Performance of SiO2-water nanofluids for single bubble-based nucleate pool boiling heat transfer

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Performance of SiO2-water nanofluids for single bubble-based nucleate pool boiling heat transfer Prasad Kangude, Atul Srivastava∗ Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

ARTICLE INFO

ABSTRACT

Keywords: Nanofluids Nucleate pool boiling Bubble dynamics Heat transfer rates

Experiments on single bubble-based pool boiling have been performed under saturated bulk conditions to understand the influence of suspended nanoparticles on bubble dynamics and the associated temperature gradients field. Water and two concentrations of silica-water nanofluid (0.005 and 0.01% (V/V)) have been subjected to isolated nucleate pool boiling on a ITO-coated borofloat heater by supplying constant heat flux. Experimental measurements have been made in a purely non-intrusive manner by employing refractive index-based rainbow schlieren deflectometry technique. Bubble dynamic parameters, such as bubble departure diameter and departure frequency, wait and growth times etc. and the temperature gradients in the bulk fluid have been mapped simultaneously in the form of schlieren images. Results on bubble dynamic parameters revealed that these parameters show more variability and assume skewed normal distribution in the case of nanofluids whereas water experiments showed insignificant variations in these parameters. Of the significant changes, the bubble departure diameter reduced, departure frequency and growth rate increased with increasing concentration of nanofluids. Schlieren images corresponding to 0.005 and 0.01% (V/V) nanofluids showed more spreading out of the superheat layer adjacent to the heater substrate than that observed in the case of water experiments. Time-averaged values of natural convection and evaporative heat transfer rates associated with single bubble-based boiling indicated that both these rates decrease in the presence of dispersed silica nanoparticles. Reduction in the overall heat transfer rate in the case of nanofluids has been explained on the basis of direct experimental measurements. In this direction, the observed phenomenon has been attributed to the role played by the suspended nanoparticles in diffusing the thermal gradients (reflected in the form of the broadening of the superheat layer) adjacent to the heater substrate along with substantially increasing the wait time of bubble inception in the case of nanofluids as compared to water-based experiments conducted under same wall superheat conditions.

1. Introduction Boiling is a two phase heat transfer process in which most of the heat is removed from the heater surface in the form of latent heat as compared to the sensible heat, which is the primary mechanism in the case of single-phase heat transfer processes. It makes boiling one of the most efficient heat transfer processes among other convection processes, as it provides significant heat transfer rates for a given temperature difference between the heater surface and bulk liquid. This has enabled boiling to be employed in many engineering applications such as small-scale electronic cooling to large-scale nuclear reactor cooling wherein, high heat flux dissipation is utmost important to maintain safe and efficient operation of the heat transferring devices. The efficiency of boiling heat transfer varies with the applied temperature difference and the various boiling regimes have been categorised based on the nature of bubble

∗

interactions and the heat transfer characteristics [1]. The regime of nucleate boiling has drawn considerable attention in recent times because it renders high heat transfer coefficients. The current demand of the heat flux dissipation in the engineering devices has been increasing day by day in view of the miniaturization of such devices as a result of technological advancement. To cope up with these challenges associated with the miniaturised systems, researchers have been seeking for new effective possible ways to enhance the thermal performance of boiling heat transfer process. In this direction, as part of recent developments, nanofluids have proven to be promising fluids to enhance the boiling heat transfer rates since they exhibit significant improvement in the thermophysical properties over that of the base fluids. Nanofluid is a stable suspension of engineered nano-size particles, which are uniformly dispersed in any conventional heat transfer fluid [2]. The nano-size particles can be made of metals (copper, silver),

Corresponding author. Department of Mechanical Engineering, IIT Bombay, Powai, Mumbai, 400076, India. E-mail address: [email protected] (A. Srivastava).

https://doi.org/10.1016/j.ijthermalsci.2019.01.027 Received 6 July 2018; Received in revised form 19 January 2019; Accepted 21 January 2019 1290-0729/ © 2019 Elsevier Masson SAS. All rights reserved.

Please cite this article as: Kangude, P., International Journal of Thermal Sciences, https://doi.org/10.1016/j.ijthermalsci.2019.01.027

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Nomenclature

Greek symbols

CHF D d f H hfg HTC k L n q T t V

δ θ

Critical heat flux Equivalent spherical bubble diameter (mm) Distance away from the centre of the color filter (mm) Bubble departure frequency (Hz) Hue (radians) Latent heat of evaporation (J/kg) Heat transfer coefficient Thermal conductivity (W/m-K) Length of test cell (m) Refractive index Heat transfer rate (W) Temperature (°C) Time (ms) Bubble volume (mm3)

Refractive index difference w.r.t bulk liquid, uncertainty Angular deflection (radians)

Subscripts bulk cyl d evap nat sp wall v

metal oxides (titania, alumina, silica), carbon nanotubes/nanofibers and polymers etc. In the initial stages of the research on the nanofluids in the context of heat transfer, majority of the researchers have reported that the suspended nanoparticles in nanofluids enhance the thermal conductivity of the fluids [2–4]. These findings led the researchers to explore the performance of nanofluids in the context of boiling heat transfer phenomenon. In this regard, it has been found that the nanofluids substantially change the performance of the boiling process in terms of heat transfer coefficient (HTC) and critical heat flux (CHF). To the best of authors knowledge, majority of the researchers have attributed these observations to the modifications in the heater surface characteristics caused by the possible deposition of nanoparticles on the heater surface during boiling process [5–8]. The surface characteristics like wettability, capillary wicking and roughness have shown to affect the bubble dynamics significantly [9–11]. In the context of nanofluid-based nucleate boiling phenomena, majority of the experimental studies have focussed on finding the plausible effects of nanofluids on the overall behaviour of the boiling process in terms of determination of HTC and CHF. Furthermore, in these studies, HTC has been calculated on an overall basis by measuring the supplied heat flux and the wall superheat. The determination of individual contribution of the various heat transfer mechanisms of boiling phenomenon such as natural convection, evaporation, transient conduction during waiting period etc. towards the overall HTC has not yet been attempted in the context of nanofluid-based nucleate boiling phenomena. Hence, this approach has its limitations towards developing detailed insight into the possible role(s) of suspended nanoparticles on the boiling process. In addition, there has been a certain level of inconsistency in the results with regard to the modification of the HTC for the nanofluid-based heat transfer studies [12–14] wherein, various authors have reported contradictory observations in terms of possible enhancement, deterioration and/or even no change in the HTC values in their respective studies [9,15]. The enhancement in HTC has been supported by the possible enhancement in the thermal conductivity and the nano-fin effects [13,16,17]. The concerned literature shows that the uniformly dispersed nanoparticles enhance the thermal conductivity of nanofluids through various mechanisms that includes Brownian motion, thermophoresis, turbulence intensification, micro convection etc. [18–20] and thus increase the heat transfer rates. The deterioration is attributed to the possible effect(s) of deposited nanoparticles on the thermal resistance to the heat flow and on the bubble dynamics [13]. Narayan et al. [15] reported that the nature of change in the HTC depends upon a parameter that is defined as the ratio of average surface roughness of the clean heater substrate to the average diameter of the nanoparticles. Based on the experimental results, the authors concluded that if the parameter is close to unity, HTC deteriorates and if it is greater than unity, HTC enhances. Considering the

