Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel

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Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel Jiwon Yu a, Seok-Won Kang b,c,∗, Rag-Gyo Jeong b, Debjyoti Banerjee d a

Posco, Dongchon-dong, Nam-gu, Pohang-si, Gyeongsangbuk-do 37859, Republic of Korea Korea Railroad Research Institute, 176 Cheoldo bangmulgwan-ro, Uiwang, Gyeonggi-do 16105, Republic of Korea c Department of Energy and Environmental Engineering, University of Science & Technology, 217 Gajeong-ro Yuseong-gu, Daejeon 34113, Republic of Korea d Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, United States b

a r t i c l e

i n f o

Article history: Received 16 January 2016 Revised 16 August 2016 Accepted 4 November 2016 Available online xxx Keywords: Nanofluids Microchannel Nanofin EDS(Energy Dispersive X-ray Spectroscopy) SEM(Scanning Electron Microscopes) CFD(Computational Fluid Dynamics)

a b s t r a c t In this study, we postulated and demonstrated that surface conditions have a dominant role in multiphase flows that leverage stable colloidal nanoparticle suspensions (i.e., nanofluids) in determining their efficacy as heat transfer fluids (HTF). Forced convective heat transfer rates during the flow of de-ionized water (DIW) and aqueous TiO2 nanofluids inside a microchannel were studied numerically as well as experimentally under constant wall temperature boundary conditions. A brief literature review of the theoretical investigations involving the thermal-conductivity of nanofluids as heat transfer fluids (HTF) was also carried out. This enabled the development of a numerical model and computational analysis for forced convective heat transfer of nanofluids in a microchannel using conventional CFD (Computational Fluid Dynamics) techniques. Experimental validation of the numerical predictions was in accordance with the predicted values of the temperature profile near the walls of the microchannel for the base fluid. Anomalous enhancement of the convective heat flux values was observed in the experiments using nanofluids (e.g., an increase of 91.9%). However, this trend was not seen in the computational analysis because the numerical models were based on continuum assumptions and flow features involving nanoparticles in a stable colloidal solution involving non-continuum effects. The anomalous enhancements are postulated to be caused by isolated and dispersed precipitation of nanoparticles on the flow conduits (the precipitated nanoparticles are called “nanofins”) which in turn enhance the surface area available for heat exchange (this is called the “nanofin effect”). The numerical validation of nanoparticle precipitation was successfully achieved by additionally considering particle tracking (i.e., DPM: Discrete Phase Model) and two-phase flow modeling based on conventional CFD and HT methods. The “nanofin effect” consists of the cumulative influence of several transport mechanisms at the solidfluid interface on a nanoscale level - arising from the increase in the effective surface area caused by the formation of surface nanofins - which in turn modulates the effective thermal impedance (resistance, capacitance, inductance, etc.) as well as thermal diodic effects. The efficacy of the nanofins depends on various parameters such as the local profiles for the wall temperature, concentration and flow rates of each phase. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Effective removal and rejection of generated heat is the key to successful operation of thermal management systems in various engineering applications. For instance, enhanced miniaturization of electric circuits has resulted in significantly (∼10 ×) higher thermal loads while the surface area available for heat dissipation has been reduced drastically (∼10 ×) (Hidrovo and Goodson, 2008). In order

∗

Corresponding author. Fax: +82314605026. E-mail address: [email protected] (S.-W. Kang).

to prevent device damage, the generated heat should be removed efficiently to enable operation below the failure temperature. Effective cooling systems are also necessary for other electrical devices with large form factors, such as for high speed rail transportation. Efficient drag reduction strategies for trains restrict the convective heat dissipation to just the ambient air (Lukaszewicz, 2009). Therefore, innovative strategies are required for the next generation of thermal management platforms for ultra-high-speed trains. Materials for Heat Transfer Fluids (HTF) and Thermal Energy Storage (TES) platforms also rely on effective schemes for heat transfer (both cooling and heating operations), such as in Concentrated Solar Power (CSP) involving Photo-Voltaic (PV) or thermal

http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001 0142-727X/© 2016 Elsevier Inc. All rights reserved.

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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power stations (TPS) (Shin and Banerjee, 2011a; Jo and Banerjee, 2014a). Development of cooling platforms to effectively remove heat from various engineered systems (as well effectively reject heat) is thus quite acute in various disciplines in contemporary human endeavors. Conventional strategies for enhancing heat removal rates focus on either augmenting the thermo-physical properties of the HTF/ TES (i.e., the coolant or the working fluid), or increasing the surface area involved in the heat exchange. Nanofluids are being explored in contemporary research in an effort to enhance the thermophysical properties of HTF/TES. On the other hand, microchannels and fins (extended surfaces) can aid in increasing the effective surface area per unit volume of convected fluid, for the purpose of augmenting the net heat transfer rates (while the typical tradeoff is an enhanced pressure-penalty and additional pump cost) (Tuckerman and Pease, 1981). Nanofluids are stable colloidal suspensions of nanoparticles in a given solvent. Particles with at least one characteristic dimension less than 100 nm are called nanoparticles (Eastman et al., 1997). Typical examples of a neat solvent (also called a “base fluid”) in nanofluid literature are as follows: water, ethylene glycol, oil, and molten salts. Nanoparticles can be comprised of organic or inorganic materials (and their mixtures). Typical organic nanoparticles include the following: cylindrical shaped carbon nanotubes (CNT), graphenes (graphite nanosheets or nano-platelets) and “Fullerenes” (or spherical shaped crystal lattices of C60). Inorganic nanoparticles can include metallic (e.g., Au, Ag, Cu, W, etc.) or ceramics/ oxides (alumina, silica, titania, ceria, magnesia, CuO, iron oxides, etc.), carbides (e.g., SiC), etc (Lee et al., 1999; Das et al., 2003; Eastman et al., 2001; Choi et al., 20 03; Wen and Ding, 20 04). Microchannels are defined as the flow conduits with hydraulic diameters that are less than 100 μm and greater than 100 nm (although some research groups have alternative definitions for the term “microchannel” for flows involving gas-liquid mixtures) (Jang and Choi, 2006; Lee and Mudawar, 2007; Jung et al., 2009; Singh et al., 2011). The nanofluid literature is replete with controversial reports regarding the anomalous enhancement of thermal conductivity of nanofluids. Some of the studies are probably flawed due to improper characterization protocols or lack thereof – such as the stability of nanoparticles in colloidal liquid suspensions. A lack of stability in nanofluids can result in agglomeration of nanoparticles. This can cause dispersed/isolated precipitation of the nanoparticles (which act as “nanofins”) and if not monitored properly, can cause the progressive buildup of micro/meso-sized particles on sensor surfaces (or heater surfaces) thus leading to potential fouling effects. To complicate the landscape of the nanofluid literature, often, many of these papers claim to have used nanoparticles of a particular size without any experimental verification of their size distribution to begin with (or if the size distribution changed during the progression of the experiment). Such tests are easy to perform yet often neglected. Images of nanoparticles or test surfaces are relatively easy to measure using electron-microscopy techniques such as Scanning Electron Microscopy (SEM). The proper design of experiments requires a fair share of due diligence. Due diligence requires that such verification steps for agglomeration/ precipitation be performed both before and after experiments. For example, Lee et al., (1999) and Das et al., (2003) found up to 36% enhancement for the thermal conductivity of water and ethylene glycol when doped with Al2 O3 and CuO nanoparticles. Additionally, Eastman et al., (2001) reported that the thermal conductivity of ethylene glycol was enhanced by 40% when doped with Cu nanoparticles (< 10 nm). Choi et al., (2003) reported that the thermal conductivity of epoxy was enhanced by 300% when doping with single-walled CNTs. Wen and Ding (2004) reported a 31% enhancement in the thermal conductivity of aqueous nanoflu-

