International Journal of Heat and Mass Transfer 133 (2019) 677–685

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Superwetting copper hydroxyl nitrate wicks for the sweating-boosted aircooling on finned tubes

https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.1090017-9310/� 2018 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: li01@cec.sc.edu (C. Li).

Pengtao Wang, Wei Chang, Guanghan Huang, Mohammad Alwazzan, Benli Peng, Tamanna Alam,Chen Li ⇑Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 August 2018Received in revised form 13 December 2018Accepted 15 December 2018

Keywords:Copper hydroxyl nitrate (Cu2(OH)3NO3)Superwetting wicksSweating-boost air coolingEvaporative heat transfer

Air cooling system (ACS) gains more attention because of the global water crisis, however its applicationsare limited by the inherent low heat transfer coefficient of air. Evaporative heat transfer is promising toaddress the challenge in ACS. By mimicking the primary mechanism of mammals to effectively dissipateheat during physical exercise, a sweating-boosted air cooling (SBAC) strategy is proposed and experimen-tally demonstrated on plain walls in our previous study. We have shown that the copper oxide (CuO)wicks played a critical role in the thermal performance of SBAC. In this research, we develop superwettingcopper hydroxyl nitrate (Cu-HDS/NO3) wicks to further enhance SBAC on finned copper tubes. Cu-HDS/NO3 crystals are directly synthesized on copper substrates via a three-step wet chemical oxidization pro-cess. The time-dependent surface morphology and crystal structures of Cu-HDS/NO3 are characterized byscanning electron microscope (SEM) and X-ray diffraction (XRD), respectively. The newly developedwicks are superior in spreading water and thermally stable for SBAC under a wide range of working con-ditions. The performance of SBAC on a finned copper tube coated with Cu-HDS/NO3 wicks has beenexperimentally evaluated. The SBAC on as-developed wicks enhances the effective heat transfer coeffi-cient (HTC) by 379.9% and reduces the total thermal resistance by 76.1%. The effects of wall temperatureand air velocity on the thermal performance of SBAC are systematically characterized. We have shownthat the super wicking capacity well complements the SBAC at low air velocity, hence makes the superwicking Cu-HDS/NO3 more attractive in the practical applications of SBAC. The developed Cu-HDS/NO3

wicks are promising in implementing SBAC strategy over current ACS.� 2018 Elsevier Ltd. All rights reserved.

1. Introduction

Large-scale cooling systems are extensively used in extractingwaste heat to atmosphere in a wide range of applications includingpetrochemical industry, thermal power plants [1], and HVAC sys-tem [2]. They can be classified as water cooling systems (WCS)[3], air cooling systems (ACS) [4], and hybrid wet/dry cooling sys-tems (HCS). WCS prevails owing to its relatively high heat transferrate, low parasitic power consumption, and low overall cost. WCSaccounts more than 99% in cooling thermoelectric plants in theUnited States and withdrew 133 billion gallons of fresh waterper day in 2015, accounting for 41% of total freshwater withdrawaland 3% of total freshwater consumption [5]. Recent global watercrisis needs a water-efficient or even a dry solution for cooling sys-tems, which make the ACS more competitive [6]. However, the dis-advantages of ACS are in several folds: large foot print, high capital

cost, and susceptibility to the ambient temperature and humidity.The inherent limitation of air cooling is its low heat transfer coef-ficient (HTC). Typical values of air/fin-side HTC in ACS for thermalpower plants are at �10 W/(m2 K), which are two orders of magni-tudes lower than those in WCS (�1 kW/(m2 K)). Air cooling perfor-mance of HCS can be significantly enhanced using the latent heatof vaporization [7]. A small amount of water is delivered into theair flow of HCS as fine mists via spray nozzles [8] and/or throughevaporative media [9], or directly deluged over the heating sur-faces [10]. HCS consumes a significantly smaller amount of water,compared to WCS, but offers a significantly improved performancethan ACS, especially on hot days. For example, HCS with surfacedeluge cooling has been proved to be a more cost-effective optionfor a 1 MW air-cooled geothermal power plant [11]. However, HCSrequires additional peripheral components and operating costs togenerate the mists, and/or to eliminate the unevaporated miststo reduce the drift loss.

