design equation {FR} = [A]{DP} becomes FR1 ¼ A11 DP1

ð16Þ

Therefore, the FR of nanofluids can be stated as FR1 = Provide higher effective thermal conductivity compared to a base liquid (=keff). For the constraint, we can assume there will be a cost limit to adopt a new nanofluid as a coolant depending on applications. Here, we should design the morphology (microstructure) of the desired solid–liquid mixture that can satisfy the above FR. Fig. 7 shows the general morphology of nanoparticles acquired from a nanofluid [14]. For mapping from the functional domain to the physical domain, we simply assume that the effective thermal conductivity is in the form of (the simplest form based on linear variation). Thermal conductivity : k nf ¼ ð1  /Þk bf þ /k np

ð17Þ

Here, kbf and knp are determined depending on the proper selection of the materials according to the unique demand of application area. We consider the demand as a constraint (Cs). Therefore, we can choose volume fraction as DP1. However, in this case, nanofluid thermal conductivity simply is proportional to volume fraction. Therefore, we should fix it as a certain value as long as we have other critical volume as a constraint of a specific application. With such critical volume constraint,

Fig. 7. Nanoparticles [14].

82

/C ¼

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

Vp p ¼ m d3p Vf þVp 6

ð18Þ

the volume fraction is depending on m and d which are the number density of nanoparticles and size of nanoparticles. Therefore, we can choose one among number density and diameter as new DP. However, it is practically difficult to control number density. Finally, we can choose dp as DP1. The design equation is fk eff g ¼ X dp

Desired Heat Removal Performance

Coolants Properties

{CAs}

{FRs}

Nanoparticles Dispersion Structure (Morphology)

Processes (How to be created)

{DPs}

{PVs}

Physical domain

Process domain

ð19Þ

The element of design matrix can be acquired by understanding unknown mechanisms. For example, from the phenomenon of liquid layering at liquid/particle interface, it is known that with the particle size decreasing, thermal conductivity increasing excessively. Fig. 8 shows the design matrix of nanofluid based on initially proposed its concept. Through this analysis by using simple linear variation of the effective thermal conductivity, we can conclude that if we consider only one functional parameter, the best design of nanofluid is to use nanoparticles as small as possible. It means we can move to the next domain or mapping from the physical domain to the process domain. We can take care of this as a selection issue to provide the small size particles among nanoparticles/ nanofluids synthesis methods. Just now, it can be emphasized that among nanofluid preparation method, a method which can provide nanoparticles as small as possible is required. 4.2. Nanofluids’ axiomatic design evaluation In the Section 4.1.1, we already reviewed requirements of nanofluids suggested in the literature. Those are described in terms of not heat transfer but a stability

Customer domain

Functional domain

Fig. 9. Nanofluid design domain world based on Suh [5].

of colloidal suspension and chemical stability. We need to establish the appropriate design requirements of a nanofluid as a coolant for heat removal. Again, we first should ask ‘‘what we want to achieve”. In above section, we already tried to ask this and found a simple answer. However, in real application to a thermal-fluid system, the answer is not so simple. We will depict the design process of a new nanofluid on the basis of the Axiomatic Design framework. Fig. 9 shows the design domain world of nanofluids in terms of new materials design. At the development of a nanofluid, the customers in industries of thermal-fluid systems ask a better heat removal without significant pumping cost increase. In the Section 2.1, we have checked the major parameters. Therefore, we can start to design a nanofluid according to the AD theory. The top FR and DP can be stated as FR0

DP0

Design a new coolant with a better heat removal capability while preventing significant pumping cost increase. Nanofluid (or coolant with nanoparticles).

For a thermal-fluid system adopting convection heat transfer regime, the FRs of nanofluids may be stated as FR1 FR2 FR3

Fig. 8. Design matrix of nanofluid based on original concept created by Acclaro DFSSTM.

Provide high thermal performance = Q. Provide low pumping power (penalty) = W. Provide high stability of dispersion = Vt.