ids containing multi-walled CNTs. These measurements were done with the hot-wire method (HWM) which is susceptible to surface fouling arising from the precipitation of nanoparticles. Yet, none of these studies were performed with the due diligence of monitoring surface fouling during the progression of the experiments. As a consequence, several review papers and double-blind studies were generated (based on these faulty measurements) with the purpose of exploring the potential transport mechanisms that were believed to be responsible for the anomalous enhancements in the bulk property values, such as the thermal conductivity of nanofluids (Buongiorno et al., 2009; Prasher et al., 2005; Yu et al., 2008; Wang and Mujumdar, 2007). Non-invasive measurements using a more specialized apparatus, such as the Laser Flash Apparatus (LFA), are probably better suited for these types of measurements (because HWM is an invasive technique that suffers from potential complications arising from surface fouling that needs to be monitored both before and after each experimental measurement) (Singh and Banerjee, 2014; 2012; 2013; Shin and Banerjee, 2011b; Jo and Banerjee, 2011; Jung and Banerjee, 2011; Acharya et al., 2013). In contrast, the volume of reports in the nanofluid literature on forced convective heat transfer in microchannels is quite sparse (especially when compared to the volume of reports for nanofluid literature on thermal conductivity measurements) (Jang and Choi, 2006; Lee and Mudawar, 2007; Jung et al., 2009; Singh et al., 2011; Yu et al., 2011; Yu et al., 2012; Anoop et al., 2012). This is probably because experimental studies involving convective heat transfer require due diligence, which is often complicated (have to establish experimental protocols to take measurements under steady state conditions), are more complex (i.e., require more instruments such as pumps, valves, pressure and temperature sensors, etc.) and are more time consuming due to the range of additional parameters that need to be monitored – such as the pressure, temperature, flow rates, etc. (i.e., compared to experiments involving HWM). Jang and Choi (2006) reported that the cooling performance of a microchannel heat sink was enhanced by ∼10% using aqueous nanofluids containing diamond nanoparticles of 2 nm diameter and at a volume concentration of 1%. However, the authors did not show results validating that the nanoparticles were unagglomerated after the experiments (e.g., image of the nanoparticles and sensor surfaces using electron microscopy both before and after the experiments). Lee and Mudawar (2007) investigated the efficacy of heat transfer enhancement in terms of the enhanced pressure penalty associated with Reynold’s analogy and Chilton–Colburn effect (Incropera, 2011) during the flow of aqueous alumina nanofluids in a microchannel. The authors reported that the heat transfer coefficient was enhanced significantly while the pressure drop was increased marginally. Jung et al., (2009) and Singh et al., (2011) performed experimental and numerical investigations to show the advantage of various nanofluids flowing in a microchannel. The nanofluids were synthesized by doping alumina nanoparticles into various solvents such as water, ethylene glycol, and an aqueous solution of ethylene glycol. In contrast, Yu et al., (2012) showed that both the enhancement and degradation of convective heat transfer occurred during the flow of aqueous silica nanofluids depending on the magnitude of precipitation of the silica nanoparticles on the heated surfaces. This study pioneered the measurement of the magnitude and size distribution of precipitated silica nanoparticles on heated surfaces in a microchannel using electron microscopy (i.e., SEM images) both before and after the experiments. In retrospect, these results show that several inconsistent experimental results have been reported over the past decade by various research groups on the forced convective heat transfer characteristics of nanofluids flowing in a microchannel, due to a lack of due diligence. As a consequence, theoretical models that have

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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been proposed in the literature have bet on the identification of one or two winning candidates among a diverse range of transport mechanisms (when, in reality, it could be a combination of these mechanisms, such as in multiple series-parallel configurations of various non-linear thermal-impedances - arranged analogous to an electrical network). Hence, the body of efforts in the literature can be summarized to be akin to the fabled perception of the form of an elephant by an array of blind investigators. As a consequence, the proposed models in the literature are replete with controversial predictions which are often inconsistent with the whole body of experimental results in the nanofluids literature. The source of controversies can often be traced to the inconsistency in the experimental protocols across various research groups - rather than the theoretical models themselves. For instance, Singh et al., (2011) and Yu et al., (2012) proposed that Brownian motion and thermophoresis are the dominant mechanisms for the observed enhancement in heat transfer. In contrast, several other research groups (Yu et al., 2012; Qu et al., 20 0 0; Liu et al., 2011) emphasized the dominance of surface roughness in the microchannels (this is also complicated by the limitations of microfabrication techniques that cause the geometric dimensions to have high tolerances, i.e., the microchannel dimensions can vary significantly along the flow direction). Thus no two microchannel experiments (performed at two different research groups) can be regarded to be the same unless they both have characterized the same set of variables, such as the geometrical tolerances of the microchannels after the microfabrication step is accomplished (and verified again after the experiments are completed). Similar arguments can be made about nanofluid synthesis – because small variations in the synthesis protocols can yield nanofluids with vastly different material property values – even though the ingredients were the same to begin with (this is akin to the effect of individual recipes in a culinary exercise) (Singh and Banerjee, 2014; Singh et al., 2012; Shin and Banerjee, 2013; Shin and Banerjee, 2011b; Jo and Banerjee, 2014b; Jo and Banerjee, 2014c). Several factors contribute to the lack of understanding of the transport mechanisms that modulate heat transfer during the flow of nanofluids in a microchannel. For example, theoretical as well as numerical investigation of heat transfer using nanofluids have primarily focused on the thermo-physical properties (e.g., static thermal-conductivity: (Özerinç et al., 2010; Khanafer and Vafai, 2011; Assael et al., 2006)). Recently, heat transfer characteristics of nanofluids have been proposed based on dynamic thermal-conductivity related with particle migration (e.g., Singh et al., (2011) and Bahiraei and Hosseinalipour (2013)). The various approaches include theoretical predictions for suspensions of nanoparticles, correlations that depend on parameters determined by experimental observations (e.g., Özerinç et al., (2010), Khanafer and Vafai (2011) and Assael et al., (2006)), and simulations using continuum assumption based numerical models (e.g., Farsad et al., (2011), Namburu et al., (2009) and He et al., (2009)) as well as molecular dynamics simulations (e.g., Assael et al., (2006)). These modeling approaches are based on a set of experimental observations for which heat transfer enhancements were reported. However, the drawback of these models is their inability to explain the experimental data in which degradation in heat transfer was also observed in certain circumstances. In the current study, the forced convective heat transfer characteristics of aqueous titania nanofluids flowing in a microchannel were explored both experimentally and numerically. The objective of this study were as follows: (1) perform experiments involving the flow of aqueous titania (TiO2 ) nanofluids in microchannels, and (2) perform numerical simulations to explore the rudimentary set of transport mechanisms that could be responsible for the observed enhancement in the heat transfer (i.e., based on the