Bulk conditions Ebullition cycle Departure Evaporation Natural convection Superheat Heater substrate surface Vapor

extent of scatter in the primary findings of such studies reported in the literature, it is evident that a detailed understanding of the influence of suspended nanoparticles on the dynamics of bubble and the associated temperature gradients field is needed from a fundamental point of view. In addition, various challenges such as nanoparticles stability and deposition, activation of undesired nucleation site etc. posed by the nanoparticles in performing nanofluid-based isolated/single bubble boiling experiments have also severely limited the number of experimental works in this field. Wu and Zhao [14] reviewed the nanofluid-based boiling heat transfer studies and pointed out the necessity of investigation of bubble dynamics in boiling studies to understand the exact contribution of suspended nanoparticles as well as those deposited on the heated substrate surface on the boiling heat transfer. Bubble dynamics includes parameters such as bubble departure frequency and departure diameter, growth and wait times etc. as well as processes such as microlayer growth and evaporation, superheat layer adjacent to the heater surface etc. The bubble dynamics plays an important role in deciding the thermal performance of boiling process. Gerardi et al. [9] performed the nanofluid-based pool boiling experiments to examine the bubble dynamic parameters with water-based silica and diamond nanofluids. The authors employed normal high speed video-graphic technique and IR thermal imaging technique simultaneously to map the various bubble parameters such as departure diameter and frequency, wait and growth times, nucleation site density, dynamics of microlayer etc. These parameters were measured and presented in the form of average quantities over the multiple bubbles. Findings of this study showed that the bubble departure frequency decreases and wait time increases as one shifts from water to nanofluid. However, no such proper trend is observed for the case of departure diameter. Overall HTC was calculated from the pool boiling curve and was found to be reducing in the case of nanofluids. Yeom et al. [21] examined the bubble dynamics on a titanium and titania deposited zirconium wire under water based saturated pool boiling with the help of normal videography. The authors found that the bubble volume reduced and the bubble departure frequency increased with the coated wire as compared to that of bare wire. The coated wire also exhibited the enhanced natural and forced convection contribution to the overall heat flux and reduced the contribution of evaporative heat flux. To the best of the knowledge of the authors, the number of studies available in the literature that report the bubble dynamics in the nanofluid-based boiling phenomena are still very scarce. Examining bubble dynamics is important as it depends on many parameters such as type of heating profile, orientation of substrate [22], heater substrate's material [23,24] and its surface properties, working fluid [25] etc. Secondly, of these limited number of studies that have been reported, the majority have been conducted by generating multiple bubbles on 2

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the heater substrate and measurement of the bubble parameters have been performed on an averaged basis over the number of bubbles. This approach has inherent limitations as the neighbouring bubbles interact with each other and change the dynamics of the single bubble that is of interest [26]. It invokes the necessity of conducting the nanofluid-based boiling experiments under single bubble-based nucleate boiling condition. However, the presence of nanoparticles makes it difficult to achieve such conditions in normal experiments. The reason being nanoparticles deposit on the surface when the bubble grows and consequently form a porous layer on the surface, which provide the possible site(s) for more bubble nucleation. The authors believe that this might be one of the reasons that single bubble-based studies are scarce in the literature that is related to the nanofluid-based boiling heat transfer. In this direction, Hamda and Hamed [27] attempted to generate a single vapor bubble on an artificial nucleation cavity with alumina-water nanofluid as the working liquid. The authors observed that bubble size reduces and the bubble assumes more spherical shape in the presence of nanoparticles in the base liquid. The growth rate was found to increase with the nanofluid as compared to that observed in the water experiments. Based on the growth rate, the authors have concluded that the alumina-water nanofluid enhances the heat transfer rate. The above presented literature survey indicates that the majority of the experimental studies associated with the nanofluid-based boiling phenomena have primarily focussed on studying the effect of nanofluids on the overall characteristics of this process in terms of determination of overall HTC and CHF. No efforts have been made to quantify the dependence of individual heat transfer sub-processes such as natural convection, evaporation, and transient conduction etc. on the concentration of the suspended nanoparticles. In this direction, simulation studies concerned with nucleate pool boiling have constantly focused on quantifying the contribution of these heat transfer sub-processes. However, a majority of these simulation studies are limited only to pure liquids and have also been subjected to several assumptions [28–30]. In view of this, to understand the boiling process from a fundamental point of view, attempts are being made to experimentally study the possible effect of nanoparticles on the bubble dynamics and heat transfer rates. However, the scope of the already reported experimental works concerned with the bubble dynamics has been limited by the fact that these studies have primarily made use of high-speed videography for visualization and IR-based thermal camera. While the IR-based thermography is capable of providing temperature distribution on the surface of the heated surface, the technique of videography is pre-dominantly qualitative in nature in a sense that it is limited to the study of bubble dynamic parameters and cannot quantify the whole field temperature and/or its gradients in the bulk liquid. The knowledge of thermal field distribution in the bulk fluid is important for comprehensively understanding the possible influence of suspended nanoparticles on the individual contribution of various heat transfer mechanisms that are associated with the nucleate pool boiling. In this direction, experimental works by Yabuki et al. [31] and Narayan et al. [32,33] focussed on mapping the whole field temperature distribution in the boiling chamber with water as the bulk liquid, become the initial references. In view of the above discussion, it becomes imperative to investigate in real time the plausible effect(s) of suspended nanoparticles on the dynamics of a single vapor bubble and the associated thermal gradients field adjacent to the heater substrate as well as around the vapor bubble. In this direction, refractive index-based imaging techniques become important as they provide direct in-situ visualization of the bubble dynamics and simultaneously measure the spatio-temporal temperature and/or temperature gradients field across the region of interest in qualitative as well as quantitative terms. Thus, with regard to the nucleate boiling of nanofluids as working liquids, possible effect(s) of suspended nanoparticles on the various thermal sub-processes such as superheat layer on the heater substrate, part of the superheat layer enveloping the growing bubble etc. in conjunction with the bubble dynamic parameters may be explained in detail, which in turn, forms the primary motivation of the present work.

The primary objective of the present study is to investigate the possible role(s) of suspended nanoparticles in influencing various heat transfer mechanisms associated with isolated nucleate pool boiling phenomena. These mechanisms include natural convection, bubble growth (evaporation), overall heat transfer etc. In this direction, single bubble-based pool boiling experiments have been conducted for water and two concentrations of silica-water nanofluids under saturated bulk conditions. The employed concentrations of nanoparticles are 0.005% and 0.01% (V/V). The measurements have been performed in a purely non-intrusive manner using one of the refractive index-based imaging techniques, namely rainbow schlieren deflectometry. Various bubble dynamic parameters that include bubble departure diameter and departure frequency, wait and growth times have been determined from the recorded schlieren images for any given working fluid (water/nanofluid). The same set of images have further been employed to extract the quantitative data on space and time-resolved temperature gradients field with the help of suitable data reduction algorithms. Based on the quantitative data, individual contributions of natural convection and evaporation heat fluxes have been determined with water and 0.005% nanofluid as the working fluids. The relative contributions of natural convection and the evaporation heat fluxes in the case of water with respect to that of nanofluid provide the necessary experimental basis for understanding the possible influence of suspended nanoparticles on the single bubble-based boiling heat transfer process. The study becomes important as the experimental studies dedicated towards investigating the influence of suspended nanoparticles on single bubble-based pool boiling heat transfer are scarce in the open literature. In addition, to the best of the authors’ knowledge, there has been no such experimental study in the available literature that employs a non-intrusive refractive index based technique for simultaneously mapping the bubble dynamics as well as the associated temperature gradients field in quantitative terms in the context of nanofluid-based boiling heat transfer phenomena. 2. Experimental apparatus and instrumentation A specially designed optically accessible boiling chamber has been developed for conducting the pool boiling experiments. Fig. 1(a) shows the orthographic drawing of the boiling chamber and Fig. 1(c) shows its actual photograph. As shown in Fig. 1(a) and (c), the boiling chamber, made of stainless steel, is square in plan and fitted with four optical windows that are fixed on its four walls. The boiling chamber consists of two cavities; the inner open cavity and the outer annular cavity that is in between inner cavity and the outer walls of the boiling chamber. The inner cavity holds the test liquid (water/nanofluid) and thus can be termed as test cell. The outer annular cavity acts as a jacket for circulating high temperature di-ethylene glycol oil. The oil is circulated through the annular jackets with the help of constant temperature oil bath to maintain the temperature of the test liquid at its saturation temperature throughout the experimental run time. Extended surfaces have been provided in the annular jackets in an attempt to enhance the heat transfer from the hot oil to the inside test liquid. The optical windows, made up of BK7 material with λ/6 flatness, have been fixed in the steel housings and these housings have been screwed to the boiling chamber for easy overhaul. The housings have been designed in such a way that they position the optical windows on the wall of the inner cavity. Thus, the distance between two opposite walls of the inner cavity plays an important role as it decides the amount of light that can be collected by the optical windows after refraction. The optical windows are 25 mm diameter circular disks of thickness 5 mm. In order to avoid leakage of hot oil into the test cell through the optical windows, standard high temperature “O” ring has been used. The inner cavity has necessary arrangement at the bottom to fix the heater substrate at a certain height in such a way that the heater substrate can be seen through the optical windows. The heater substrate, shown in Fig. 1(b), is a thin ITO film coated borofloat glass of dimension 25 mm × 25 mm × 0.7 mm. A thin layer of indium tin oxide (ITO) is vacuum deposited on the borofloat 3

