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Energy, Exergy, and Friction Factor Analysis of Nanofluid as a Coolant for Electronics S.S. Khaleduzzaman,† R. Saidur,*,†,‡ I.M. Mahbubul,† T.A. Ward,† M.R. Sohel,† I.M. Shahrul,† J. Selvaraj,‡ and M.M. Rahman§ †

Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, 50603, Malaysia UM Power Energy Dedicated Advanced Centre (UMPEDAC), Level 4, Wisma R&D, University of Malaya, Kuala Lumpur, 59990, Malaysia § Mathematical and Computing Sciences Group, Faculty of Science, Universiti Brunei Darussalam, Tungku Link Rd, BE1410, Brunei ‡

ABSTRACT: Power dissipation, chip power consumption, and heat flux in electronic devices have been steadily increasing over the past decade, creating a need for improved methods of cooling them. Nanofluids can be used as coolant for these electronics to improve their thermal performance. This paper presents an analysis of the energy, exergy, and frictional efficiencies of different nanofluids that are used to cool electronics. This was done by creating an analytical model in which different nanofluids flowed (at 0.5 m/s) through a rectangular-shaped microchannel heat sink (with a constant heat flux). These different nanofluids consisted of water as a base fluid, with 0.4 to 2.0 vol % of copper oxide (CuO), aluminum oxide (Al2O3), and titanium dioxide (TiO2) nanoparticles. The results generally showed that thermal resistance decreases as the volume fraction of nanoparticles is increased. The CuO-water nanofluid was found to be the best coolant in terms of both minimizing thermal resistance and maximizing the pressure reduction. The energy efficiency of the heat sink increases as the volume fraction of nanoparticles increases. A maximum energy efficiency of 98.9% was obtained using the CuO-water nanofluid (at 2.0 vol %). The Al2O3-water and TiO2-water nanofluids (also at 2.0 vol %) produced a maximum energy efficiency of 77.5% and 68.4%, respectively. The lowest exergy losses were: 19.2, 20.9, and 25.1 W for TiO2-water, Al2O3-water, and CuO-water nanofluids (all at 0.4 vol %), respectively. The dimensionless friction factor was reduced as the nanoparticle volume concentration increased. Also, the pumping power increased (to a high of 0.0173 W) as the mass flow rate increased.

1. INTRODUCTION Modern electronics consumers are continuously demanding technological improvements such as increased transistor densities, miniaturization, and other innovations designed to obtain faster computational speeds. Greater heat fluxes are generated as a consequence of these innovations, which in turn requires the thermal management of these electronic components to be improved.1 The increased cooling demands of next generation 3D integrated chip designs imply that a future switch to liquid cooling systems is inevitable.2 Before designing a liquid cooling system for electronics, properties such as the: heat transfer coefficient, thermal resistance, energy and exergy efficiency, friction factor, and pumping power must be calculated. Therefore, it is prudent to derive analytical solutions for determining these parameters, prior to experimental analysis. Tuckerman and Pease3 tested a compact, water-cooled integral heat sink for integrated circuits. They found that, for laminar flow in confined channels, the heat transfer coefficient (h) scaled inversely with channel width, making microscopic channels desirable. They measured a maximum power dissipation density of 790 W/cm2 with a thermal resistance of 0.1 °C/W for a 1 cm2 area, whereas a high pressure reduction of 2 bar was also observed. Chein and Huang4 studied silicon microchannel heat sink performance using Cu-water nanofluid. They showed the performance of heat sink greatly improved due to an increase of thermal conductivity and thermal dispersion effect. Sohel et al.5 experimentally investigated heat transfer enhancement of a © 2014 American Chemical Society