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“nanofin effect”) (Singh and Banerjee, 2014; Singh et al., 2012; Nelson et al., 2009; Sathyamurthi and Banerjee; 2009). Isolated and dispersed precipitation of nanoparticles from a nanofluid leads to the formation of nanoscale protrusions or extended surfaces (“nanofins”) within the flow conduits – thus effectively leading to transient variation in the surface roughness of the microchannels during the progression of the experiments (even though from a macro-scale perspective – steady state conditions have been achieved). The “nanofin effect” includes the cumulative effects of various transport mechanisms arising from the increase in the effective surface area of the heat exchanging surfaces which is caused by the formation of nanofins from the precipitation of nanoparticles (this could also be achieved by artificially engineered nanostructures that are explicitly micro/nano-fabricated on a heatexchanging surface). The formation of nanofins in turn modulates the effective thermal impedance values (such as the interfacial values of resistance, capacitance, inductance, etc.) at the solid-fluid interface as well as the thermal diodic effects at the solid-fluid interface. This is discussed briefly in this section. Density oscillations of the fluid phase in the vicinity of a solid surface (due to non-continuum flow regimes as well as surface adsorption of fluid molecules on the surface of the nanoparticle) can act as a thermal inductor while the modulation of specific heat capacity (associated with these density oscillations of the fluid phase at the solid-fluid interface of the nanoparticle) acts as a thermal capacitor. The density oscillations in the fluid phase (especially for a multi-component or multi-species fluid system) can also lead to concentration gradients for which one of the components or species has a higher concentration in the vicinity of the solid surface (i.e., at the solidfluid interface of the nanoparticle). This concentration gradient induced by the presence of the solid surface can either aid or hinder heat transfer. This depends on the co-variance or contra-variance of the temperature gradient and the concentration gradient (depending on the nanoparticle temperature being hotter or colder than the fluid phase). This gives rise to diodicity in heat transfer which is the same temperature difference between the solid surface/ nanoparticle and the fluid phase – the magnitude of the corresponding flux will be modulated depending on the directionality of the temperature gradient in relation to the directionality of the concentration gradient. Hence, the nanofin effect is exacerbated (i.e., due to a combination of the thermal impedance network configuration and thermal diodicity) by the enhancement in the effective surface area of the heat exchanging surfaces arising from the dispersed and isolated precipitation of nanoparticles (or artificially engineered surface nanostructures). This study verifies the postulate that the “nanofin effect” is the dominant mechanism for the observed enhancements in forced flow convective heat transfer using nanofluids within microchannels (in contrast, excessive precipitation of nanoparticles leads to surface fouling – causing degradation of heat transfer). In other words, the hypothesis of this study is that the surface effects have a more dominant role while the thermo-physical properties of the nanofluids have a recessive role among all the underlying transport mechanisms involved in heat transfer for multi-phase flows of colloidal suspensions such as in nanofluids in microchannels. Experimental results were compared with numerical predictions for operational conditions that included two different values of TiO2 nanoparticle concentrations (at mass concentrations of 0.005 and 0.01%), three values for the volume flow rates (30, 35 and 40 μl/min) and three values for the wall temperatures (45, 60 and 75 °C). In addition, experimental images were obtained with Scanning Electron Microscopy (SEM) and characterization of the materials was performed with Energy Dispersive X-ray Spectroscopy (EDS) after the conclusion of the experiments.

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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2. Numerical modeling 2.1. Assumptions TiO2 nanoparticles are readily soluble in water - which results in the synthesis of stable aqueous nanofluids – essentially due to their inherent affinity (hydrophilicity) and small size (e.g., ∼100 nm). In addition, the solvent phase (or the base fluid, i.e., water) and the TiO2 nanoparticles are expected to be in thermal equilibrium, i.e., with zero relative velocity. Thus, the nanofluid samples used in the microchannel experiments are approximated using continuum models because the Knudsen number is larger than 0.1 for the microchannel design that was implemented in this study. In the numerical simulations, forced convective heat transfer during the flow of nanofluids in a microchannel is simply described using a Newtonian model, which is consistent with the experimental results in the literature for the range of titania (TiO2 ) nanoparticle concentrations used in this study. However, it is recognized that for higher values of nanoparticle concentrations and different nanoparticle morphologies (size, shape, material composition, etc.) nanofluids can exhibit non-Newtonian rheological behavior (Singh and Banerjee, 2014; Singh et al., 2012). A commercial software package (i.e., Fluentۛ v6.3.26) was used to solve the governing equations and to perform the numerical simulations. The governing equations for the forced convective heat transfer process involve assumptions for incompressible and laminar flows under steady state conditions. In addition, it was assumed that radiation is not significant, and the thermophysical properties of nanofluids are temperature dependent. The coupled momentum and energy equations that were implemented in the 3-D numerical models for nanofluids are

1 μ (v • ∇ )v = − ∇ p + ∇ 2v ρ ρ

(1)

(v • ∇ )T = α∇ 2 T

(2)

A microchannel with a rectangular cross section was constructed with the Gambitۛ pre-processor software to implement the 3-D axisymmetric numerical model for mesh-generation. The length of the modeled microchannel was 24 mm to be consistent with the experimental configuration. The inlet and outlet ports of 400 μm diameters were modeled to be located at the end of the microchannel and on the top surface shown in Fig. 1 so that they were consistent with the configuration used in the experiments. At the inlet surface, uniform velocity and temperature boundary conditions were imposed, and an outflow boundary condition was imposed at the outlet. An isothermal heating condition (constant temperature boundary condition) was imposed on the bottom wall of the microchannel. In the experiments, the bottom wall of the microchannel was fabricated with a Pyrex wafer substrate. The Pyrex wafer was heated from below using an array of strain gage heaters in the experiments, and the wall temperature, in contact with the working fluid, was measured with an array of Thin Film Thermocouples (TFT). Adiabatic surface conditions were imposed on the remaining walls of the microchannel – because it is expected that the very low thermal conductivity of the PDMS materials (e.g., k = 0.15 W/m-K) and relatively large volume of the PDMS substrate (compared to the total volume of the fluid in the microchannel) would lead to negligible heat loss from these walls in comparison to the net heat transfer to the convecting fluid – thus leading to zero gradients in the fluid temperature at the microchannel walls comprised of PDMS. 2.2. Thermophysical properties of nanofluids The thermophysical properties of nanofluids are theoretically derived using models of immiscible solid-liquid mixtures. Thus, the

Fig. 1. Schematic diagram showing the flow of the working fluids (deionized water/ DIW or aqueous TiO2 nanofluids) in a microchannel with a rectangular cross section of 1 mm in width and 55 μm in height for which the bottom surface is a thin Pyrex wafer. The convecting fluid inside the microchannel transfers heat from the bottom wall of the microchannel which is regarded to be at a constant temperature. The side walls of the microchannel are regarded to be adiabatic because they are fabricated with a thick PDMS substrate that is adhesively bonded onto the Pyrex wafer.