Eqs. (1) and (2) show that thermo-physical properties (q, l, cp and k) of a coolant are important parameters affecting thermal performance and pumping power. Here, density and heat capacity are fully dependent from selections of materials regardless of morphology of nanofluids (dispersion structure of nanoparticles) as above-mentioned in the figure of nanofluid design domain world. Therefore, we can select thermal conductivity and viscosity as DPs. In addition, dispersion stability is very essential requirement of nanofluids. In Fig. 4, we showed the total potentials depending on the separation distance. If particle B is

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

approaching particle A in the origin, there is an energy barrier, Vmax to interrupt the approach. In case of Vmax 6 0, particles agglomerate without any interruption. Therefore, the higher Vmax is, the more stable dispersion can be achieved. As the third functional requirement, we propose Vmax. DP1 DP2 DP3

knf lnf Vmax

Every step that we decompose a sub-level for detailed design, we should check coupled relations. The design matrix of this level FRs may be written as 8 9 2 9 38 X ? ? > > < FR1 > = < DP1 > = 6 7 ð20Þ FR2 ¼ 4 ? X ? 5 DP2 > > > > : ; : ; ? ? X FR3 DP3 According to the AD theory, an uncoupled design should have the following population: 9 2 9 8 38 X 0 0 > > = = < Q > < k nf > 7 6 ¼ 4 0 X 0 5 lnf ð21Þ W > > > > ; ; : : 0 0 X V max VT However, Eqs. (1) and (2) show viscosity can affect not only pumping power, but also heat removal capacity and the stability can add some additional effects in case of addition of some minor components such as surfactants and polymers. 8 9 2 9 38 X x x > > < Q > = < k nf > = 6 7 W ¼ 4 0 X x 5 lnf ð22Þ > > > > : ; : ; VT V max 0 0 X The small x indicates that the element has a relatively small effect on thermal performance or pumping power. For checking the Independence Axiom, here the matrix is upper triangular. Therefore, even though the matrix does not show ideal design, the independence of FRs can be guaranteed if and only if the DPs are determined in a proper sequence. Equation suggests that we can set the Vmax first, before deciding on viscosity. Here is an interesting thing. If we assume that naturally Vmax has sufficient level to prevent the agglomeration, the design matrix is reduced as follows: 

FR1 FR2



 ¼

X

?

?

X



DP1 DP2



 !

Q W



 ¼

X

x

0

X



k nf



lnf ð23Þ

However, according to top–down view, the above-mentioned design matrixes showing decoupled design are based on Eqs. (1), (2) and (12) introducing an additive of stabilizer (the stabilizer can affect Q and W). In reality of nanofluid preparation so far, (with bottom-up view) the design matrixes are as follows:

9 2 8 X
9 38 x < k nf = x 5 lnf ; : X V max   x k nf X lnf x X x

83

 or

Q W



ð24Þ

Fig. 10 shows the design matrixes for each design. The reason why the present nanofluids are in coupled design can be recognized through the sub-level design process. We first look into the backing theories based on research achievements so far in nanofluid area in order to find proper design parameters. The backing theories are based on features of nanoparticles such as particle size, shape and its number density as key changes in the new coolant. There are some mechanisms to explain nanofluid thermal conductivity enhancement: Brownian motion, liquid layering, and surface atom numbers. In Brownian motion of colloidal particles, particles move through liquid and possibly collide, thereby the collisions enable direct solid– solid transport of heat from one to another expecting to increase thermal conductivity. Brownian motion is characterized by the particle diffusion constant D, given by the Stokes–Einstein formula D¼

kBT 3pld

ð25Þ

where kB is the Boltzmann constant, l is the fluid viscosity, and d is particle diameter [15]. An interface effect that could enhance thermal conductivity based on interfacial resistance concept is the layering of the liquid at the solid particle interface, by which the atomic structure of the liquid layer is significantly more ordered than that of bulk liquid. Given that crystalline solids (which are obviously ordered) display much better thermal transport than liquids, such liquid layering at the interface would be expected to lead to a higher thermal conductivity [15]. As a heat boat concept of Choi [1], higher surface atom number is an advantage of nanoparticles. It is noteworthy to recognize that all suggested mechanisms may be enhanced with decreasing the particle diameter. For particle shape, the sphericity can be used as its representative. Particle sphericity is used as a measure of how spherical an object is. As such, it is a specific example of a compactness measure of a shape. The sphericity defined by Wadell, w, of a particle is the ratio of the surface area of a sphere (with the same volume as the given particle) to the surface area of the particle [16]: w¼