minichannel heat sink using Al2O3-water nanofluid. They found the heat transfer coefficient enhanced up to 18% successfully. These studies showed the potential of nanofluids as a good liquid coolant for electronics devices. A nanofluid is a solid−liquid mixture that consists of a base fluid and nanoparticles. The term “nanofluid” was first introduced by Choi.6 Nanofluids are prepared by dispersing nanometer-sized particles (generally less than 100 nm) in a base fluid such as water, ethylene glycol, propylene glycol, oil, and other conventional heat transfer fluids. The addition of high thermal conductivity metallic nanoparticles (e.g., copper, aluminum, silver, etc.) to the base fluid increases the thermal conductivity of the mixture, thus enhancing its heat transfer capability. Bhattachary et al.7 numerically studied the impact of Al2O3water nanofluid on rectangular microchannel heat sink (MCHS) and found that the nanofluid coolant improves MCHS performance by reducing its thermal resistance. Also, Ebrahimi et al.8 investigated the temperature contours and thermal resistance on microchannel heat sink with multiwalled carbon nanotubes (MWCNTs)/water nanofluid. They showed that the microchannel heat sink temperature gradient was decreased with the increase of nanolayer thickness of Received: Revised: Accepted: Published: 10512

March 25, 2014 May 26, 2014 May 30, 2014 May 30, 2014 dx.doi.org/10.1021/ie501242b | Ind. Eng. Chem. Res. 2014, 53, 10512−10518

Industrial & Engineering Chemistry Research

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Table 1. Thermophysical Properties of Water and Nanoparticles18,19 properties

water

Al2O3

TiO2

CuO

density, ρ (kg/m3) viscosity, μ (N·s/m2) specific heat, cp (J/kg·K) thermal conductivity, k (W/m·K)

994.2 724.6 × 10−6 4178 0.6248

3970

4157

6500

765 46

710 8.4

535.6 20

channel has not yet been attempted. Therefore, the objective of this paper is to perform an analytical exergetic analysis to determine the performance of different nanofluid coolants. This will involve calculations of the energy efficiency, exergy loss, friction factor, and pressure reduction of different nanofluids flowing through a rectangular microchannel heat sink.

MWCNTs. They also found that thermal resistance decreased about 9% compared to water at fixed pumping power (Pp = 2.5 W) with 1.0 vol % of nanofluid. Farsad et al.9 showed 4.5% improvement of cooling performance by using Al2O3-water nanofluid compared to water as base fluid in copper MCHS. Also, they report that the nanofluid reduced both the thermal resistance and temperature of heat sink. Ho et al.10 experimentally measured the friction factor and pumping power in a microchannel heat sink by using Al2O3-water nanofluid. They discovered that the friction factor slightly rises when the nanofluid is used. Several other studies have also focused on microchannel based heat sinks with nanofluids.11 Most studies on the thermal performance of electronics cooling systems using nanofluids are based on heat transfer analysis, which neglects an examination of the energy, exergy, and waste heat. In order to improve a cooling system’s performance, it is necessary to optimize the energy consumption by balancing its utilization and/or recovering the waste heat. Exergy is defined as the maximum available work in a substance during a process that brings the system back to equilibrium with a heat reservoir. Exergy is that portion of energy that can transform to another form of energy. Analysis of exergy is necessary for improving the energy efficiency and minimizing losses, because it quantifies the location, type, and magnitudes of waste and losses.12 Exergy is destroyed in any process that involves a temperature change. Also, exergy keeps a significant contribution for the environmental benefit and economics of energy technologies rather than energy. Some researchers analyzed the energy and exergy associated with hot water electronic cooling systems. Kasten et al.13 proposed using hot water to cool electronic data centers in order to obtain a high system exergy. Numerical modeling of a manifold microchannel heat sink is used as the proof of principle for cooling the microprocessors of this data center. Also, Zimmermann et al.14 experimentally studied the energy and exergy efficiency of electronic cooling (also using hot water as a coolant). They showed that water temperatures as high as 60 °C are sufficient to cool microprocessors with over 90% energy efficiency. Moreover, Hamut et al.15 analyzed the performance of a coolant circuits in a vehicle during high ambient temperatures and applied the second law of thermodynamics to examine areas with low exergy efficiency. Similarly, Zaki et al.16 applied second law analysis of a water chiller cooler that was located in the intake of a gas turbine and used to cool the intake air. They showed that the exergetic power gain ratio declined at an average of 8.5%. Pandey et al.17 experimentally investigated the effects of nanofluids and water as coolants by studying the heat transfer, frictional losses, and exergy losses. They found that the nondimensional exergy loss was lowest with 2 vol % of nanofluids, for a coolant flow rate up to 3.7 L/min. Water gave the least losses for increased flow rates beyond 3.7 L/min. The literature review just presented reveals that the energy and exergy performance of nanofluid coolants in the micro-