properties are highly dependent on the particle volume fraction which is defined as the volume of nano-particles in a unit volume of base fluid (or sovent). For non-aqueous nanofluids, anomalous enhancements in specific heat capacity, beyond the classical model expressed as Eq. (4), were experimentally observed in recent studies (Shin and Banerjee, 2011a; Jo and Banerjee, 2014a; Shin and Banerjee, 2013; Shin and Banerjee, 2011b; Jung and Banerjee, 2011; Shin and Banerjee, 2011b; Jo and Banerjee, 2014b). However, for typical aqueous nanofluids, the density and specific heat capacity are traditionally expressed using the mixture rule as follows (Farsad et al., 2011):

ρn f = (1 − φ )ρ f + φρs

(3)

(ρ c p )n f = (1 − φ )(ρ c p ) f + φ (ρ c p )s

(4)

Moreover, the effective viscosity of nanofluids has been generally estimated for the case of extremely low concentrations of fine spherical particles, i.e., using Einstein’s equation (Farsad et al., 2011): However, it was found that this model yields underestimated values for the effective viscosity compared to measured data. Thus, a generalized model proposed by Nielsen (Murshed et al., 2008) is used in this study as follows:

μn f = μ f (1 + 1.5φ p )eφ p /(1−φm )

(5)

The Feng–Kleinstreuer (F-K) model (Kleinstreuer and Feng, 2012) is used to estimate the effective thermal conductivity. This model is based on the model proposed by Koo, Kleinstreuer and Li (also known as the “KKLmodel”) (Kleinstreuer and Li, 2008). This model is derived by considering additional contributions from the micro-scale mixing effect due to the Brownian motion of dispersed nanoparticles on the static value of thermal conductivity of a basefluid (solvent) shown below:

kn f = kstatic + kBrownian ,

(6)

where kstatic is the thermal conductivity of the mixture (i.e., Maxwell model), and kBrownian is the enhanced thermal conductivity by micromixing. This is determined with the following expression:

kBrownian = 49500

kB

6π μ f d p

  (ρ c p )n f φ 2 T¯ ln T¯ − T¯

(7)

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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array of TFTs. The array of TFTs was calibrated with an infrared camera immediately after the microfabrication and prior to starting each experiment. Additionally, the PDMS substrate containing the microchannel was aligned with the Pyrex wafer (containing the array of TFTs) and adhesive bonding was performed following exposure of both substrates to oxygen plasma by Reactive Ion Etching (RIE). Adhesive bonding of the two substrates prevents the test fluids from leaking from the microchannel during the experiments because a considerable pressure drop can occur during the flow of the test fluids in the microchannel.

3.2. Experimental procedure

Fig. 2. Comparison of experimental data by Zhang et al. (2007) with the predictions from the F-K model (Kleinstreuer and Feng, 2012) for the thermal conductivity of aqeuous titania nanofluids.

In particular, it has been shown that the predictions from this model are consistent with experimental measurements for aqueous nanofluids containing metal-oxide nanoparticles with a small size range (20 < dp < 50 nm) and at a low volume fraction (i.e., ∼5%) with mixture temperatures below 350 K (Kleinstreuer and Feng, 2012). In the experiments performed in this study, the average diameter of the spherical nanoparticles was 50 nm. Because the maximum volumetric concentration used in the experiments was ∼ 0.0 0 02%, the F-K model was used to calculate the effective thermal conductivity values that were used in this study. As shown in Fig. 2, the predictions from the F-K model are consistent with the experimental results reported by Zhang et al. (2007), especially for relatively low values of volumetric concentrations of nanoparticles (i.e., less than 1.5%). 3. Experimental details 3.1. Experimental setup A schematic diagram of the experimental apparatus used in this study for measuring the thermal performance of the test fluids (DIW and titania nanofluids) during forced convective heat transfer in microchannels is shown in Fig. 3(a). Additionally, Fig 3(b) is a picture of the experimental setup showing the test section as well as the flexible film heater. A fluid was first heated when it flowed through the microchannel, and the temperatures on the heated surface were measured and monitored using an array of TFTs (Thin Film Thermocouples). A constant volumetric flow rate was maintained with a syringe pump (Pump 11 Pico Plus, Havard Apparatus). A flexible film electrical heater (KHR-2/10-P, Omega) was attached onto the bottom surface of the Pyrex wafer substrate and connected to a DC power supplier (SPS 200-50-K025, American Reliance Inc.). The TFT signals were recorded with a Data Acquisition System (DAQ, NI SCXI-1303, National Instruments) and monitored with control software (Labview, National Instruments). The array of the K-type TFT was fabricated in-situ in the Pyrex wafer substrate which serves as the bottom surface of the microchannel fabricated in a PDMS substrate. The steps for the microfabrication involved a standard photolithography process followed by physical vapor deposition (PVD) of Chromel and Alumel layers (to achieve the K-type thermocouples). The details of the microfabrication process have been described in a previous publication (Yu et al., 2012). Surface temperature values along the flow direction on the bottom surface (i.e., the heated surface) of the microchannel were recorded by the

The nanofluids were simply synthesized based on the “twostep” method (Fedele et al., 2011): (i) dispersion of the nanoparticles in a base fluid (i.e., DIW) and (ii) repetitive sonication (e.g., more than 2 times for 1 h) for stabilization. The homogeneity and the colloidal stability of nanofluids are significant parameters that validate the reliability of nanofluids prior to real applications. The degree of particle agglomeration in nanofluids in terms of longterm colloidal suspension stability can be assessed from the zeta potential generally measured with the direct light scattering (DLS) method (Fedele et al., 2011). In the DLS measurement, the mean diameter and zeta potential of the particles in the suspension were approximately 129.3 ± 0.4 nm and −36.8 ±1.4 mV, respectively. Additionally, Fig. 4 shows the particle size distribution plot of the TiO2 -DIW nanofluids. It was confirmed that the mean diameter of the particles in suspension is larger than the value (i.e., 50 nm) given by the manufacturer; however, the nanofluids used in this study have a moderate stability because the zeta potential was in a range from −31 to −40 mV (Salopek et al., 1992). To validate the hypothesis proposed in this study, experiments were performed using the experimental procedure described next. Initially, a control experiment was performed using DIW as the test fluid. Convective heat transfer during the flow of the test fluid was measured for three flow rates (30, 35 and 40 μl/min) and three wall temperatures (45, 60 and 75 °C). Steady state conditions (hydrodynamic and thermal) were achieved in approximately 1 h The data acquisition for the temperature signals was done with the control software. Forced convective heat transfer to the test fluid was calculated based on the fluid temperature values at the inlet and outlet of the microchannel. Second, the experiments were repeated for the aqueous titania (TiO2 ) nanofluids for two different mass concentrations (0.005 and 0.01%). The control experiments using DIW were then repeated immediately after the nanofluids experiments. The last experiment is the most significant experiment because it provides useful information on the efficacy of the nanofluids in forced convective heat transfer experiments. If the results of the control experiments conducted before and after the nanofluids experiments are significantly different, it could be concluded that the enhancement of heat transfer with the nanofluids is not primarily due to the superior thermo-physical properties (or bulk properties) of the nanofluids. Moreover, if the results for the nanofluids experiments and those for the repeated control experiments are similar (or if the results from the two control experiments are different), it can be inferred that surface modification of the microchannel was caused by the flow of the nanofluids (in the intervening experiment) – which in turn caused the results from the two successive control experiments to be different. The measured values of the fluid inlet, fluid outlet and wall temperature in the microchannel as well as the calculated values of the forced convective heat transfer were compared to the predictions from the conventional models and to previous reports in the literature on the thermal characteristics of nanofluids flowing in a microchannel (Jung et al., 2009; Qu et al., 20 0 0).