As p1=3 ð6V p Þ2=3 ¼ Ap Ap

ð26Þ

where Vp is volume of the particle and Ap is the surface area of the particle. In reality, we can judge the sphericity in 2-D TEM images of particles. Therefore, the sphericity practically is defined as follows [17]:

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Fig. 10. Uncoupled design, decoupled design and coupled design created by Acclaro DFSSTM.

w¼

Da ¼ Dp

pffiffiffiffiffiffiffiffiffiffiffi 4A=p P =p

1=2

ð27Þ

Sphericity ranges from 0 to 1 and smaller sphericity shows higher thermal conductivity based on Hamilton and Crosser model as shown in Fig. 11. For non-circular particles, the diameter may be defined as a representative value by borrowing the definition of the hydraulic equivalent diameter given in Eq. (28). d p ¼ Dh ¼

4A P

ð28Þ

Therefore, sphericity again becomes the function of primary particle size.

w¼

Da p1=2 d p ¼ Dp P 1=2

ð29Þ

In terms of thermal conductivity increase, smaller particle size is preferred because thermal conductivity is inversely proportional to dp. For a fixed volume fraction, the number density of particles (m, #/unit volume) is determined by the selection of dp according to the equation m¼

6 /V p d 3p

ð30Þ

The number density can contribute to distribution of particles in liquid volume resulting in decision of interparticle distance.

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

85

100

10 al2O3-tetra SiO2-tetra Ag-tetra C-tetra

Knf /Kbf

SiO2-cube Ag-cube C-cube al2O3-octa

Knf /Kbf

al2O3-cube

al2O3-tetra al2O3-cube

10

al2O3-octa al2O3-sp

SiO2-octa Ag-octa C-octa al2O3-sp SiO2-sp Ag-sp

1 0

0.2

0.4

0.6

0.8

1

C-sp

1 0

0.2

Volume fraction

0.4

0.6

0.8

1

Volume fraction

Fig. 11. Effects of sphericity on effective thermal conductivity based on Hamilton and Crosser model. (tetrahedron  0.671, cube  0.806, octahedron  0.846, and sphere  1).

Therefore, the DP1 can be decomposed into three specific FRs according to the effective thermal conductivity relation. FR11 FR12 FR13

Control primary particle number per unit volume Control primary particle shape Control primary particle size

DP11 DP12 DP13

m w dp

2

X

6 ¼40 0

0 X 0

38 9 0 > = 7 05 w > : > ; dp X

In the literature of nanofluids, viscosity is also depending on the size, shape, and volume fraction of nanoparticles like thermal conductivity. Here is the essential issue of nanofluids design. Viscosity shares same DPs as thermal conductivity with similar proportional relations. For stability, we can get the following information from the literature of colloidal science: V A ¼ AS=L=S ða=12H o Þ

8 9 2 X < FR11 = FR12 ¼ 4 ? : ; FR13 ? 2 X ¼40 0

? X ? 0 X 0

9 38 ? < DP11 = ? 5 DP12 : ; DP13 X 38 9 0
ð32Þ

ð33Þ

for Ho  a where AS/L/S is the combined Hamaker constant for the solid in the liquid and can be estimated from the equation [21] AS=L=S ¼ AS þ AL  2ðAS AL Þ1=2 ð31Þ

This equation suggests that we can set the value of particle size dp first, before deciding shape and number density of particles because we can control other DPs according to the above-mentioned relations. The DP2 is decomposed into three specific FRs according to the effective viscosity relation.

ð34Þ

This value is determined by selection of liquid and solid materials.   2pakTV 22 C22 1  v S mix þ 2pakTS el VS ¼ ð35Þ V1 2

FR21 FR22 FR23

Control primary particle number per unit volume Control primary particle shape Control primary particle size

where a ( d) is the particle radius, V1 the solvent molecular volume, V2 the polymer molecular volume, C2 the adsorbed amount of polymer (number of chains/area), and v the Flory polymer-solvent interaction parameter; Smix and are geometric functions that depend on the form of the segment concentration profile [18]. Therefore, DP3 is decomposed into specific FRs.

DP21 DP22 DP23

m w dp

FR31 FR32 FR33

Increase electrostatic repulsion (VR) Decrease London van der Waals attraction (Va) Increase steric repulsion (Vs)

DP31 DP32 DP33

f a (=dp/2) C (adsorbed amount of polymer (or surfactant)) or d (adsorbed layer thickness)

9 2 8 X > = < FR21 > 6 FR22 ¼ 4 ? > > ; : ? FR23

? X ?