2. METHODOLOGY 2.1. Nanofluids. In this paper, three types of nanofluids have been analyzed: Al2O3-water, TiO2-water, and CuO-water. The thermophysical properties of these nanoparticles and water at 33 °C (306 K) are presented in Table 1. The thermophysical properties of the Al2O3-water, TiO2water, and CuO-water nanofluids for 0.4%, 0.8%, 1.2%, 1.6%, and 2.0% volume fractions must first be calculated. The fundamental properties including thermal conductivity (knf), viscosity (μnf), density (ρnf), and specific heat (cp,nf) were obtained from Hamilton and Crosser,20 Brinkman,21 Pak and Cho,22 and Xuan and Roetzel23 models, respectively. This is shown in eqs 1−4: k nf =

k p + (n − 1)k f − (n − 1)φ(k f − k p) k p + (n − 1)k f + φ(k f − k p)

kf

(1)

In eq 1, a spherical shape is assumed for the nanoparticles, so that n = 3. 1 μnf = μ (1 − φ)2.5 f (2) ρnf = (1 − φ)ρf + φρp

(3)

(ρc p)nf = (1 − φ)(ρc p)f + φ(ρc p)p

(4)

2.2. Rectangular Microchannel Heat Sink (MCHS). 2.2.1. Energy Analysis. In the present work, the thermal performance of a copper microchannel is investigated.13 Figure 1 shows a schematic view of the microchannel heat sink that

Figure 1. Schematic view of the rectangular microchannel heat sink.

was considered in this analysis. The dimensions of this microchannel are listed in Table 2. For the analytical analysis, the heating test chip as a source of heat was assumed (that position is the bottom of the microchannel). The following assumptions were considered for this analysis: • The flow is incompressible, at steady state, and laminar. 10513

dx.doi.org/10.1021/ie501242b | Ind. Eng. Chem. Res. 2014, 53, 10512−10518


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Table 2. Geometric Dimension of the Copper Rectangular Microchannel Heat Sink channel width, Wc [mm]

channel wall thickness, Wfin [mm]

channel height, Hc [mm]

channel length, L [mm]

number of channels, n

thermal conductivity of copper, kcopper [W/m·K]

0.17

0.17

1.7

8.5

62

401

• The heat source produces a constant heat flux, and there is no heat loss from the surface. • The effect of body forces is neglected. • The thermophysical properties of nanofluids are constant. The hydraulic diameter (Dh) is the ratio between the crosssectional area over the wetted perimeter as shown in eq 5. Dh =

4WcHc 2(Wc + Hc)

microchannel sidewalls) to the coolant is determined from eq 13 (assuming fully developed flow).14 R conv =

(5)

ηfin =

(6)

m × Hc =

(7)

R bulk =

The Prandtl number (Pr) is the ratio of momentum diffusivity to thermal diffusivity of nanofluids, as shown in eq 8: ⎛ c pμ ⎞ ⎟ Pr = ⎜ ⎝ k ⎠nf (8)

Nuk nf Dh

(9)

(10)

Kasten et al. have introduced a one-dimensional thermal resistance model that is used to calculate the total thermal resistance (Rtotal) of the heat sink (per unit heat transfer area), as shown in eq 11:

η1st =

(11)

dbase kcopper

(16)

R base + R conv Abm

(17)

mċ p(Tnf,out − Tnf,in) Q̇

(18)

2.2.2. Exergy Loss. Exergy loss refers to irreversible losses that occur outside the control volume. It is a loss in work availability. In contrast, exergy destruction refers to irreversible losses within the control volume.25 It is proportional to the entropy of a process.12 Exergy destruction occurs when heat is transferred across a finite temperature difference. Some examples of this are heat transferred from electronics to a heat sink, heat transferred from the microchannel walls to the coolant, power loss to the environment, and friction between the coolant and channel walls of the heat sink. Exergy losses can be minimized by reducing the temperature difference of heat transport.14 The rate of exergy loss is calculated by assuming there is no work or heat transfer