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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Fig. 3. (a) Schematic diagram and (b) picture of the experimental setup.

Fig. 4. Particle size distribution plot of the TiO2 nanoparticles in suspension measured with the DLS method.

Fig. 5. Plot of the predicted values from the numerical simulations for the temperature profile of the test fluid (DIW) in the vicinity of the wall and along the flow direction in a microchannel for different flow rates. The solid icons represent the experimental measurements recorded by the array of TFTs.

3.3. Measurement uncertainty 4. Results and discussions The measurement uncertainty (ω) is evaluated with Eq. (8) which was first suggested by Kline and McClintock (1953).

 ωq =

∂ qω ω ∂ x1 1

2



∂ qω + ω ∂ x2 2

2



∂ qω + ··· + ω ∂ xn n

2  12 (8)

The heat removal rate and convective heat transfer coefficient depend on various variables (which are represented by x1 , x2 , . . ., xn in the above equation) such as the thermophysical properties (density and specific heat) of a working fluid, height of the microchannel, flow velocity, and temperature. In this study, the majority of these variables were controlled, and only the temperature was measured. Thus, Eq. (8) can be written as follows:

ωqw qω

=

ω(Tw ) Tw

(9)

The maximum measurement uncertainty of the current experiments is estimated to be 3.18%.

4.1. Numerical predictions Numerical analysis using the material property values of DIW was done to validate the accuracy of the numerical model as well as to obtain a baseline estimate (for the purpose of evaluating the efficacy of the nanofluids during forced convective heat transfer in microchannels). Fig. 5 shows a comparison of the values for the fluid temperature near the heated wall between the experimental data and numerical predictions during the flow of DIW in a microchannel under steady state conditions. For all wall temperature conditions, the numerical predictions were observed to be consistent with the experimental measurements. Hence, it was concluded that the numerical model presented in this study is reasonably accurate. The numerical analysis for the flow of nanofluids was done with the same boundary conditions and initial conditions as that of DIW. This enabled a comparison of the simulations for the nanofluids with the baseline case (DIW). The results are represented with non-dimensional parameters, Nusselt number (Nu) and Pêclet number (Pe), and are shown in Fig. 6. The mathematical represen-

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Fig. 6. The Nusselt number as a function of the Pêclet number for DIW and TiO2 nanofluids at (a) 0.005 wt.% and (b) 0.01 wt.%.

tation of Nu and Pe are provided below:

Nu =

hDh k

Pe = Re · P r =

(10) u Dh

α

(11)

The half-filled symbols in Fig. 6 represent the simulation results. The figure shows that the differences between the nanofluids and DIW were not significant. It was calculated that the differences between the numerical and experimental results were approximately 28% and 43% on average for the 0.005 wt.% and 0.01 wt.%, respectively. Because the numerical models were based on continuum assumptions (i.e., single-phase fluids with enhanced thermalproperties predicted by the theoretical model (i.e., F-K model)), the enhancement by the numerical simulations were very small compared to the experimental measurements. It was concluded that due to the very low concentration of nanoparticles in the base fluid, the thermophysical property values were not affected significantly, and therefore, the differences were not appreciable. The thermal characteristics of the nanofluids based on the experimental investigations will be discussed in the next section; however, it is clear that the thermo-physical properties of the nanofluids in the case of very low concentrations do not have a dominant role. 4.2. Experimental results The hydrodynamic characteristics of test fluids flowing in a microchannel were reviewed initially. Because the flow rates used in this study are significantly small, the values for the Reynolds numbers are also extremely small ranging from 1.7 to 3.3. This means

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that the range of flow rates explored in this study are in the realm of creeping flow regimes. The entrance length for a low Reynolds number flow in a pipe can be predicted with various correlations in the literature (e.g., Sahu et al. (2012), Sparrow et al. (1964)). According to these correlations, the entrance length is approximately 5% of the product of the hydraulic diameter and the Reynolds number. The maximum entrance length in this study is approximately 20 μm, which is negligible compared to the axial length of the microchannel (24 mm) used in the current study. Thus, it is safe to assume that the measurements were performed for a fully developed flow regime. Experimental results regarding the convective heat transfer of the test fluids (DIW and TiO2 nanofluids at concentrations of 0.005 wt.% and 0.01 wt.%) flowing in a rectangular microchannel are described in Fig. 6. In this plot, the Pêclet number (Pe) and Nusselt number (Nu) represents the thermal-fluid flow behavior of a fluid and the convective heat transfer coefficient, respectively. The Nusselt number ranged from 0.004 to 0.015, which is considerably smaller than the theoretical values in macroscale physics. For example, considering two parallel plates with one plate under a constant heat flux and the other insulated (similar to the environment of the current experiments), the theoretical value of the Nusselt number is 5.384. In addition, it is known that the Nusselt number is constant regardless of the flow rate (which is represented by the Pêclet number) for a fully developed internal flow according to conventional (macroscale) heat transfer theory. However, the results for DIW (obtained from both experiments and numerical predictions) definitely show a linear increase in the Nusselt number with an increase in the Pêclet number shown in Fig. 6. Similar discrepancies have been reported in the literature (e.g., Jung et al. (2009), Qu et al. (20 0 0)). Qu et al. (20 0 0) reported that the Nusselt number for experiments performed for water flowing in a trapezoidal microchannel is nearly 1, which is much lower than the values predicted by conventional theory. The authors mentioned that the discrepancy potentially arises from the effects of surface roughness on the walls of the microchannel. In addition, experimental studies on forced convective heat transfer of Al2 O3 nanofluids in a microchannel conducted by Jung et al. (2009) showed quite similar results to those in this study. In addition to the extremely low values of the Nusselt number (compared to the theoretical predictions) that were obtained in this study, a linear relationship between the Nusselt number and Reynolds number was observed. The value of the Nusselt number was ∼0.1 when the Reynolds number was ∼50. Jung et al. argues that it is unrealistic to expect an infinite heat transfer coefficient value as the hydraulic diameter of the channel approaches zero. Because the Nusselt number is proportional to the product of the hydraulic diameter and heat transfer coefficient, it is plausible to obtain small values for the Nusselt number for a microchannel with a small hydraulic diameter. That is, although conventional heat transfer theory is applicable to predict heat transfer of fluids flowing in macroscale channels, it is inappropriate to apply conventional theory to fluids flowing in microchannels. In this sense, the results in the current study are consistent with those shown in previous reports in the literature. Furthermore, remembering that this study is in the realm of a creeping flow and that the Pêclet number is relatively small, diffusive heat and the mass transfer rate become significant. For instance, heat transfer along the flow direction might result in a discrepancy in the results in macroscale theory. In general, the hydraulic diameters of microchannels are very small, and similar discrepancies had been reported by various research groups (Jung et al., 2009; Park et al., 2016; Alvarino et al., 2015). The experimental results for the convective heat transfer of aqueous TiO2 nanofluids are shown in Fig. 6. In this figure, the results for the control experiments using DIW were also plotted as a reference to compare with the results for the nanofluids. The

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Fig. 8. Scanning Electron Microscopy (SEM) images after performing experiments and contour plots by numerical simulations showing precipitation of TiO2 nanoparticles on the heat exchanging surface (bottom surface) of the microchannel: (a) Experimental observation (b) Numerical analysis at a mass concentration of 0.005 wt.% (LEFT) and 0.01 wt.% (RIGHT).