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supply for resistive heating. To provide proper electrical connections, the two legs of the ITO film have been coated with highly conductive silver paste and consequently, electric wire leads have been attached to these legs by using high temperature silver epoxy. Single bubble has been generated on the heater substrate by providing it a concentrated heat flux. To achieve concentrated heat flux, ITO coating is chemically washed off the substrate to a shape, as shown in Fig. 1(b). Owing to the inherent characteristics of this shape - high electric resistance at the central portion due to the reduced current passage area, it facilitates generation of relatively higher amount of thermal energy at the central portion, in accordance with Joule's law of heating (P = I2R). As a result, more heat is available at the central portion, which acts as the concentrated heat flux and leads to the inception of single vapor bubble. Thus, the effective heating area is the central portion of the ITO film of size 7 ( ± 1) mm × 5 ( ± 1) mm. Two ‘K’- type calibrated thermocouples with an accuracy of ± 0.5 °C have been used to measure the temperature of the bulk liquid and the temperature at the bottom of the heater substrate during the experimental run time. In order to avoid loss of fluid and to maintain the atmospheric pressure in the test cell during experiments, reflux condenser has been installed on the top of the test cell. It is a heat exchanger device, which helps in condensing the vapor that gets evaporated during boiling process and pours it back to the test cell. Room temperature water is circulated through the reflux condenser by using constant temperature water bath to condense the vapor. Rainbow schlieren imaging technique has been utilized to visualize the dynamics of the vapor bubble along with mapping of real time space-resolved temperature gradient field in the bulk liquid adjacent to the heater substrate as well as around the growing isolated bubble. Schematic diagram of the optical configuration of the schlieren-based visualization technique has been shown in Fig. 2(a). The schlieren setup employs two optical components that are achromatic collimating lens (L1) and de-collimating lens (L2). As shown in Fig. 2(a), the setup consists of a 250 Watt white light source. The light rays emitting from the source are collected and focused onto a micron-size aperture (500 μm) by using a convex lens to form a point source at the focal plane of the collimating lens (L1). The diverging light beam from the

Fig. 1. Schematic of the pool boiling apparatus; Orthographic as well as an isometric drawings of the boiling chamber (a) (All dimensions are in mm), schematic of ITO film coated heater substrate (b) and photographic view of the boiling chamber (c) [34].

glass. This ITO layer has a high electrical resistance of 10 Ω/sq. This property of ITO film facilitates the resistive heating of the borofloat glass. A DC power source (0–5 A, 0–32 V) is employed to provide the electric

Fig. 2. Schematic of the rainbow schlieren deflectometry setup (a) and digital image of the rainbow color filter employed in the experiments (b). The principle of color redistribution depending on the strength of temperature gradients has also been shown schematically [34]. 4

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aperture has been collimated to 50 mm diameter beam by using a 100 mm plano-convex lens with a focal length of 1000 mm. The optically accessible boiling chamber has been placed in between L1 and L2 in the path of the collimated light beam. The collimated beam passes through the optical windows of the boiling chamber and gets collected by the central portion of the de-collimating lens (L2), which focuses it on the plane of the color filter. The color filter is a thin transparent photographic film on which different colors have been printed in continuous manner in the radial direction (Fig. 2(b)) as per the methodology proposed by Greenberg et al. [35]. The color filter has been placed at the focal plane of the de-collimating lens (focal length: 500 mm). A high speed color CMOS camera (IDT vision, NX8S1, pixel size: 8.8 μm) with Navitar 12X zoom lens has been placed close to the color filter to record the transients of the single bubble boiling in the form of color schlieren images. The sensitivity of the schlieren measurement depends inversely on the aperture size and varies in direct proportion with the focal length of the de-collimating lens. Thus, proper values of these two parameters have been chosen in the present experimental setup in order to achieve high sensitivity without compromising on the light intensity and in turn on the camera recording speed. When collimated beam of light passes through the undisturbed region of the test fluid, which is maintained at uniform temperature throughout, it travels straight and parallel to the optical axis and gets focused at the central red spot of the color filter, as shown by solid lines in Fig. 2(a). Thus, the undisturbed region of the test fluid is mapped in the form of uniform distribution of red color in the recorded schlieren image. When the light beam probes through the thermally disturbed region, such as thermal boundary layer on the heater substrate, the light rays undergo refraction away from the optical axis. The magnitude and the direction of the refraction angle depend upon the strength and the orientation of the temperature gradients that prevail in the thermally disturbed portion of the test fluid. Stronger temperature gradient regions make the light rays to undergo large angular deflection and vice-a-versa. The refracted light rays get focused onto the color filter away from its centre depending on the extent of refraction (as shown by dotted lines in Fig. 2(a)) and thus, different color distribution is observed in the recorded schlieren images. With reference to the schematic of the refraction of light rays shown in Fig. 2(b), the increasing order of temperature gradient regions is thus identified in the form of continuous variations of colors from Yellow → Green → Blue → Magenta. As mentioned earlier, Red color shade corresponds to the uniform bulk conditions. For easy interpretation of the schlieren image, Greenberg et al. [35] proposed a method to convert the schlieren image from RGB space to the HSI space so that each color can be identified with the unique parameter called hue. Hue is an intensity independent parameter and hence any minor possible fluctuation in the intensity of the light source does not affect it. The value of hue varies linearly from zero to 2π as one moves from the central red band to the outermost magenta band (Fig. 2(b)). As the hue value corresponds to a specific amount of refraction, which in turn depends on refractive index gradient, qualitative as well as quantitative study of refractive-index dependent temperature gradients field in the boiling chamber can thus be performed. Thus, the observation made through the rainbow schlieren-based non-intrusive measurements help develop a detailed understanding of the effect of suspended nanoparticles in the base fluid on the temperature field around the vapor bubble as well as adjacent to the heated substrate, in addition to the bubble dynamic parameters.

Nanofluid preparation is a crucial process in which uniformly dispersed suspension of nanoparticles in the base fluid is prepared. The nanofluid should be stable and coagulation free for time duration that are considerably longer than that of each experimental run. Two concentrations 0.005% and 0.01% (V/V) of silica-water nanofluids were prepared in house by two step process for the present study. Spherical silica nanoparticles of average size of 18 nm were used to make the desired nanofluids. The powdered form of silica nanoparticles were purchased from the SigmaAldrich company (USA). A Millipore DI water dispenser has been used to collect the de-ionized (DI) water (resistivity = 18.5 MΩ-cm at T = 25 °C), which acts as the base fluid for nanofluid preparation. To prepare a certain volumetric concentration of nanofluid, mass of the silica nanopowder corresponding to the required volume concentration was determined by following the approach discussed in Ref. [36] and weighed with the help of a professional weight balance (Citizon) with an accuracy of ± 0.001 g. The weighed nanopowder was dispersed into an appropriate quantity of de-ionized (DI) water and then, this solution was kept for ultra-sonication for 2–3 h. The sonicator used for ultra-sonication was bought from “Oscar Ultra sonication Pvt. Ltd”. No surfactant has been added in the nanofluid. An examination of the nanofluid stability revealed that in-house prepared nanofluid remained stable for more than 6 h without any visible sedimentation, which is long enough compared to the total duration (≈3 h) over which the boiling experiments have been conducted.