Equation 11 shows how the overall thermal resistance is determined from the sum of the different resistance components in the system. Conduction heat transfer through the base plate of the heat sink (Rbase) can be calculated from eq 12. R base =

(15)

The heat removal capability (in terms of chip heat flux) is used to compare cooling concepts. The dissipated power of the chip is assumed to have a constant value of 90 W.13 From the first law of thermodynamics, the energy efficiency (η1st) for various volume fraction of nanofluid is the ratio of calories computed power removed by nanofluids over the devoted electrical power (Q̇ ). This is shown in eq 18.

13

R total = R base + R conv + R bulk

L(Wc + Wfin) 2n ρc pV̇

Tnf,out = Tchip − Q̇

The heat transfer coefficient (h) can be determined by using eq 10.

h=

2h × Hc kcopperWfin

The difference in the flow field and varying volumetric flow rate creates various temperatures and heat transfer patterns along the microchannel outlet position. In the heating test chip region, the chip temperature (Tchip) is kept constant and equal to 80 °C (which is the maximum allowable limit for chips). The outlet temperature (Tnf,out) can be determined by using eq 17.14

The Nusselt number (Nu) for laminar flow in a rectangular microchannel, which is a function of both Reynolds number (Re < 2000) and Prandtl number, is shown in eq 9:24 ⎛ D h ⎞0.81⎛ Hc ⎞−0.79 0.62 1/3 Nu = 0.1165⎜ Re Pr ⎟ ⎜ ⎟ ⎝ Wcd ⎠ ⎝ Wc ⎠

(14)

In eq 15, kcopper is the thermal conductivity of the microchannel heat sink. The thermal resistance associated with the heat transfer to the bulk nanofluid flow (Rbulk) is calculated from eq 16.14

ρnf V̇ n(Wc + Hc)μnf

tanh(m × Hc) m × Hc

where:

The flow distribution was assumed to be uniform (within the microchannel), and the dimensionless Reynolds number (Re) can be determined from eq 7: Re =

(13)

In eq 13, Hfin and ηfin represent the fin height and the fin efficiency, respectively. The fin efficiency (ηfin) is calculated by eq 14.

The inlet and mean velocity (um) of the nanofluids were assumed to be 0.5 m/s. This value is used to calculate the Reynolds number and mass flow rate (ṁ ) as follows: ṁ = numρnf Ac

Wc + Wfin Wch + 2hηfinHfin

(12)

where dbase denotes the base thickness and kcopper is the thermal conductivity of copper. The thermal resistance for convective heat transfer (Rconv) from the heat sink’s copper fins (i.e., the 10514



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showing a percent increase of 5.18% by using nanofluids. Shah et al.27 reported a thermal resistance of 0.39 K/W for an air cooled heat sink package. Zimmermann et al.14 reported a thermal resistance of 0.28 K cm2/W for a microchannel manifold heat sink, using hot water as the coolant. Figure 3 shows the effect of varying the CuO volume concentration on the resulting thermal resistance components.

between the system and surroundings. Exergy loss for a steady state nanofluid cooling system can be expressed by eq 19.17 E loss = Te[Cnf ln(Tnf,out /Tnf,in)]

(19)

Exergy loss caused by a reduction in fluid pressure can be neglected for liquids, because they are incompressible.26 The environmental temperature (Te) is assumed to be the same as the nanofluid inlet temperature. The heat capacity rate (Cnf) can be found by using eq 20. Cnf = (c p)nf ṁ

(20)

2.2.3. Pumping Power. The friction factor of the rectangular microchannel for laminar flow is indicated by eq 21.11

f=

56.9 Re

(21)

Pressure reduction (ΔP) through the microchannel heat sink is determined from the following equation: ΔP = f

2 L ρnf um Dh 2

Figure 3. Thermal resistance with nanofluid (CuO-water) nanoparticle volume fraction.