Fig. 7. Effect of the sequence of experiments on heat transfer performance: The figures show a plot of the Nusselt number as a function of the Pêclet number for sets of experiments performed with DIW (first set, before the flow of nanofluids), TiO2 nanofluids, and DIW (second set of experiments after the flow of nanofluids). Experiments were performed for aqueous nanofluids with TiO2 nanoparticle mass concentration of: (a) 0.005 wt.% and (b) 0.01 wt.%.

two separate figures represent the mass concentration of the TiO2 nanoparticles in the base fluid (DIW) at 0.005% and 0.01%, respectively. As can be seen in Fig. 6, the Nusselt number significantly increases when the nanoparticles are added to the base fluid with similar values for the Pêclet number. The levels of increment are dependent on the concentration of the nanoparticles. As the concentration of the TiO2 nanoparticles increase, the Nusselt number also tends to increase. The TiO2 nanofluids at a mass concentration of 0.01% show a 53.4% ∼ 91.9% enhancement in the Nusselt number compared to that of the base fluid. When the mass concentration changes to 0.005%, the enhancement in the Nusselt number ranges from 27.1% ∼ 47.9%. The result shows that the convective heat transfer of TiO2 nanofluids is enhanced, and this result is consistent with previous reports in the literature concerning forced convective heat transfer of various nanofluids flowing in a microchannel (e.g., Jang and Choi (2006), Lee and Mudawar, (2007), Jung et al., (2009), Singh et al., (2011)). To obtain a satisfactory explanation for these enhancements, experiments were designed and performed strategically. That is, control experiments using DIW were repeated immediately after the experiments involving the nanofluids (i.e., using the same microchannel apparatus). Fig. 7 shows the results for these strategic experiments when the concentration of TiO2 nanoparticles were 0.005 wt.% and 0.01 wt.%, respectively. In this figure, the unfilled symbols represent the results for the control experiment with DIW for the first time (i.e., before conducting the experiments with the nanofluids). The half-filled symbols represent the results from the second set

of experiments performed with DIW (which were done after performing the experiments with the nanofluids with the concentration specified by the corresponding symbol). In most cases, the Nusselt number for the DIW experiments (that were obtained both before and after performing the experiments with the nanofluids) showed significant differences, and the Nusselt number values were significantly elevated for the second set of DIW experiments that were performed after the nanofluids experiments. Specifically, the Nusselt numbers obtained from the experiment with DIW, which was done right after the experiments with the TiO2 nanofluids, showed similar or even higher levels of enhancements when compared to those for the nanofluids experiments. At higher mass concentration values (i.e., 0.01%), although the level of enhancement in the Nusselt number is slightly lower (than those of the nanofluids at a lower mass concentration), it is apparent that the results for the second set of experiments involving DIW have changed anomalously (this shows that the heat transfer values depend on the sequence of the experiments). These results imply that the enhancement of convective heat transfer for nanofluid coolants flowing in a microchannel are not dominated by the change in the thermo-physical property values. It is more plausible that during the flow of the nanofluids in the microchannel, the morphology on the heat exchanging surfaces were modified, and this modification is the dominant mechanism for the enhancement in the convective heat transfer. To support this conjecture, it is necessary to check whether there is any modification of the surface geometry on the heated surfaces in the microchannel. Because heat exchange occurs at the bottom surface of the microchannel, these surfaces were characterized with Scanning Electron Microscopy (SEM). The images obtained with SEM are shown in Fig. 8(a). The images for the heated surfaces used in the experiments involving nanofluids with different concentrations of nanoparticles are shown in these images. To avoid crosscontamination issues, each surface was exposed to a nanofluid of only one concentration (hence, a new microchannel apparatus with a fresh clean surface was used each time the experiment was performed using a nanofluid of different concentration). The images show that precipitation of very tiny particles (i.e., potentially agglomerated nanoparticles) is observed for each case shown in Fig. 8(a). Material characterization was performed with Energy Dispersive X-ray Spectroscopy (EDS) to verify that the elemental com-

Please cite this article as: J. Yu et al., Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel, International Journal of Heat and Fluid Flow (2016), http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.11.001

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Fig. 9. Energy Dispersive X-ray Spectroscopy (EDS) of the precipitated nanoparticles.

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energy balance equations). The differences are that the motion of the nanoparticles is determined by the Lagrangian trajectory method based on Newton’s second law (Wen et al., 2009). Furthermore, to explore the “nanofin effect”, the deposition model based on wall-particle interactions was implemented by coupling the UDF (User-Defined Function) code with the DPM model in Fluentۛ by referring to a previous study on classical impact dynamics and Hertzian theories for particle adhesion (Brach and Dunn, 1992). Fig. 8(b) depicts the nanoparticles deposited on the bottom surface of the microchannel, and the numerical analysis results show a coincident trend with the experimental measurements. In other words, it was observed that more particles were deposited at a higher mass concentration (i.e., 0.01 wt.%) in both the experimental and numerical results. 5. Conclusions