2.1. Experimental methodology

that contains combined effect of RGB as H = tan

saturation for at least 2–3 h. After the degasification period, single bubble is generated on the heater substrate by providing constant heat flux using the technique of resistive heating. The high-speed color camera integrated with the schlieren system records the color schlieren images of the boiling process with a spatial resolution of 1600 × 1200 pixels at a frame rate of 1000 Hz. Following the principle of image formation in schlieren-based visualization, the hue distributions recorded in the form of rainbow schlieren images provide a direct measure of the strength of thermal gradients prevailing in the field of view. Thus, these images are further used to quantify the bubble dynamic parameters as well as the associated temperature gradients in the bulk liquid. For each nanofluid experiment, separate heater is used to avoid the possible effect of nanoparticles deposition in the previous experiment on the boiling process of the next experiment. 2.2. Preparation of nanofluid

3. Data reduction methodology The methodology followed for extracting quantitative data in the form of whole field temperature (and/or its gradients) distribution and heat transfer rates from the recorded rainbow schlieren images has been discussed in detail in one of our recent works [32]. The present section provides a brief description of the steps followed in the context of the present experimental images. Each schlieren image stores a path integrated 2D information of refractive index dependent parameter (i.e. temperature gradient in the present study) in the form of color distribution. For quantitative analysis, as suggested by Greenberg et al. [35], the schlieren image needs to be transformed from RGB space to HSI space in order to avoid the complexities associated with the RGB space, such as optical intensity dependence, dependence on pixel to pixel gain variations within a given detector array etc. In HSI space, hue is a unique parameter that eliminates all such complexities and provides a single numeric value 1

(

3 (G B ) 2R G B

). Defining

hue in this manner is necessary for quantitative analysis, to ensure that the continuously graded color filter has, at any of its spatial location, a color transmission function that is described by a single parameter. As schlieren technique works on the deflection of light rays under the influence of varying refractive index field, the relation between refractive index distribution and the corresponding angular deflection forms the basis for evaluation of refractive-index dependent variable(s) (i.e. temperature gradient) in quantitative terms.

The nanofluid-based single bubble pool boiling experiments have been carried out with water, 0.005% (V/V) and 0.01% (V/V) silica-water nanofluids under saturated bulk liquid conditions. For a given working liquid (water/nanofluid), experiments have been performed for two different constant heat fluxes i.e. 34 and 47 kW/m2. In an attempt to minimize the effect of dissolved gases on the boiling phenomenon, at the start of each experiment, test fluid is degasified by maintaining its temperature at 5

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Fig. 3. Calibration curves along the radial direction of the color filter; water (a) and 0.005% silica-water nanofluid (b).

Following the above mentioned approach, angular deflection (θ(x,y)) corresponding to the hue value stored in each pixel is calculated with the help of calibration curve. As shown in Figure (3), the calibration curve relates the hue values associated with the different colors with their distances (d(x,y)) measured on the color filter from the central red color band (with reference to the color filter shown in Fig. 2(b)). Such calibration curves are plotted before every experiments. A linear fit is made through the hue values as a function of radial distance to get the continuous data (as seen in Fig. 3). With the help of the linear fit equation, the spatial map of hue distribution (recorded in the form of schlieren images) is then converted into the two-dimensional distribution (map) of radial distances. Subsequently, the angular deflection distribution in the region of interest is determined by applying geometric transformation and the Snell's law to the radial distance data. The mathematical relation between angular deflection and the refractive index gradient for the line of sight averaged measurement can be given as:

(x , y ) = d (x , y )/(fl nbulk ) = L

1 n dz n r

[39]. Following this, the thermal gradients field adjacent to the heater substrate has been mapped using numerical one step discretization method. It is to be mentioned here that while the dependence of bubble dynamic parameters (departure diameter and frequency, growth time etc.) on concentration of suspended nanoparticles has been studied for 0.005 and 0.01% (V/V) concentration of nanoparticles, the quantitative analysis of rainbow schlieren images to retrieve whole field temperature distribution and heat transfer rates has been restricted to water and 0.005% nanofluids concentration. Relative high turbidity of the bulk fluid with 0.01% concentration of suspended nanoparticles limits the spatial resolution of the recorded schlieren images for such cases. Furthermore, at such concentrations, the initial experiments revealed that, for the given intensity of the light source and the specifications of the color camera employed, it becomes difficult to ensure a linear variation of hue distribution while calibrating the rainbow filter. These factors contribute towards relatively higher levels of errors in the quantitative data retrieved from such images.2 With the whole field temperature distribution determined through Equation (3), the area-averaged instantaneous natural convectionbased heat transfer rates have been obtained by applying the principle of energy balance at the heater substrate surface in the liquid (Equation (4)):

(1)

It should be noted that to get the refractive gradient field, it is necessary to invert Equation (1). In the present single bubble case, it becomes challenging as the refractive index is expected to change in the direction of propagation of light. To overcome this difficulty, axisymmetric nature of the single bubble as well as axisymmetry in the associated temperature gradients has been realized.1 The axisymmetric assumption makes it possible to use the Abel inversion transformation to get the refractive index difference ( (r , y )) field from the angular deflection field, as can be seen in Equation (2) [37]. Thus, the Abel inverted field represents the refractive index field at any sectional plane of the vapor bubble instead of the path averaged one. The integral in Equation (2) has been solved by one of the numerical approaches, as proposed by Chehouani and Fagrich [38].

(r , y ) =

n (r , y ) nbulk

1=

(x , y )

1 r

x2

r2

dx

qnat =

(2)

n dn

dT

wall

(4)

Here, the differential term “ T / y wall ” represents the spatiallyaveraged quantity over the surface (Awall) of the heater substrate. Awall represents the surface area of the heater substrate. It has been chosen to be a circular area around the nucleation site, the radius of which has been taken as the average value of departure diameter of the water vapor bubble for any given working fluid in the experiments. The basis of the selection of such area is that the heater surface can be assumed to be at uniform temperature over this area. Instantaneous evaporative heat transfer rates have been determined by feeding the experimentally measured bubble dynamic parameters, such as bubble departure diameter and bubble growth rate to the mathematical expression given by Equation (5). Equation (5) is based on the conditions that the bubble grows entirely due to the evaporation of the microlayer as well as the superheat layer around the vapor bubble and the inertia-controlled growth is comparatively small. This assumption holds good only for low heat flux experiments/low wall superheat experiments and hence can be justified in the present set of experiments.

The Abel inverted refractive index field is then converted to the temperature field directly by Equation (3).

T = Tbulk +

kAwall T y

(3)

The refractive index dependence of working fluid on temperature is calculated by the empirical relation given by Bashkatov and Genina 1 Heating profile generated on the glass substrate by locally etching the ITOcoating results into an almost axisymmetric temperature distribution with temperature being maximum right at the centre of the heated substrate, which in turn acts as the nucleation site for single bubble generation. The axisymmetric nature of temperature profile on the glass substrate was further confirmed using an IR thermal imaging camera.

2 These limitations may be addressed through the use of high power white light source and integrating a color CMOS camera with considerably higher levels of spatial as well as temporal resolutions.