(22)

Finally, the required power to pump (Pp) the nanofluid through the channel is calculated with eq 23. ṁ Pp = ΔP ρnf (23)

(Only the CuO-water nanofluid is considered because this nanofluid was found to give the best results (Figure 2).) The rate of conductive heat transfer through the copper base plate is unaffected by the nanofluids, so the thermal resistance of the base plate (Rbase) is constant. This heat is then convectively transferred from the base plate to the heat sink fin of the microchannel. The convective thermal resistance (Rconv) significantly declines as the nanoparticle volume fraction increases. (This is due to heat absorption by fluids and an increase in fluid temperature.) The thermal resistance of the bulk flow rate (Rbulk) increases as the nanoparticle volume fraction increases. Although the total circulated area is fixed, the flow rate rises as the volume fraction increases. Figure 4 shows the effective change in energy efficiency as the nanoparticle volume fraction is varied. The energy

3. RESULTS AND DISCUSSION 3.1. Thermal Resistance and Energy Efficiency. The effects of nanoparticle volume concentration on thermal resistance and pressure reduction are shown in Figure 2.

Figure 2. Thermal resistance and pressure reduction characteristics with nanoparticle volume fraction.

These results show that the thermal resistance declines and pressure reduction rises as the nanoparticle volume fraction is increased. The lowest thermal resistance found was 0.000179 Kcm2/W (9.92 × 10−5 K/W) for the CuO-water nanofluid. The Al2O3-water and TiO2-water nanofluids’ minimum thermal resistances were 0.000181 and 0.000182 Kcm2/W, respectively. The decreasing rate of thermal resistance compared with pure water (the base fluid) was found to be 4.19%, 3.17%, and 2.74% for the CuO-water, Al2O3-water, and TiO2-water nanofluids, respectively (at 2.0 vol %). The pressure reduction was identical for all three nanofluids. The minimum and maximum pressure reductions were 1853 Pa (at 0.4 vol %) and 1929 Pa (at 2.0 vol %), respectively. The maximum pressure reduction can be compared with the base fluid (pure water) pressure of 1834 Pa,

Figure 4. Energy efficiency with nanoparticle volume fraction.

efficiency rises significantly as the nanoparticle volume fraction increases. The maximum energy efficiency is 98.90% for CuOwater nanofluids (at 2.0 vol %). Energy efficiencies of 77.47% and 68.25% were obtained for the Al2O3-water and TiO2-water nanofluids, respectively (for the same volume fraction). This can be compared to pure water, which had an energy efficiency of 9.22%. The energy efficiency of the CuO-water nanofluid increased by 70.73%, as the volume concentration was increased from 0.4% to 2.0%. 3.2. Exergy Loss. Figure 5 shows the exergy loss variation with nanoparticle concentration. Exergy loss increases as the 10515



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dominates over friction factor. The reverse is true at low densities. The relationship between friction factor and volume fraction is shown in Figure 7. For the Al2O3-water and TiO2-

Figure 5. Variation of exergy loss with nanoparticle volume fraction for different coolant.

nanoparticle volume fraction is increased. This variation is a function of the heat capacity rate, inlet and outlet of coolant temperature, etc. The heat capacity rate decreases as the nanoparticle volume fraction increases. The heat capacity depends on the mass flow rate and the specific heat of the nanofluid. The mass flow rate rises as the nanoparticle volume fraction (density) increases, but the specific heat decreases. The increase in mass flow has a much more significant effect on heat capacity than the reduction of specific heat. Thus, the system heat capacity rate declines, and the exergy loss increases, as the nanoparticle volume fraction rises. Exergy losses for the CuOwater, Al2O3-water, and TiO2-water nanofluids were found to be 25.09, 20.91, and 19.23 W (at 0.4 vol %), respectively. The highest exergy loss (85.93 W) occurs for the CuO-water nanofluid at 2.0 vol %. Maximum exergy losses of Al2O3-water and TiO2-water nanofluids were found to be 67.81 and 60.02 W, respectively (at the same volume fraction). Pandey et al.17 found similar results, like exergy loss rises with the increase of volume fraction and flow rate for Al2O3-water nanofluid. The scaled exergy loss, as defined by Pandey et al.,28 is the ratio of exergy loss over the maximum heat transfer rate (ΔEloss/Qmax). Figure 6 shows the scaled exergy loss for three