9 38 > = < DP21 > 7 5 DP22 > > ; : X DP23 ? ?

86

9 2 8 X < FR31 = FR32 ¼ 4 0 ; : 0 FR33 2 X ¼40 0

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

0 X 0 0 X 0

9 38 0 < DP31 = 0 5 DP32 ; : X DP33 38 9 0 < f = 0 5 dp : ; X d

ð36Þ

Through this process, we found that all DPX of the first level are coupled with particle size, dp(DP13 = dp, DP23 = dp, DP32 = dp/2). Even, FR1 and FR2 share same DPs in the sub-level. Fig. 12 shows the overall design matrix including the coupling analysis of the DPs. We used the Acclaro DFSSTM Version 4.3. In Fig. 12, the red cell means the coupled design. A few cells above and below the diagonal are also highlighted with a blue background in addition to diagonal cells. Theses cells are preventing the design matrix from being decoupled resulting in coming close to ideal design in terms of

AD. It is to be noted that the coupling at the specific design matrix is the nature of nanofluid where a change in a design parameter regarding nanoparticles and stabilizer affects all of the performance parameters in a thermal-fluid system adopting convection heat transfer. It means that because two FRs of pumping power and thermal performance are coupled with same DPs of size, number and shape of nanoparticles in sub-level even though first level with DPs of thermal conductivity and viscosity seems to be independent, to achieve the original goal of nanofluid is difficult based on the present approach methods in the literature. Even, as we showed, the approach only with thermal conductivity improvement in previous section can lose the essential coupling of a thermal-fluid system adopting convection heat transfer. The present study shows such difficulty logically by using the axiomatic design approach. Fig. 13 shows the tree of nanofluid axiomatic design. A feedback junction (F), found when there’s a coupled design and indicates that feedback (red-lines) is required and that the Independence Axiom is violated. The ultimate goal of

Fig. 12. Design matrix of nanofluid created by Acclaro DFSSTM.

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

87

Fig. 13. Tree of nanofluid axiomatic design created by Acclaro DFSSTM.

this study, however, is to give a guideline or roadmap for how to approach in nanofluid development to reduce the trial-error procedure of time and cost. At least, this tree shows the possibility of nanofluid standard communication protocol for what we should focus on and make an agreement in the study of nanofluids. To realize the original ideas of nanofluid, we should seek some ways to reduce couplings in design parameters. Suggestion 1: (To remove FR3 or decouple FR3): Use materials of naturally and relatively good dispersion characteristics. For example, a metal oxide makes better stability due to hydration than one of a pure metal. In this way, we can discard the third FR regarding stability. Design will be simplified. However, we can lose the merit of higher thermal conductivity of metal compared to metal oxide. Suggestion 2: Control design parameters to reduce the viscosity increase and to increase thermal conductivity, respectively. It is known that a few viscosity-increasing factors such as controls of hydrophilicity or hydrophobicity: poor wetting in powders causes cavitations, foaming on shearing, and increased viscosity [10]. However, this is also a coupling factor affecting both thermal conductivity and viscosity. Fortunately, it is known that the particle shape has the stronger effect on viscosity rather than thermal conductivity while the particle diameter has the stronger effect on thermal conductivity [19].

We can redesign the design matrix. For example, FR12 DP12

Control particle size dp

FR22 DP22

Control particle shape w (P1/2)

Fig. 14 shows the improved design matrix and tree of nanofluids. It is noted that the design matrix of nanofluids can be easily referenced by other researchers and efficiently improved with new research achievements for design parameters. We can additionally consider constraints depending on application area in boundary of the AD theory. In case of electronic industry, as a base fluid, water is most widely used. However, water has a difficulty to be used in electronic cooling units in terms of electric conductivity based on dielectric constant. Most of electric cooling units have used dielectric fluids such as FC-72. Therefore, the selection of materials has the following constraints in terms of AD: – Cs: Low dielectric constant: In case of nuclear industry, radioactivity in a coolant is an important source of radiation external to a reactor. The radioactivity results

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I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

Fig. 14. A promising design matrix and tree of nanofluid created by Acclaro DFSSTM.

from: (i) by neutron activation of the coolant; (ii) by the activation of impurity atoms included in the coolant; and (iii) by radioactive atoms coming into coolant from the walls of the coolant channels in the reactor [20]. Nanoparticles will be considered as impurity.