6

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qevap = m v hfg =

v

D 2 dD hfg 2 dt

concentrations of silica-water nanofluids have been shown in Figure (4). The images correspond to single vapor bubble generated in a saturated pool of respective liquids under constant heat flux condition of q = 34 kW/m2. As discussed in Section 2, rainbow schlieren imaging technique forms an image by redistributing various color shades across the field of view from the original uniform color background as the light rays travel through the variable refractive index region of the test fluid (upon setting up of the temperature gradient field). Sharp color redistributions in the images represent the presence of strong temperature gradients whereas weak color contrast in the schlieren images corresponds to nearly undisturbed uniform temperature bulk conditions. Following this, irrespective of the nanofluid concentrations, clear color re-distribution observed in the vicinity of the heated substrate (on either side of the vapor bubble) in the images shown in Figure (4) indicates towards the presence of strong temperature gradients in these regions. Continuous variation of colors from Magenta→ Blue → Green → Yellow, as one moves away from the heated substrate in the y-direction indicates towards the decreasing strength of thermal gradients. Thus, magenta and blue color shades seen in the images at the heated substrate represent relatively stronger thermal gradients than that indicated by the green and yellow color shades away from the heated substrate. As one moves further away from the yellow color shade in the y direction, one can see almost uniform red color distribution, which indicates towards zero or very weak thermal gradients region. This region corresponds to the uniform temperature bulk liquid as the light rays mapping this region travel almost straight and fall on the central red band of the color filter without undergoing any considerable refraction. Thus, the spatial extent of the color re-distribution in the ydirection provides a direct measure of the thickness of the thermal (superheated) boundary layer near the heated substrate. In general, boiling of saturated liquid occurs on the heated substrate when it is maintained at temperatures greater than the saturation temperature of the liquid. It results in the formation of thermal boundary layer in the vicinity of the heated substrate with temperature of liquid in the layer being greater than that of the saturation temperature of the liquid. In view of this, such thermal boundary layer is also often termed as the superheat layer. Irrespective of the working fluids, images in Figure (4) show various physical processes that are associated with nucleate boiling, such as bubble inception, bubble growth and departure, and waiting periods followed by inception of the next bubble. These images also show a range of thermal sub-processes associated with nucleate boiling, such as development of superheat layer on the heated substrate, envelopment of a part of superheat layer around the vapor bubble as the bubble grows out of the superheat layer, scavenging of part of superheat layer upon bubble departure in the wake region of departing bubble. Bubble inception is characterised by transient form of conduction heat transfer from the heated surface that leads to the formation of small vapor nucleus at the nucleation site after setting up of superheat layer on the heated surface. Bubble growth process is primarily governed by two processes; inertia-controlled growth and thermally controlled growth. The initial part of the growth is governed by inertial-controlled phenomenon wherein, the vapor bubble grows due to the pressure difference that exists across the bubble interface. As the bubble grows through the superheat layer, it carries/pulls a part of the superheat layer

(5)

For performance evaluation of nanofluids-based heat transfer with respect to water as the working fluid, the time-averaged values of natural convection and the evaporative heat transfer rates have been determined by averaging the respective instantaneous heat transfer rates over the complete ebullition cycle. Subsequently, the overall heat transfer rate has been expressed as the sum of the spatio-temporal averaged values of natural convective and evaporative heat transfer rates and is given by Equation (6):

qoverall = qnat

avg

+ qevap

(6)

avg

4. Uncertainty analysis The experimental measurements carried out using non-intrusive, optical measurement techniques (e.g. rainbow schlieren deflectometry, as in the present case) are prone to errors that get induced due to various unavoidable factors such as misalignment of the optical components, slight fluctuations in the ambient conditions, uncertainties associated with the data reduction algorithm and the inherent uncertainties in the input parameters of the experiments (supplied heat flux, volume concentrations of nanoparticles etc.). In an attempt to quantify the uncertainties associated with the present schlieren-based measurements, the approach proposed by Kline and McClintock [40] and further implemented by Naylor and Duarte [41] in the context of interferometrybased measurements has been followed in the present study. Following this approach, the total uncertainty involved in the computation of the natural convective heat transfer rate can be expressed as:

qnat =

qnat k

2

k

+

qnat A

2

2

A

+

qnat

( ) T

y

T

y (7)

The uncertainties associated with the optical misalignment have been reduced to the max-extent possible by carefully aligning the various components of the rainbow schlieren system. Table 1 summarizes the uncertainties associated with the various parameters that eventually propagate into the determination of natural convection rate. The uncertainties in the measurement of temperature gradients field depend on the uncertainties associated with parameters that include calibration curve, angular deflection, Abel inversion transformation, temperature dependence of refractive index etc. In this regard, uncertainties in the temperature gradient field have first been estimated with the help of error propagation formula (similar to that given by Equation (7)) and the uncertainties associated with the independent parameters have been summarized in Table 1. Subsequently, uncertainty associated with the natural convection rate has been determined by using Equation (7). The maximum uncertainty involved in the determination of natural convective heat transfer rate has been found to be ≈ 14% and ≈16% respectively in the case of water and 0.005% (V/V) nanofluid experiments. The uncertainty associated with the measured evaporative heat transfer rate can be expected to be small as it depends on only one experimentally measured parameter (departure diameter) and has been found to be ≈ 1%.

Table 1 Uncertainty values associated with the major individual parameters.

5. Results and discussion The bubble dynamics and the temperature gradient field associated with the single bubble isolated pool boiling has been studied for different volume concentrations of silica-water nanofluid under saturated bulk conditions. The results have been interpreted in qualitative as well as quantitative terms on the basis of images recorded using rainbow schlieren deflectometry technique. Rainbow schlieren images of vapor bubble at various time instants during bubble growth and wait times for water and two 7

Parameter

Uncertainty (0.005% (V/V) nanofluid)

Linear deflection Angular deflection Abel inversion transformation Bulk temperature Thermal conductivity Temperature dependence of refractive index Temperature field Rate of change of bubble volume

0.5 mm 0.001 radians 0.0022 0.5 °C 0.001 W m−1 oC 1 × 10−5 °C −1

−1

1.2 °C 6.41 × 10−8 m3 s−1

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Fig. 4. Rainbow schlieren images of single vapor bubble recorded at various time instants during one complete ebullition cycle for water (a), 0.005% nanofluid (b) and 0.01% nanofluid (c) under constant heat flux condition (q = 34 kW/m2).

along its periphery due to the viscous effects, as can be seen in the initial images presented in Fig. 4((b) and (c)). When the pressure difference achieves a static equilibrium with the opposing surface tension effects, thermally driven growth process begins to dominate the bubble growth. During this process, bubble grows in size due to the evaporation of liquid from the microlayer and the superheat layer around the vapor bubble. Once the bubble volume increases beyond a certain limit, the upward acting buoyancy force exceeds the counteracting surface tension and adhesion forces (that tend to resist the bubble detachment from the surface), finally leading to the bubble departure. Upon bubble departure, surrounding cold liquid rushes in to fill up the departed bubble volume. At the same time, part of the superheat layer gets pulled up in the wake region of the departing bubble (can be seen in Fig. 4, images corresponding to t/tcyl = 0.43, 0.84, 1 in the second and third row of the figure). Both these mechanisms occur simultaneously and create a lot of mixing in the wake region that tends to disrupt the localised superheat layer in the vicinity of the heated substrate. The disrupted thermal boundary layer is reformed by the transient form of heat conduction to the adjacent liquid from the heated surface and subsequently, the whole process repeats itself. Time taken by such process to repeat itself is termed as ebullition cycle. Thus, the various thermal sub-processes that co-exist with the bubble growth and its subsequent departure play significant role in enhancing the heat transfer rates in addition to the latent heat transfer in the form of bubble departure. Influence of nanoparticles concentration on the bubble dynamics and the associated thermal sub-processes can be distinctively seen in Figure (4). By close examination of the instantaneous images shown, it can easily be discerned that increasing nanoparticle concentrations reduce the growth time and increase the wait time of the vapor bubble ebullition cycle. For instance, in the case of base fluid (water), the nondimensionalized growth time and wait time are ≈ 0.95 and ≈ 0.05 respectively, while, growth times reduce by almost 92% & 93% and wait times increase by almost 862% & 525% respectively in the case of 0.005% and 0.01% nanofluids. It is pertinent to mention here that though the trends presented in Figure (4) have been inferred based on only one ebullition cycle of each experimental case, similar trends have been observed on the basis of statistical averaging of several number of cycles in the respective experiments. These details have been presented in Section 5.1 that is focussed on bubble dynamics. Effect of the presence of nanoparticles on the profile of the superheat layer formed on the heater substrate can be seen from Fig. 4(b and c) as compared to the case of base fluid. In this direction, from the experimental data shown, the superheat layer can be seen to be more diffused/spread out in the vertical direction (perpendicular to the heater substrate) in the