The surface deluge cooling can be characterized as simultane-ous convective and evaporative heat transfer, where the liquid film

Nomenclature

A exposed surface area of finned tubeACS air cooling systemCp thermal capacity of waterD water–vapor mass diffusion coefficientDTG differential thermogravimetricHCS hybrid wet/dry cooling systemHDS hydroxyl double salth, HTC heat transfer coefficient, W/(m2 K)hfg latent heat of vaporization, kJ/kgk thermal conductivity, W/(m�K)m00 evaporation rate of water, kg/sNu Nusselt numberp air pressure, PaPr Prandtl number_Q volume flow rate, ml/minR thermal resistance, (K�m)/Wr radius of curvatureRe Reynolds numberRH relative humiditySBAC sweating-boosted air coolingSEM scanning electron microscopeSh Sherwood numberT temperature, �CV velocity of air, m/sU liquid wicking rate, ml/sW width of slots in fins, W = 2mmWCS water cooling systemXRD X-ray diffraction

Y mass fraction

Greek symbolsg fin efficiencyh contact angleq density, kg/m3

U thermal loads, W/ dimeter, mmv heat loss, %

Subscriptsconv convective heat transferD dynamiceq equivalent parametersevap evaporative heat transferf finfb fiberglassin inletl liquidmass mass transfer coefficientm log meanout outletv vaporw wallr root areas surfacest smooth copper tubetot total

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evaporation plays a dominant role. Similar heat transfer processeshave been extensively employed in various systems, such as waterfilm falling along the internal channel walls in air humidifiers [12],falling film evaporation outside horizon tubes in desalination sys-tems [13], and falling film of refrigerant in evaporators [14]. Theevaporation rates of liquid film are closely related to air properties(e.g., temperature and relative humidity (RH)), air flow conditions(e.g., natural convection [15], laminar [16], or turbulent [17]), sur-face temperatures, and the configuration of liquid film [18].Increasing the air velocity is an obvious way to enhance the liquidfilm evaporation, but it significantly increases the operating costs.Reducing the liquid film thickness is another option to improve theevaporative heat transfer, because a thinner liquid film leads tohigher evaporation temperature and mass concentration at theliquid-air interface [19]. Obtaining a homogeneous thin liquid filmis challenging in the practical applications of falling liquid filmevaporation. The distribution of liquid film with a small thicknesscould be more effectively promoted by modifying surface morphol-ogy with a porous layer [20,21], polypropylene fabric laid [22], andmicro groves [23], and/or by changing surface wettability with flu-orocarbon coatings [24], and plasma treatment [25].

Since more efficient evaporative heat transfer in HCS holds pro-mise to address the challenge of ACS, by emulating the primarymechanism of mammals to effective dissipate heat during physicalexercise, a sweating-boosted air cooling (SBAC) strategy was pro-posed and experimentally demonstrated in our previous studies[26,27]. Water droplets were directly dripped on the surfaces,instead of forming a liquid film by flowing excess water over theheating surfaces. Water spread and formed a thin liquid filmwithin the micro-scale wicks. This near-surface water drippingmethod significantly reduced the drift loss, compared with tradi-tional HCS. The water usage efficiency was near 100%, as the onlywater consumption was for evaporation. A relative constant HTCof 180 W/(m2 K) was achieved on a grooved copper substrate

coated with CuO wicks at thermal loads of 2.9–7.2 kW/m2 and anair velocity of 6.0 m/s. However, the wetting capacity of atomiclayer deposited TiO2 thin films and CuO wicks was too weak tospread water globally over a large flat surface (size: 2 by 2 in.),herein microgrooves and/or copper woven meshes were used topromote the water spreading. More effective SBAC requires super-wetting wicks that are durable, cost-effective, scalable, and com-patible with complex copper surfaces.

Copper hydroxyl salts (Cu-HDS) have gained extensive atten-tion due to their unique crystal structures, which can be taken asa quarter of anionic sites (AOH) in an octahedral unit of Cu(OH)2are replaced by negative ions, such as NO3