position of the precipitated nanoparticles (as shown in Fig. 8(a)) is the TiO2 nanoparticles. Three distinct peaks, which represent oxygen, silicon, and titanium, were observed shown in Fig. 9. The silicon peak and part of the oxygen peak comes from the pyrex glass substrate (which was the bottom surface of the microchannel). The existence of a titanium peak and the absence of other peaks in the precipitates indicate that they are comprised of agglomerated TiO2 nanoparticles (which were precipitated during the execution of the experiments). These results support the hypothesis that there is a modification of the surface geometry on the heat exchanging surfaces which results in the enhancement of the forced convective heat transfer characteristics (both for the nanofluids experiments and the second set of DIW experiments). In other words, the precipitated nanoparticles form ‘nanofins’ which have a more dominant role in enhancing forced convective heat transfer than the change in the thermo-physical property values of the coolant. The results presented in this study are consistent with the previous reports in the literature that explored the role of nanoparticle precipitation on heat transfer (e.g., Yu et al. (2012), Nelson et ;al. (2009)). Yu et al. (2012) reported that both degradation and enhancement of heat transfer depends on the level of precipitation of SiO2 nanoparticles. The experimental results involving degradation of heat transfer for SiO2 nanofluids were associated with excessive precipitation and agglomeration (almost a uniform coating of the heated surface with precipitated nanoparticles). However, in this study, the experimental results involving the enhancement of the heat transfer for SiO2 nanofluids were associated with dispersed and isolated precipitation (the heated surface was dotted with isolated precipitates that potentially acted as “nanofins”). Similarly, in this study, only isolated precipitation of TiO2 nanoparticles was observed in the SEM images (shown in Fig. 8(a)) leading to the enhancement of heat transfer in the experiments (both the nanofluids experiments and the second set of DIW experiments). The reason for the more dispersed and isolated precipitation of the TiO2 nanoparticles (compared to that of the SiO2 nanofluid experiments reported in a previous study (Yu et al., 2012)) is possibly due to the enhanced stability of the TiO2 nanofluids (compared to that of the SiO2 nanofluids) as well as the lower affinity of the pyrex glass substrate for TiO2 nanoparticles (compared to that of the SiO2 nanoparticles). In addition, it was reported that the classical impact and adhesion theory for macro-scale particles is valid for the prediction of the collision dynamics involving nano-sized particles (Jung et al., 2012). Thus, the numerical simulation based on a combined Euler and Lagrange method (i.e., DPM: Discrete Phase Model) was performed to validate the experimental results observed in Fig. 8(a). In this simulation, the base fluids are still assumed to be a continuous phase, and the flow and heat transfer behavior are governed by the general Navier Stokes equation (i.e., mass, momentum and

Experimental validation was performed for numerical predictions performed in this study involving forced convective heat transfer of TiO2 nanofluids in a microchannel for a laminar flow regime (in the realm of a creeping flow regime). The PDMS microchannel (with a hydraulic diameter, Dh , of 105.5 μm) was integrated with a Thin-Film Thermocouple (TFT) array, which was microfabricated in-situ, and was used to measure the temperature variations at the wall under constant heat flux conditions. Additionally, numerical modeling using the Feng–Kleinstreuer (FK) model for predictions of the thermal conductivity of nanofluids was done for comparison with the experimental results for the same experimental configurations including the wall temperatures, flow rates, and concentrations. As a result, it was concluded that the isolated precipitation of the nanoparticles at the heated wall (which behaved as “nanofins”) was the most dominant heat transfer mechanism for the flow of nanofluids (with very low mass concentrations of nanoparticles) in the microchannel. Hence, the interfacial phenomenon is shown to be the more dominant mechanism rather than the thermo-physical properties of nanofluids. The enhancements observed in the experiments were not predicted by the conventional numerical models because the numerical models accounted for the change in the thermo-physical property values only and did not incorporate the effect of precipitation (i.e., the “nanofin effect”). However, the precipitation of nanoparticles was successfully shown in the numerical analysis that considered both particle tracking (i.e., DPM: Discrete Phase Model) and two-phase flow modeling which can provide insights for a better understanding of the fundamental mechanism for the sticking of nanoparticles on the heated wall. Acknowledgments This work was supported with grant from Qatar National Research Foundation (QNRF). This research was also supported by a grant from R&D Program of the Korea Railroad Research Institute, Republic of Korea. References Acharya, S., Alvarado, J., Banerjee, D., 2013. Report on carbon nano material workshop: challenges and opportunities. Nanoscale Microscale Thermophys. Eng. 17 (1), 10–24. Alvarino, P.F., Jabardo, J.M.S., Agras, J.D.P., Valle, J.G.D., 2015. Self-diffusion assessment in laminar developed flow of nanofluids in microchannels. Int. J. Therm. Sci. 98, 113–123. Anoop, K., Sadr, R., Yu, J., Kang, S., Jeon, S., Banerjee, D., 2012. Experimental study of forced convective heat transfer of nanofluids in a microchannel. Int. Commun. Heat Mass Transf. 39 (9), 1325–1330. Assael, M., Metaxa, I., Kakosimos, K., 2006. Thermal conductivity of nanofluids–experimental and theoretical. Int. J. Thermophys. 27 (4), 999–1017. Bahiraei, M., Hosseinalipour, S.M., 2013. Particle migration in nanofluids considering thermophoresis and its effect on convective heat transfer. Thermochem. Acta 574, 47–54.

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[m5G;November 22, 2016;8:56]

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Brach, R.M., Dunn, P.F., 1992. A mathematical model of the impact and adhesion of microspheres. Aerosol Sci. Tech. 16, 51–64. Buongiorno, J., et al., 2009. A benchmark study on the thermal conductivity of nanofluids. J. Appl. Phys. 106 (9), 094312. Choi, E.S., Brooks, J.S., Eaton, D.L., 2003. Enhancement of thermal and electrical properties of carbon nanotube polymer composites by magnetic field processing. J. Appl. Phys. 94 (9), 6034–6039. Das, S.K., Putra, N., Thiesen, P., 2003. Temperature dependence of thermal conductivity enhancement for nanofluids. J. Heat Transf. 125 (4), 567–574. Eastman, J.A., Choi, S.U.S., Li, S., 1997. Enhanced thermal conductivity through the development of nanofluids. In: Proceedings of the 1996 MRS Fall Symposium, December 2, 1996 - December 5. Boston, MA, USA. Anonymous Materials Research Society, pp. 3–11. Eastman, J.A., Choi, S.U.S., Li, S., 2001. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78 (6), 718–720. Farsad, E., Abbasi, S., Zabihi, M., 2011. Numerical simulation of heat transfer in a micro channel heat sinks using nanofluids. Heat Mass Transf. 47 (4), 479–490. Fedele, L., Colla, L., Bobbo, S., Barison, S., Agresti, F., 2011. Experimental stability analysis of different water-based nanofluids. Nanoscale Res. Lett. 6 (1), 1–8. He, Y., Men, Y., Zhao, Y., 2009. Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions. Appl. Therm. Eng. 29 (10), 1965–1972. Hidrovo, C.H., Goodson, K.E., 2008. Active microfluidic cooling of integrated circuits. In: Meindl, J., Bakir, M. (Eds.), Electrical, Optical, and Thermal Interconnections for 3D Integrated Systems. Artech, Boston, pp. 293–330. Incropera, F.P., 2011. Fundamentals of Heat and Mass Transfer. John Wiley & Sons. Jang, S.P., Choi, S.U.S., 2006. Cooling performance of a microchannel heat sink with nanofluids. Appl. Thermal Eng. 26 (17-18), 2457–2463. Jo, B., Banerjee, D., 2011. Enhanced viscosity of aqueous silica nanofluids. Dev. Strat. Mater. Comput. Des. II 32, 139–146. Jo, B., Banerjee, D., 2014. Enhanced specific heat capacity of molten salt-based nanomaterials: effects of nanoparticle dispersion and solvent material. Acta Mater. 75, 80–91. Jo, B., Banerjee, D., 2014. Effect of dispersion homogeneity on specific heat capacity enhancement of molten salt nanomaterials using carbon nanotubes. J. Sol. Energy Eng. 137 (1), 011011. Jo, B., Banerjee, D., 2014. Viscosity measurements of multi-walled carbon nanotubes-based high temperature nanofluids. Mater. Lett. 122, 212–215. Jung, S., Banerjee, D., 2011. Enhancement of heat capacity of nitrate salts using mica nanoparticles. Dev. Strat. Mater. Comput. Des. II 32, 127–137. Jung, J., Oh, H., Kwak, H., 2009. Forced convective heat transfer of nanofluids in microchannels. Int. J. Heat Mass Transf. 52 (1-2), 466–472. Jung, S.-C., Bang, J.-G., Yoon, W.-S., 2012. Applicability of the macro-scale elastic contact theories for the prediction of nano-scaled particle collision with a rigid flat surface under non-adhesive and weakly-adhesive conditions. J. Aerosol Sci. 50, 26–37. Khanafer, K., Vafai, K., 2011. A critical synthesis of thermophysical characteristics of nanofluids. Int. J. Heat Mass Transf. 54 (19), 4410–4428. Kleinstreuer, C., Feng, Y., 2012. Thermal nanofluid property model with application to nanofluid flow in a parallel-disk system—part I: a new thermal conductivity model for nanofluid flow. J. Heat Transf. 134 (5), 051002. Kleinstreuer, C., Li, J., 2008. Discussion: effects of various parameters on nanofluid thermal conductivity (Jang, S. P., and Choi, S. D. S., 2007, ASME J. Heat Transfer, 129, pp. 617–623). J. Heat Transf. 130 (2), 025501. Kline, S.J., McClintock, F.A., 1953. Describing uncertainties in single sample experiments. Mech. Eng. 75 (1), 3–8. Lee, J., Mudawar, I., 2007. Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels. Int. J. Heat Mass Transf. 50 (3-4), 452–463. Lee, S., Choi, S.U.S., Li, S., 1999. Measuring thermal conductivity of fluids containing oxide nanoparticles. J. Heat Transf. 121 (2), 280–289. Liu, Y., Cui, J., Li, W., 2011. Effect of surface microstructure on microchannel heat transfer performance. J. Heat Transf. 133 (12), 124501. Lukaszewicz, P., 2009. Running resistance and energy consumption of ore trains in Sweden. Proc. Inst. Mech. Eng. Part F 223 (2), 189–197. Murshed, S.M.S., Leong, K.C., Yang, C., 2008. Investigations of thermal conductivity and viscosity of nanofluids. Int. J. Therm. Sci. 47, 560–568.