case of nanofluids (Fig. 4(b and c)). The extent of diffusion/spread out of the superheat layer increases with increasing volume concentration of nanofluids. In an attempt to provide quantitative evidence to these observations made on the basis of the schlieren images shown in Fig. 4, hue values (that in turn represent the strength of temperature gradients) have been measured along the y-direction starting from the heated substrate at a certain fixed x location (corresponding to 175th pixel location (pixel size ≈ 16 μm) from the centre of the bubble along the length of the heated substrate) when t/tcyl = 0.5 for water and nanofluids cases and the observed variations have been plotted in Figure (5). The hue values shown in Figure (5) are the average of the values recorded over the fixed time instants of four different cycles. It is clearly evident from Figure (5) that an increase in the nanoparticle concentration tends to spread out the superheat layer considerably. For instance, the extent of hue (thermal gradient) variations is restricted over a significantly short distance (≈0.60 mm) from the surface of the heated substrate in the case of base fluid. In contrast, the corresponding vertical stretches of the variations in the hue values for 0.005% and 0.01% (V/V) concentration of nanofluids can be observed over larger distance (≈0.90 mm). Such spreading out of the superheat layer adjacent to the heater substrate in the case of nanofluidsbased experiments can be attributed to the plausible influence of Brownian motion and the thermophoresis effects of the suspended nanoparticles in the superheat layer. In addition, it has been observed that the suspended nanoparticles deposit and form a porous layer around the nucleation site on the heater substrate during the bubble growth. Such porous layer acts as a thermal resistance to the heat flow from the heated substrate to the adjacent liquid and thus contributes towards the stretching out of the superheat layer in the case of nanofluids.3 These plausible reasons explaining the observed trends find support in the already reported works [42–44] wherein the role(s) of similar phenomena (e.g. Brownian motion and thermophoresis) on nanofluids-based heat transfer processes have been discussed based on interferometry and rainbow schlieren techniques based measurements. The spread out of the superheat layer in the case of nanofluids is also seen to affect the other thermal sub-processes. In this regard, a

3 To justify the influence of deposited layer of nanoparticles on the profile of superheat layer in the bulk liquid adjacent to the heated substrate, separate set of natural convection-based experiments have been performed on the clean as well as nanoparticle-deposited surfaces with water as the bulk liquid. Initial findings showed that the superheat layer on the nanoparticle-deposited heated substrate gets relatively more stretched out in comparison to that observed in the case of clean heated substrate.

8

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actual vapor bubble [45,46]. The volume of an actual vapor bubble is calculated from the recorded schlieren image wherein, the bubble is considered axisymmetric and thus can be considered to be formed by stacking of a number of circular disks of thickness equal to the pixel size. Following this, the volume and the departure diameter of the vapor bubble can respectively be calculated by the following geometric expressions: i=h

V= i=1

Dd =

3

4

Di2 × pixelsize

6V

(8)

(9)

Where, Di represents the diameter of a circular disk at any ith location (i is an index which varies from bubble base to its apex position). The above-mentioned parameters have been measured over a number of bubble cycles in a given experiment and the inherent variations in these parameters have been presented in the form of bar charts in Figure (6). The data presented in Fig. 6(a) clearly reveal that the bubble parameters (departure diameter, departure frequency, wait time) do not show any significant variations in the case of base fluid and thus indicate towards stable single bubble nucleation. However, with increasing nanofluids concentrations, the presented bubble parameters show substantial amount of variations and the scatter of these parameters increases with increasing concentration (Fig. 6(b) and (c)). The bar charts presented in Figure (6) provide the direct evidence of unstable characteristics/features of nucleation in the case of nanofluid experiments due to the presence of suspended nanoparticles in the bulk fluid. The average values of the bubble parameters have been determined to help understanding the possible effects of increasing concentrations of nanofluids on these parameters. It has been found that the average bubble departure diameter decreases and the average departure frequency increases as one moves from base fluid case to 0.01% (V/V) nanofluid case. The observed trends may be explained as follows: The bubble departure diameter is primarily governed by the balance between the upward acting buoyancy force and the oppositely acting surface tension and adhesion forces [47]. Hence, a reduction in the departure diameter with increasing concentration of nanoparticles, as observed in the present analysis, can be attributed to the decreasing strength of surface tension force as the dynamic contact angle of the bubble interface at the contact line has been found to decrease with increasing nanoparticle concentrations. Similar observations with regard to the dependence of contact angle on nanoparticles concentration have also been reported in one of our recent works (Kangude et al. [34]), wherein a clear reduction in the dynamic contact angle with increasing concentrations of dilute nanofluids has been experimentally shown. In addition, a range of other researchers (e.g. Kim et al. [10], Jeong et al. [48], Gerardi et al. [9]) have also reported similar trends with regard to the contact angle based on the measurements of static contact angle on nanoparticles deposited surfaces. Decreasing strength of surface tension force can also be attributed to the possible reduction in the values of surface tension of nanofluids when compared to the surface tension value of the base fluid (water). However, surface tension values reported in the recent experimental studies for various concentrations of nanofluids show lot of scatter. Recently, Bhuiyan et al. [49] and Moosavi et al. [50] have experimentally shown that the surface tension values do not change significantly for the concentrations of nanofluids that have been employed in the present experiments as compared to that of base fluid. Hence, it is quite reasonable to consider that the values of surface tension do not affect the bubble diameter/dynamics that significantly for the current cases of low concentrations of nanofluids. With reference to the data presented in Figure (6), the average wait time can be seen to increase quite significantly from base fluid to

Fig. 5. Hue variations along the y-direction measured from the heater substrate at a fixed x location near the vapor bubble for water and two concentrations of nanofluids (q = 34 kW/m2). The error bars represent standard deviations.

small portion of superheat layer enveloping the vapor bubble that is visible in the form of light green and yellow shades of hue in the images shown in Fig. 4(b and c) is to be observed in the case of 0.005% and 0.01% (V/V) silica nanofluids respectively. On the other hand, no such color shades of hue are seen around the water vapor bubbles. The presence of such color shades, which in turn indicate the prevalence of the thermal gradients, around the growing vapor bubble in the case of nanofluids indicate that the bubble growth is additionally aided by the evaporation of the liquid layer enveloping the bubble. The contribution of this component to the bubble growth depends on the strength of the thermal gradients that exist in the liquid layer. With reference to the color filter shown in Fig. 2(b), increase in the strength of thermal gradients is characterised/reflected by the changing shades of color/ hue from yellow to magenta as one moves towards the bubble interface from the bulk liquid. Furthermore, the nanofluid-based experiments show the strong scavenging effect of superheat layer in the wake region of the departing bubble. This scavenging phenomenon may be identified in the form of darker shades of green and yellow colors prevailing in the wake region (Fig. 4(b and c) of the upward moving bubble as compared to the lighter shades of only yellow color that is to be observed in the base fluid experiment (Fig. 4(a)). Thus, the images shown in Figure (4) provide direct experimental evidence of the influence of varying concentrations of suspended nanoparticles on the various thermo-physical sub-processes that govern the single bubble-based nucleate pool boiling heat transfer phenomena in qualitative terms. 5.1. Bubble dynamics Various bubble dynamic parameters such as bubble departure diameter, departure frequency, growth and wait times, volumetric growth rate etc. have been measured from the recorded sequence of schlieren images for water and two concentrations of nanofluids. Growth time is the time taken by a bubble from its inception up to its departure and wait time is the time followed by bubble departure to the next bubble inception. The sum of growth time and wait time is referred to as ebullition period/cycle. The bubble departure frequency indicates the rate at which bubble departs the heated substrate and it has been determined for each bubble separately by inverting the associated ebullition period of a given bubble. Subsequently, it has been averaged over the number of bubble cycles. The bubble departure diameter has been presented in the form of equivalent spherical diameter by calculating the diameter of a completely spherical bubble, which occupies the same volume as that of the 9

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Fig. 6. Variations in the departure diameter, departure frequency and wait time for the case of water (a), 0.005% SiO2 nanofluid (b), and 0.01% SiO2 nanofluid (c) (q = 34 kW/m2).