Figure 7. Friction factor with nanoparticle volume faction.

water nanofluids, the friction factor gradually decreases as the nanoparticle volume fraction increases, but for the CuO-water nanofluid, the friction factor declines at a much greater rate. Compared with pure water, the maximum decrease in friction factor is 5.31% for the CuO-water nanofluid. The decline in friction factor was 0.76% and 1.11% for the Al2O3-water and TiO2-water nanofluids, respectively. These results indicate that the greater density of the CuO-water nanofluid performed better than the other two nanofluids in reducing friction factor. Decreasing the friction factor will improve the overall thermal performance of the system. Reducing the friction factor will also cause small changes in pressure reduction, due to quicker flow contraction at the microchannel inlet and expansion at the outlet. However, this has a very minor effect on the overall calculation and can be neglected.29 Pumping power is a function of the mass flow rate, density, and pressure reduction. Figure 8 shows that the pumping

Figure 8. Pumping power with mass flow rate.

Figure 6. Scaled exergy loss (ΔE/Qmax) with nanoparticle volume fraction.

power increases as the mass flow rate rises. A fixed inlet flow velocity of 0.5 m/s and a volume fraction of 0.4% results in a pumping power of 0.0166 W. The mass flow rates at these conditions were found to be 0.00910, 0.00901, and 0.00902 kg/ s for CuO-water, Al2O3-water, and TiO2-water nanofluids, respectively. A comparison between pure water and all of the nanofluids (2.0 vol %) showed a 5.18% difference in maximum pumping power. The maximum pumping power was 0.0173 W at 2.0 vol % of nanoparticles, where the mass flow rate was calculated to be 0.0099, 0.0094, and 0.0095 kg/s for CuOwater, Al2O3-water, and TiO2-water nanofluids, respectively. Pumping power becomes more significant for higher mass flow rates, and as a result, the exergetic performance will decrease.

different types of nanofluids with varying nanoparticle volume fractions (from 0.4% to 2.0%). The exergy losses shown in this figure are similar to those shown in Figure 5. Among the three coolants, the scaled exergy loss was lowest for the 0.4 vol % of TiO2-water nanofluid. 3.3. Friction Factor and Pumping Power. Friction factor depends on the Reynolds number as well as the density and the volumetric flow rate of the nanofluids. Increasing the nanoparticle volume fraction increases the nanofluids Reynolds number, density, and volumetric flow rate, while reducing the friction factor. At high densities, the effect of volume fraction 10516



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ΔP = pressure reduction (Pa) Q̇ = total heat dissipation from chip (W) Re = Reynolds number R = thermal resistance (K/W) um = inlet velocity (m/s) Pp = pumping power (W) T = temperature (K) V̇ = volumetric flow rate (m3/s) Wc = channel width (m) Wcd = center-to-center distance of microchannel (m) Wfin = channel wall thickness (m) W = water

4. CONCLUSIONS In this study, the energy efficiency, exergy loss, friction factor, and pumping power parameters were analyzed to determine the thermal performance of different nanofluid coolants in a rectangular microchannel heat sink. Three types of nanofluids were examined: CuO-water, Al2O3-water, and TiO2-water. The following conclusions can be made on the basis of this analysis: (1) The thermal resistance decline and pressure reduction rise as the nanoparticle volume fraction is increased. (2) The maximum improvements of energy efficiency for CuO-water, Al2O3-water, and TiO2-water nanofluids (for 2.0 vol %) were 98.90%, 77.47%, and 68.35%, respectively, compared with pure water. (3) The exergy loss increases as the nanoparticle concentration is increased. (4) The friction factor decreased as either the Reynolds number or volume fraction of nanofluids was increased. (5) The maximum pumping power was increased by 5.18% using nanofluids with 2.0 vol %, as compared with pure water (for 0.5 m/s fixed inlet velocity). Improvements are indicated by a decrease in thermal resistance and friction factor or an increase in energy efficiency. Increased exergy loss or pumping power will reduce the performance of the heat sink. The results show that nanofluids have a higher performance than liquid water for all of these aspects. The CuO-water nanofluid provided the best results, so this is recommended over the Al2O3-water and TiO2-water nanofluids. It is recommended that future analysis be performed with lower nanofluid flow rates. This would result in a decreased required pumping power and reduced exergy loss, giving better overall thermal performance.