�, SO42�, and ClO4

�. Thepresence of AOH groups in Cu-HDS enables a strong affinity towater [28], while the spaces between weakly bonded 2-D lamellarstructures adsorb more water molecules [29]. Among Cu-HDS, cop-per hydroxyl nitrate (Cu-HDS/NO3) is particularly attractive due toits commercial applications as a precursor for preparing CuO [30]and Cu(OH)2 [31]. Traditional methods focus on synthesizing Cu-HDS/NO3 nanoparticles via precipitation, liquid–solid methods, orhydrothermal process [32]. However, applying these nanoparticlesas surface coatings would lead to high thermal resistance and poordurability. Directly growth Cu-HDS/NO3 crystals on copper sub-strates can dramatically reduce the contact thermal resistance,which is critical for the heat dissipation. Few synthesis methodshave been reported, such as electrochemical depositions [33].These methods, however, cannot fabricate the Cu-HDS/NO3 crys-tals on complex copper surfaces. Recently, copper hydroxyl sulfate(Cu-HDS/SO4) was synthesized on a copper-coated nickel substrateusing a wet chemical process [34]. Herein, a similar procedure isdeveloped to directly grow the Cu-HDS/NO3 crystals on finnedcopper tubes.

The aim of this study is to develop superwetting wicks onfinned copper tubes for SBAC. Cu-HDS/NO3 crystals are directlysynthesized on copper substrates using a three-step chemical

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oxidation process. The surface morphology and crystal compo-nents of Cu-HDS/NO3 are characterized with scanning electronmicroscope (SEM) and X-ray diffraction (XRD), respectively. Thewetting capacity and the thermal stability of Cu-HDS/NO3 are char-acterized by droplet dynamics wetting tests and thermalgravimet-ric analysis (TGA), respectively. SBAC on finned copper tubescoated with Cu-HDS/NO3 wicks are experimentally evaluated.The effects of water supply, air velocities, and surface temperatureon the SBAC are systematically investigated.

2. Synthetization and characterization of the Cu-HDS/NO3

crystals

Fig. 2. Time-dependent evaluation of crystal components characterized by XRDpatterns.

2.1. Synthetization of the Cu-HDS/NO3 crystals

The finned copper tube is ultrasonically soaked in acetone for10 min to remove the residual of oil/grease, then rinsed withmethanol, isopropanol and distilled water consecutively, and driedwith nitrogen gas. The sample is immersed into diluted sulfuricacid (10 wt%) to remove native copper oxide, rinsed with distilledwater, and dried with nitrogen gas. The primary solution is pre-pared by dissolving potassium chlorate (KClO3, 0.02 M) in distilledwater, and its pH value is adjusted to 3 by adding several drops ofdiluted sulfuric acid (10 wt%). The cleaned sample is kept in theprepared solution at 60 �C for 12 h, then copper nitrate trihydrate(Cu(NO3)2�3H2O, 0.1 M) is added into the primary solution andkept at 60 �C for another 120 h. The as-prepared sample is rinsedwith distilled water and dried in a convection oven at 60 �C for 1 h.

The time-dependent evolution of surface morphology and crys-tal components of Cu-HDS/NO3 wicks, shown in Figs. 1 and 2, arecharacterized by SEM (Zeiss Ultra Plus FESEM) and XRD (RigakuMiniFlex II desktop X-ray Diffractometer), respectively. After 12 hreaction in the primary solution, the color of sample changes fromthe reddish brown to the raw umber. Cubic crystal structures ofcuprite forms, which is identified from the XRD spectra (Cu2O,marked with d, PDF#05-0667). The chemical reaction in oxidizingcopper by KClO3 can be given as

6Cuþ ClO�3 ! 3Cu2Oþ Cl� ð1Þ

After adding copper nitrate, the grain size of Cu2O crystalincreases, resulting in partially filling of gaps between grains after12 h, and micro-scale butterfly-like crystals forms randomly after

Fig. 1. Time-dependent evolution of the surface morphology of Cu-HDS/NO3 crystals. SE24 h, (d) 96 h. The inserts show the photo image of samples at the related times. (e) Cro

24 h. The XRD spectrum indicates the monoclinic Brochantite crys-tal forms firstly (Cu4(OH)6SO4, marked with ▲, PDF#43-1458),then the Rouaite follows (Cu2(OH)3NO3, marked with w, PDF#15-0014). The involved reaction can be expressed as [32]

2Cu2Oþ SO2�4 þ 4H2O ! Cu4ðOHÞ6SO4 þ 2Hþ þ 4e� ð2Þ

Cu2Oþ NO�3 þ 2H2O ! Cu2ðOHÞ3NO3 þHþ þ 2e� ð3Þ

The reaction in Eq. (3) dominates the synthetization processbecause the reaction in Eq. (2) is inhibited by a low concentrationof SO2�

4 , which is only used for adjusting the pH value of the pri-mary solution. More crystals germinate and grow with an increas-ing reaction time, resulting in a color change from the reddish tothe blue-green. After 96 h, Cu-HDS/NO3 crystals fully cover thecopper substrate with a thickness of 73.6 ± 2.8 mm (Fig. 1(e)).