0.005% nanofluid and again decreases, as the nanoparticle concentration is increased to 0.01% but still remains significantly higher than that observed in the base fluid. The observed increment in wait time with reference to the base fluid is expected as the heater substrate temperature was found to increase in the experiments conducted with the nanofluid as the bulk medium (over the base fluid experiments), which clearly suggests that higher superheat levels are required to achieve bubble nucleation in the nanofluids. As the heat fluxes supplied to the heater substrate are constant for water as well as nanofluid experiments, it may reasonably be expected that the nanofluid would take more time to reform the thermal boundary layer after bubble departure and maintain it at a higher superheat level as compared to that in the case of water-based experiments. On the other hand, the time variation of the volumetric growth of the vapor bubble showed a clear enhancement in the growth rate as the bulk fluid is changed from water to nanofluids. This trend is quantitatively presented in Figure (7), which shows the volumetric growth rate of vapor bubble for water and nanofluids. It is to be mentioned here that the data pertaining to the initial stages of the vapor bubble growth are affected by relatively higher levels of experimental uncertainties and hence have not been included in the present discussion. These uncertainties arise primarily due to the fact that the bubble grows quite rapidly in the initial stages and the rate

at which experimental data may be recorded is limited by the maximum frame rate of the high speed camera employed for data acquisition, which, in turn, depends on the light intensity available for scanning the region of interest. In the present work, with the intensity available from the white light source, the experimental data in the form of rainbow schlieren images have been recorded at 1000 frames/second. As evident from the slope of the profiles and the ebullition periods shown in Figure (7), the bubble grows relatively much faster in the case of 0.005% and 0.01% (V/V) nanofluid and its growth rate decreases significantly as one moves from 0.01% (V/V) to the base fluid. This trend can be attributed to the increased contribution of the microlayer evaporation to the bubble growth in the case of 0.005% and 0.01% (V/ V) nanofluids as compared to that in the case of water-based experiments. It has been observed that the suspended nanoparticles deposit and form a porous layer around the nucleation site on the heater substrate during the bubble growth. This phenomenon is widely known in the boiling community and has been reported by a range of researchers [8,10,11]. The implications of such deposition of porous layer can be in the form of reduction in the microlayer thickness as well as enhancement in the flow pathways to the microlayer by improving the surface wettability and the capillary wicking flow. As a result, formation of dry patch is inhibited/suppressed, which tends to enhance the contribution 10

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to the increased extent of the spread-out of the superheat layer in the vicinity of the heater substrate surface. In quantitative terms, it is interesting to note that the 0.005% (V/V) silica-water nanofluid raised the heater substrate temperature by almost 2 °C under the same level of heat flux as employed in the water experiments. This observation of an increment in the heater substrate temperature in the case of 0.005% nanofluid has been explained in the following discussion. For performance evaluation of nanofluids in the context of isolated nucleate pool boiling, magnitudes of natural convective heat transfer rates have been determined (Equation (4)) using the temperature gradient fields (as obtained through the quantitative analyses of the recorded schlieren images) for water and 0.005% nanofluid under two supplied heat flux conditions (q1 = 34 and q2 = 47 kW/m2). In quantitative terms, the relative contributions of natural convection and evaporative heat transfer rates to the overall heat transfer rates have been presented in the form of bar charts in Figure (9). It is evident from Figure (9) that natural convective heat transfer rates increase as one moves from water to 0.005% nanofluid concentration for both the levels of supplied heat flux values (i.e. q1 and q2). It implies that the strength of the thermal gradients prevailing in the vicinity of the heater substrate is stronger in the case of nanofluid as the working medium. The evaporative heat transfer rate is seen to follow the same trend as that of the natural convection rate with increasing nanoparticles concentration (from 0% to 0.005% (V/V)). While the present analysis reflects an increase in the overall heat transfer rates with nanofluids as the bulk medium (Figure (9)), the thermocouple attached to the heated substrate showed an increase in its surface temperature by ≈ 2 °C in the case of 0.005% nanofluid in comparison to water for the same levels of constant heat flux. The increased substrate temperature suggests that the nanofluid is unable to transport heat effectively from the heater substrate and thus part of the thermal energy is stored in the heater substrate that leads to an increase in its surface temperature. It, in turn, implies that 0.005% nanofluid reduces the natural convective heat transfer rate as compared to that of water. Thus, the thermocouple-based measurements of heated substrate surface temperature contradict the results presented in Figure (9). The observed differences may be explained in the following manner: Quantitative analysis of the rainbow schlieren images performed for retrieving whole-field information on temperature distribution and heat transfer rates does not consider the conjugate heat transfer between the heater substrate and the adjacent working fluid. Instead, it directly takes into account the net effect of conjugate heat transfer as reflected in the form of substrate temperature. In view of the fact that the natural convective heat transfer rate has been calculated based on the measured substrate temperature, this approach results in the increased heat transfer rates in the case of 0.005% nanofluid. Hence, the results presented in Figure (9) showed enhancement in the heat transfer rates at the cost of increased heater substrate temperature. On the other hand, these results can also be interpreted as 0.005% silica-water nanofluid tend to reduce the thermal performance of the heater substrate by increasing its stored internal thermal energy in the form of increased temperature in comparison to that of water. In order to develop more clarity on the above presented discussion, separate experiments performed with water and 0.005% nanofluid as the working medium, which resulted into the same substrate temperature in both the cases, have been analysed for heat transfer rates. The corresponding results have been presented in Figure (10), which clearly reveal the possible impact of nanoparticles on the strength of various heat transfer rates under constant heater substrate temperature. It can clearly be seen from Figure (10) that the natural convection as well as evaporative rates reduce due to the addition of nanoparticles in the base fluid, as compared to their relative contributions in the case of base fluid (water). Thus, the results presented in Figure (10) support the above possible explanation provided for explaining the trend of the results depicted in Figure (9). With reference to Figure (10), the possible reduction in the natural convection rate in the case of nanofluid

Fig. 7. Volumetric growth of vapor bubble with time for water and two concentrations of nanofluids. The end point in each curve indicates the bubble departure from the heated substrate. The average ebullition period for water, 0.005 and 0.01% (V/V) is ∼180 ms, 83 ms and 54 ms respectively.

of the microlayer evaporation [51]. Furthermore, possible Brownian motion effects that are associated with the suspended nanoparticles in the micro/macro layer may also contribute towards maintaining the layer at nearly constant temperature and thus result into faster evaporation of the microlayer. However, direct experimental evidence to explain these phenomena is still not available. In that context, the integration of a high-speed thermal imaging camera to capture the real time dynamics of microlayer growth and its evaporation forms a possible solution and is the scope of the future extent of this work.4 5.2. Temperature distribution and heat transfer rates In order to understand the plausible mechanisms through which suspended nanoparticles affect the various thermal processes/sub-processes such as superheat layer at the heater surface, envelopment of superheat layer around the vapor bubble etc., whole-field, axisymmetric temperature gradient distributions have been determined from the recorded sequence of schlieren images following the data reduction methodology discussed in Section 3. The quantitative analyses have been performed for water and 0.005% (V/V) silica-water nanofluid. Based on these analyses, relative contributions of natural convection and evaporative heat transfer to the overall heat transfer rates have been computed. Figure (8) shows the whole field temperature distribution plots for water and 0.005% nanofluid. Following the line of discussion made earlier in qualitative terms on the basis of schlieren images shown in Figure (4), Figure (8) reveals the possible impact of suspended nanoparticles on the superheat layer in the form of diffusion of the thermal disturbance deeper into the bulk fluid in comparison with that observed in the water-based experiment. A noticeable scavenging phenomenon upon the bubble departure can also be observed from the temperature plots of nanofluids experimental data for time instant t/tcyl = 0.22 (Fig. 8(b)). The possible existence of the scavenging phenomenon in the nanofluid experiments can be attributed 4 A high-speed thermal imaging camera can be employed to capture the real time, space-resolved temperature distribution of the heater surface underneath a growing vapor bubble. Thermal images captured by the camera can provide real time dynamics of the microlayer growth and evaporation and the associated temperature field of the heater surface, which might prove to be useful to investigate the possible mechanisms through which nanoparticles affect the contact line dynamics and thus lead to significant changes in growth and wait times.