– Constraint (Cs): Low coolant activation: Finally, we suggest evaluating nanofluids designed through this AD work with the overall heat/flow performance (HFP). For example, Webb [23] suggested its representative ratios for the quantification of the heat transfer

I.C. Bang, G. Heo / Applied Thermal Engineering 29 (2009) 75–90

efficiency and the pressure drop efficiency. These have been used for engineering analysis and design [24]. The overall heat/flow performance (HFP) can be used in order to quantify pumping penalty. We can redefine the ratios for nanofluids. hnf EHT ¼ hbf Dpnf EPD ¼ Dpbf EHT HFP ¼ EPD

ð37Þ ð38Þ ð39Þ

In pursuit of desired nanofluid performance, HFP must exceed one. We assure that the present design study for nanofluid AD contributes to shedding light in development of the optimized nanofluid or a standard nanofluid. 5. Conclusions This paper presents an axiomatic design analysis of nanofluids as an innovative coolant. For the AD approach, the recent achievements in nanofluids can be used with the help of colloid science. It gives clearer understanding for why there is a lack of agreement between experimental results from different groups. At a parametric level, the design of a nanofluid is inherently coupled due to the characteristics of thermal-fluid system sharing DPs between heat performance and flow performance; the design parameters physically affect each other sharing sub-level parameters for nanoparticles with making a feedback loop. The present approach can provide the design matrix as the standard communication protocol in the nanofluid research in order to bring its practical use forward. Further research achievements and ideas to decouple the design parameters of nanofluids are needed. Appendix. Coupling relation of the nanofluid design matrix The coupling between the FRs and DPs in the nanofluid design matrix can be identified with considering the previous research results. Jacopo [25] acquired the following correlations based on Pak and Cho [26]’s experimental data for thermal conductivity and viscosity: lnf ¼ lbf ð1 þ 39:11/ þ 533:9/2 Þ for

Al2 O3

2

ðA-1Þ

lnf ¼ lbf ð1 þ 5:45/ þ 108:2/ Þ for k nf ¼ k bf ð1 þ 7:47/Þ for Al2 O3

TiO2

ðA-2Þ ðA-3Þ

k nf ¼ k bf ð1 þ 2:92/  11:99/2 Þ

TiO2

ðA-4Þ

for

The heat removal capability and the pumping power can be k 0:5

expressed as Q / lnf0:3 and W / l0:25 nf in terms of thermal connf

ductivity and viscosity. Comparing the two nanofluids under the fixed concentration of 0.01 vol%, the alumina nanofluid has the RHS values of

k 0:5 f l0:3 f

 0:928 and 1.096,

89

respectively while the titania nanofluid has the RHS values of

k 0:5 f l0:3 f

 0:992 and 1.016. In addition, Maiga et al. [27] has

used the following correlations for the same kind of alumina nanofluid: lnf ¼ lbf ð1 þ 7:3/ þ 123/2 Þ for 2

