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

Highlights

• The enhanced thermal performance of nanofluids was resulted from the isolated precipitation of nanoparticles.

• The Enhancement (by the ``nanofin effect'') was also shown in the flow of DIW after the flow of nanofluids.

• 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'' depends on the flow rates, wall temperatures, and mass concentrations of nanoparticles.

• Both the thermo-physical properties of nanofluids and migration of nanoparticles at the solid-fluid interface are key factors.

Abstract

In this study, we postulated and demonstrated that surface conditions have a dominant role in multi-phase 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 solid-fluid 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.

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 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 power stations (TPS) (Shin and Banerjee, 2011Shin and Banerjee, 2011a, Jo and Banerjee, 2014aa). 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 thermo-physical 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 trade-off 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 nano-sheets 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., 2003, Wen and Ding, 2004). 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 Al₂O₃ 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 nanofluids 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, Singh et al., 2012, Shin and Banerjee, 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 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., 2000, 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 ``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 heat-exchanging 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 solid-fluid 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.