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Greek Symbols

Δ, change or difference ρ, density (kg/m3) μ, dynamic viscosity (N·s/m2) η, efficiency φ, nanoparticle volume fraction Subscript

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AUTHOR INFORMATION

Corresponding Author

*Tel: +603 7967 7611. Fax: +603 7967 5317. E-mail: saidur@ um.edu.my.

base, liquid that nanoparticles are suspended in bm, bottom plate bulk, greater portion c, channel conv, convective e, environmental f, fluid in, inlet loss, property loss after undergoing a process max, maximum nf, nanofluid out, outlet p, particle first, first law of thermodynamic

REFERENCES

(1) Selvakumar, P.; Suresh, S. Convective performance of CuO/water nanofluid in an electronic heat sink. Exp. Therm. Fluid Sci. 2012, 40, 57. (2) Renfer, A.; Tiwari, M.; Brunschwiler, T.; Michel, B.; Poulikakos, D. Experimental investigation into vortex structure and pressure drop across microcavities in 3D integrated electronics. Exp. Fluids 2011, 51 (3), 731. (3) Tuckerman, D. B.; Pease, R. F. W. High-performance heat sinking for VLSI. Electron Device Lett. 1981, EDL-2 (5), 126. (4) Chein, R.; Huang, G. Analysis of microchannel heat sink performance using nanofluids. Appl. Therm. Eng. 2005, 25 (17−18), 3104. (5) Sohel, M. R.; Khaleduzzaman, S. S.; Saidur, R.; Hepbasli, A.; Sabri, M. F. M.; Mahbubul, I. M. An experimental investigation of heat transfer enhancement of a minichannel heat sink using Al2O3−H2O nanofluid. Int. J. Heat Mass Transfer 2014, 74, 164. (6) Choi, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. In Developments and Applications of Non-Newtonian Flows; Siginer, D. A., Wang, H. P., Eds.; ASME: New York, 1995; Vol. FED-231/MD-66, pp 99−105. (7) Bhattacharya, P.; Samanta, A. N.; Chakraborty, S. Numerical study of conjugate heat transfer in rectangular microchannel heat sink with Al2O3/H2O nanofluid. Heat Mass Transfer 2009, 45 (10), 1323. (8) Ebrahimi, S.; Sabbaghzadeh, J.; Lajevardi, M.; Hadi, I. Cooling performance of a microchannel heat sink with nanofluids containing cylindrical nanoparticles (carbon nanotubes). Heat Mass Transfer 2010, 46 (5), 549. (9) Farsad, E.; Abbasi, S. P.; Zabihi, M. S.; Sabbaghzadeh, J. Numerical simulation of heat transfer in a micro channel heat sinks using nanofluids. Heat Mass Transfer 2011, 47 (4), 479.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful to University of Malaya for financial support under the High Impact Research MoE Grant UM.C/ 625/1/HIR/MoE/ENG/40 (D000040-16001) from the Ministry of Education Malaysia.

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NOMENCLATURE Abm = bottom area of microchannel heat sink (m2) Ac = channel area (m2) C = heat capacity rate (kW/K) cp = specific heat (J/kg·K) Dh = hydraulic diameter of the fluid flow (m) E = exergy (W) f = friction factor Hb = bottom plate thickness (m) Hc = channel height (m) h = heat transfer coefficient (W/m2·K) k = thermal conductivity of nanofluid (W/m·K) L = channel length (m) ṁ = mass flow rate of coolant through channels (kg/s) Nu = Nusselt number n = number of cooling channels 10517



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