k nf ¼ k bf ð1 þ 2:72/ þ 4:97/ Þ

for

ðA-5Þ

Al2 O3

ðA-6Þ

Al2 O3 k 0:5 f l0:3 f

This alumina nanofluid has the RHS values of  0:989 and 1.021. Even though the same materials-based nanofluids are used, the performances can be different. When we compared the properties acquired by different groups, some group’s nanofluid could acquire the better performance through a less coupling without recognizing the effect of coupling. As to the third functional requirement of the high stability, there are some of relevant experimental data. Li et al. [28] evaluated nanofluids stability based on zeta potential f of the copper nanoparticle surface caused by pH change. For pH 9.5, it showed Vmax  10 kT with 26 mV f while for pH 3, it showed Vmax < 0 with 5 mV f. On the other hand, Lee et al. [29] showed that pH change had the effects on the thermal conductivity of the CuO nanofluid. For examples, the CuO nanofluids with +30 mV f and 30 mV f, respectively for pH 3 and 11 revealed about 10% higher thermal conductivity compared to one with pH 8. Therefore, the design matrix, Eq. (24) represents the coupling of a nanofluid design due to sharing the sublevel design parameters such as size, number and shape of nanoparticles, as well as the stabilizer. References [1] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of Non-Newtonian Flows, FED-vol. 231/MD-vol. 66 (1995). [2] S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, Journal of Heat Transfer 121 (1999) 280–289. [3] J.A. Eastman, S.U.S. Choi, W. Li, L.J. Yu, Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Applied Physics Letter 78 (2001) 718–720. [4] X. Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: a review, International Journal of Thermal Sciences 46 (2007) 1–19. [5] N.P. Suh, Axiomatic Design: Advances and Applications, Oxford University Press, New York, NY, USA, 2001. [6] L. Gosselin, A.K.D. Silva, Combined ‘heat transfer and power dissipation’ optimization of nanofluid flows, Applied Physics Letters 85 (18) (2004). [7] R.B. Mansour, N. Galanix, C.T. Nguyen, Effect of uncertainties in physical properties on forced convection heat transfer with nanofluids, Applied Thermal Engineering 27 (2007) 240–249. [8] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, fourth ed., Wiley, 1996. [9] R.L. Hamilton, O.K. Crosser, Thermal conductivity of heterogeneous two component systems, I and EC Fundam 1 (1962) 182–191. [10] R.J. Pugh, L. Bergstrom, Surface and colloid chemistry in advanced ceramics processing, Surfactant Science Series 51, Marcel Dekker, Inc., New York, 1994.

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[11] Y.H. Kuk, Colloids and Surfactants, DaeKwang Ltd., 2002 (in Korean). [12] A.J. Schrauth, N.P. Suh, Axiomatic design of non-wetting hemocompatible surfaces, in: Proceedings of International Conference on Axiomatic Design, Firenze, 2006. [13] Y. Xuan, Q. Li, Heat transfer enhancement of nanofluids, International Journal of Heat and Fluid Flow 21 (2000) 58–64. [14] I.C. Bang, S.H. Chang, Boiling heat transfer performance and phenomena of Al2O3-water nanofluids from a plain surface in a pool, International Journal of Heat and Mass Transfer (2005) 2407–2419. [15] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer 45 (2002) 855–863. [16] H. Wadell, Volume, shape and roundness of quartz particles, Journal of Geology 43 (1935) 250–280. [17] L.F. Hakim, J.L. Portman, M.D. Casper, A.W. Weimer, Aggregation behavior of nanoparticles in fluidized beds, Powder Technology 160 (2005) 149–160. [18] D.H. Napper, Polymeric Stabilization of Colloidal Dispersions, Academic Press, London, 1983. [19] K. Kwak, C. Kim, Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol, Korea–Australia Rheology Journal 17 (2005) 35–40. [20] J.R. LaMarsh, A.J. Baratta, Introduction to Nuclear Engineering, Addison-Wesley Series in Nuclear Science, 2001.

[21] F.M. Fowkes, Advances in ceramics, Ceramic Powder Science, vol. 21, American Ceramic Society, 1987, p. 412. [22] D.A. Drew, S.L. Passman, Theory of Multicomponent Fluids, Springer, Berlin, 1999. [23] R.L. Webb, Principles of Enhanced Heat Transfer, Taylor and Francis, New York, 2005. [24] E.H. Ridouane, A. Campo, Heat transfer and pressure drop characteristics of laminar air flows moving in a parallel-plate channel with transverse hemi-cylindrical cavities, International Journal of Heat and Mass Transfer (2007) 3913–3924. [25] J. Buongiorno, Convective transport in nanofluids, Journal of Heat Transfer 128 (2006) 240–250. [26] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151–170. [27] S.E.B. Maiga, S.J. Palm, C.T. Nguyen, G. Roy, N. Galanis, Heat transfer enhancement by using nanofluids in forced convection flows, International Journal of Heat and Fluid Flow 26 (2005) 530– 546. [28] X. Li, D. Zhu, X. Wang, Evaluation on dispersion behavior of the aqueous copper nano-suspensions, Journal of Colloid and Interface Science 310 (2007) 456–463. [29] D. Lee, J. Kim, B.G. Kim, A new parameter to control heat transport in nanofluids: surface charge state of the particle in suspension, Journal of Physical Chemistry B 110 (2006) 4323–4328.