Namburu, P.K., Das, D.K., Tanguturi, K.M., 2009. Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties. Int. J. Therm. Sci. 48 (2), 290–302. Nelson, I.C., Banerjee, D., Ponnappan, R., 2009. Flow loop experiments using polyalphaolefin nanofluids. J. Thermophys. Heat Transfer 23 (4), 752–761. Özerinç, S., Kakaç, S., Yazıcıog˘ lu, A.G., 2010. Enhanced thermal conductivity of nanofluids: a state-of-the-art review. Microfluid. Nanofluid. 8 (2), 145–170. Park, S.-H., Kim, T.H., Jeong, J.H., 2016. Experimental investigation of the convective heat transfer coefficient for open-cell porous metal fins at low Reynolds numbers. Int. J. Heat Mass Transf. 100, 608–614. Prasher, R., Bhattacharya, P., Phelan, P.E., 2005. Thermal conductivity of nanoscale colloidal solutions (nanofluids). Phys. Rev. Lett. 94 (2), 025901. Qu, W., Mala, G.M., Li, D., 20 0 0. Heat transfer for water flow in trapezoidal silicon Microchannels. Int. J. Heat Mass Transf. 43 (21), 3925–3936. Sahu, M., Singh, P., Mahapatra, S.S., 2012. Prediction of entrance length for low Reynolds number flow in pipe using neuro-fuzzy inference system. Exp. Syst. Appl. 39 (4), 4545–4557. ´ D., Filipowic, ´ S., 1992. Measurement and application of zeta-poSalopek, B., Krasic, tential. Rudarsko Geolosko Naftni Zbornik 4, 147–151. Sathyamurthi, V., Banerjee, D., 2009. Non-linear dynamical analyses of transient surface temperature fluctuations during subcooled pool boiling on a horizontal disk. Int. J. Heat Mass Transf. 52 (23–24), 5608–5623. Shin, D., Banerjee, D., 2011. Enhanced specific heat of silica nanofluid. J Heat Transf 133 (2), 024501–1–4. Shin, D., Banerjee, D., 2011. Enhancement of heat capacity of molten salt eutectics using inorganic nanoparticles for solar thermal energy applications. Dev. Strat. Mater. Comput. Des. II 32, 119–126. Shin, D., Banerjee, D., 2011. Enhancement of specific heat capacity of high-temperature silica-nanofluids synthesized in alkali chloride salt eutectics for solar thermal-energy storage applications. Int. J. Heat Mass Transf. 54 (5-6), 1064–1070. Shin, D., Banerjee, D., 2013. Enhanced specific heat capacity of nanomaterials synthesized by dispersing silica nanoparticles in eutectic mixtures. J. Heat Transf. 135 (3), 032801. Singh, N., Banerjee, D., 2014. Nanofins: Science and Applications. Springer, New York. Singh, P.K., Harikrishna, P., Sundararajan, T., 2011. Experimental and numerical investigation into the heat transfer study of nanofluids in microchannel. J Heat Transf 133 (12), 121701. Singh, N., Shin, D., Banerjee, D., 2012. Nanoscale Effects in Multiphase Flows and Heat Transfer, Microelectronics to Nanoelectronics: Materials, Devices & Manufacturability. CRC Press, pp. 309–348. Sparrow, E.M., Lin, S.H., Lundgren, T.S., 1964. Flow development in the hydrodynamic entrance region of tubes and ducts. Phys. Fluids 7 (3), 338–347. Tuckerman, D.B., Pease, R.F.W., 1981. High-performance heat sinking for VLSI. Electron Device Lett. 2 (5), 126–129. Wang, X., Mujumdar, A.S., 2007. Heat transfer characteristics of nanofluids: a review. Int. J. Therm. Sci. 46 (1), 1–19. Wen, D., Ding, Y., 2004. Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids). J. Thermophys. Heat Transf. 18 (4), 481–485. Wen, D., Zhang, L., He, Y., 2009. Flow and migration of nanoparticle in a single channel. Heat Mass Transf. 45, 1061–1067. Yu, W., France, D.M., Routbort, J.L., 2008. Review and comparison of nanofluid thermal conductivity and heat transfer enhancements. Heat Transf. Eng. 29 (5), 432–460. Yu, J., Kang, S., Jeon, S., 2011. Investigation of convective heat transfer of aqueous nanofluids in microchannels integrated with temperature nanosensors, Paper No. IMECE2011-64082. In: Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition, November 11-17. Anonymous Denver, Colorado. Yu, J., Kang, S., Jeon, S., Banerjee, D., 2012. Heat transfer measurements for flow of nanofluids in microchannels using temperature nano-sensors. Front. Heat Mass Transf. (FHMT) 3, 013004. Zhang, X., Gu, H., Fujii, M., 2007. Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles. Exp. Therm. Fluid Sci. 31 (6), 593–599.

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