11

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Fig. 8. Whole field temperature distribution plots at various time instants; (a) Water and (b) 0.005% (V/V) nanofluid (q = 34 kW/m2).

Fig. 9. Comparison between magnitudes of various heat transfer mechanisms in water and 0.005% nanofluid for q1 = 34 kW/m2 (a), q2 = 47 kW/m2 (b). (The error bars represent standard deviations).

can be explained on the basis of the observed changes in the thickness of the superheat layer on the heater substrate, as shown earlier in Figure (4) and Figure (8). With nanofluid as the bulk medium, Figures (4) and (8) clearly show that the superheat layer is more spread out (stretched in the vertical direction) and thus the same temperature difference (ΔT) across the superheat layer gets spread over larger distance in the case of nanofluid, as compared to that observed in the base fluid (water) case. This leads to a reduction in the strength of thermal gradients ( T y , y being the direction perpendicular to the heater substrate surface) that prevail in the superheat layer, which in turn result into the deterioration in the natural convection heat transfer rate, as quantitatively shown in Figure (10). These observations also provide an experimental basis to explain the earlier presented increasing trend of wait times in the case of nanofluids (shown in Figure (6)). With nanofluid as the bulk medium, it takes more time to reform the thermal boundary layer adjacent to the heater substrate after bubble departure as well as to maintain it at required superheat levels for the next bubble nucleation. The reduction in evaporation rate with nanofluids vis-à-vis water, as shown in Figure (10), can be attributed to the significant increase in the waiting times for 0.005% and 0.01% (V/V)

( )

Fig. 10. Comparison between magnitudes of various heat transfer mechanisms in water and 0.005% nanofluid for ΔTsp = 6 °C. (The error bars represent standard deviations). 12

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Table 2 Validation of the measured overall heat transfer rates with the RPI model. Volumetric concentration of SiO2 nanofluids (%)

Overall heat transfer rate (W) q1

0 (Water) 0.005

q2

Present data

RPI model

% difference

Present data

RPI model

% difference

0.157 0.293

0.161 0.310

−2.48 −5.48

0.449 0.552

0.461 0.587

−2.60 −5.96

nanofluid as compared to that observed in the water experiments (as can be seen from the results of the present experiments shown earlier in Figure (6)). It can be inferred from Figure (7) that the instantaneous evaporative rate is relatively higher in the nanofluid experiments during the growth period in comparison with that of water-based experiment. However, due to a significant increase in wait times in the case of nanofluid experiments, the evaporative rate averaged over the ebullition period has been found to be decreasing as the concentration of dilute nanofluid is increased from 0% (water) to 0.005% (V/V). In an attempt to verify the accuracy of the measured heat transfer rates, the RPI heat flux-partitioning model [52,53] has been invoked and the overall heat transfer rates determined by following the present analysis have been compared with that obtained on the basis of the RPI model. The comparison of these two sets of results in the form of overall rates and RPI model-based heat transfer rates for water as well as 0.005% nanofluid experiments and for both the supplied heat flux values have been summarized in Table 2. The percentage error data presented in Table (2) shows quite a good agreement between the results of the present experiments and the RPI model based overall heat transfer rates in the case of water as the working medium. However, in the case of 0.005% nanofluid experiment, the present work under predicts the overall heat transfer rates as compared to RPI model-based values with increased margins. This increased error percentage is expected as the input parameters fed to the RPI model, mainly the heat transfer coefficient value for a horizontal heated plate, are corresponding to the water as the working fluid. Experiments on silica-water nanofluid-based isolated pool boiling reveal that the suspended nanoparticles tend to diffuse the thermal gradients present in the superheat layer adjacent to the heater substrate and thus spread out the spatial extent of the superheat layer. This phenomenon results into the alleviation of the average value of the natural convective heat transfer rate in the case of nanofluids in comparison with that of the water-based experiments. Based on the observed increasing trend of the evaporative growth rate of the vapor bubble with the nanoparticles concentration (Figure (7)), one expects that the rate of removal of vapor from the heated substrate would increase with the increasing nanoparticles concentration. However, it has also been found that there is substantial increase in the wait times as one changes the working fluid from water to nanofluids. This increment in wait times has been found to overshadow the effect of the increased vapor bubble growth rate on the net vapor removal rate from the heated substrate. As a results, the value of evaporative heat transfer rate averaged over the ebullition period reduces with increasing concentration of the nanoparticles suspended in the base fluid. Thus, the experiments conducted in the present study reveal that the uniformly dispersed silica nanoparticles in the base fluid (water) tend to reduce the thermal performance of the heater substrate in the context of single bubble-based nucleate pool boiling under saturated bulk conditions. Performance evaluation of nanofluids in the case of sub-cooled pool boiling configuration forms the scope of future extension of the present work.

of silica-water nanofluids on the dynamics of single vapor bubble and the associated thermal gradients field under saturated bulk conditions. Temperature gradients, in the vicinity of the heated substrate as well as around the single vapor bubble, have been recorded in the form of rainbow schlieren images. These images have been subjected to quantitative analysis to determine the individual contribution of various thermal sub-processes (such as natural convection, evaporative growth) towards the overall heat transfer rates that can be achieved from the heated substrate for any given concentration of nanofluid employed. Experimental findings on bubble dynamics parameters (e.g. departure diameter, departure frequency, wait and growth times etc.) showed more variability with increasing concentrations of dilute nanofluids. The bubble departure diameter was found to reduce with increasing nanoparticle concentration. Wait time increased significantly in the case of nanofluids over the water case whereas the growth time was observed to be decreasing as the nanoparticle concentrations was increased from 0% (water) to 0.01% (V/V). Plausible mechanisms explaining these observations with regard to the dependence of wait and growth times on nanoparticles concentrations have been discussed. Temperature gradients field recorded in the form of hue distributions clearly revealed that the suspended nanoparticles tend to diffuse the thermal gradients and lead to the spreading out of the superheat layer in the direction normal to the surface of the heated substrate as compared to that observed in the case of water-based experiments. Performance evaluation study showed that the strength of natural convection and evaporative heat transfer rates decreased as one moved from water to 0.005% nanofluid. The deteriorating trend of these two thermal sub-processes with increasing concentration of suspended nanoparticles has been explained on the basis of the observed increased spread out of the superheat layer in the nanofluids experiments that were performed under same wall superheat conditions as that in the case of water. The work reported in the manuscript becomes important as, to the best of the authors’ knowledge, it is one of the first experimental studies which elucidates the possible influence of suspended nanoparticles on the bubble dynamic parameters as well as on the temperature field and, in turn, on the individual contribution of the heat transfer mechanisms associated with the single vapor bubble-based nucleate pool boiling phenomenon.

6. Conclusions

References

Conflicts of interest None declared. Acknowledgments The rainbow schlieren deflectometry (RSD) set up employed in the present work was built with the partial financial support received from the Department of Science and Technology (DST), India through the Grant ID SR/S3/MERC/0030/2012. The authors acknowledge the support received from DST, India. The authors would like to thank Mr. Surya Narayan for assisting in developing the MATLAB code for the data reduction analysis.

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