M images of samples after reaction times of (a) 0 h (the Cu2O crystal), (b) 12 h, (c)ss-section of Cu-HDS/NO3 wicks after a duration of 96 h.

680 P. Wang et al. / International Journal of Heat and Mass Transfer 133 (2019) 677–685

2.2. Liquid wicking capacity of the Cu-HDS/NO3 wicks

The liquid wicking performance of Cu-HDS/NO3 wicks is evalu-ated by droplet dynamics wetting tests [35]. A 10 ml water dropletis gently loaded on the wicks, and its volume during the spreadingprocess is recorded by a high-speed camera at 100 fps (Micro-Ex4,Phantom). The wetting process consists of three stages, namelydirect impacting, spreading under gravity (Fig. 3(a)), and spreadingdriven by the capillary invasion (Fig. 3(b)) [36]. The water wickingrate, U, is obtained from the droplet’s volume changing at a giventime, given as [37]

U ¼ 14pr2h3D 3hD

drdt

þ 4rdhDdt

� �ð4Þ

Fig. 4. Thermalgravimetric analysis curves of the Cu-HDS/NO3 wicks.

where r and hD are the radius of curvature and the dynamics contactangle of water droplets, respectively, which are determined fromthe profiles of water droplet as shown in Fig. 3(b). The wicking ratereduces significantly at the stage of gravity-driven spreading on theCu-HDS/NO3 wicks, as shown in Fig. 3(c). After 0.1 s, the wickingrate keeps constant (about 2.16 ml/s) when the liquid spreading isdriven by the capillary invasion. The time-dependent evaluationof wicking rates on the CuO wicks is similar as that on the Cu-HDS/NO3 wicks, but the wicking rate of CuO is about 0.68 ml/s,accounting for 31.5% of that on the Cu-HDS/NO3 wicks.

2.3. Thermal stability of the Cu-HDS/NO3 crystals

The thermal stability of as-prepared Cu-HDS/NO3 crystals isevaluated using thermalgravimetric analysis (TGA, Q5000SA, TAInstruments) at a heating rate of 10 �C/min in air atmosphere.TGA curve demonstrates a single-step thermal decomposition ofCu-HDS/NO3 at the temperature range of 225–315 �C (Fig. 4). Thetotal weight loss is 33.2 wt%, which agrees well with the theoreti-cal weight loss of 33.8 wt% [38] and the other’s experimental dataof 34.7 wt% [39]. The differential thermogravimetric (DTG) curveindicates that the thermal decomposition becomes significant at279.1 �C, which is much higher than the operational temperatureof ACC (typically 40–60 �C). Therefore, Cu-HDS/NO3 wicks arehighly thermally stable for its application in SBAC.

Fig. 3. Wetting capacity of the Cu-HDS/NO3 wicks. The evolution of water droplet profilwater wicking rates on the Cu-HDS/NO3 wicks.

3. Experimental system and data processing

3.1. Experimental system

An experimental system is set up to evaluate the thermal per-formance of SBAC on a finned copper tube coated with Cu-HDS/NO3 wicks (Fig. 5(a)). It consists of four sub-systems: a windtunnel, a water dripping system, a hot water system, and a dataacquisition system. Air flow is driven with a blow fan, controlledby a Variac variable transformer and measured with an airvelocity transmitter (FMA903R-V1, Omega). The temperature(21.0 ± 0.5 �C) and RH (55 ± 3%) of inlet air are measured with aRH/Temp transmitter (HX-94C, Omega). Hot water, driven with acirculating water bath (RTE-4DD, Neslab), is used to simulate ther-mal loads on the finned tube. The inlet/outlet temperatures andflow rates of hot water are measured with T-type thermocouplesand a flowmeter (FPR1504, Omega), respectively. The wall temper-ature of finned tube is measured with T-type thermocouplesmounted on the backside of the finned tube. All the data are col-lected with a data acquisition unit (34972A, Agilent) and recordedwith a LabVIEW program.

The finned tube is installed vertically in the duct of wind tunnel.The fins are cut with several slots (W = 2 mm), which are mountedwith fiberglass wicks (/fb = 4 mm) for global liquid transportation

e during spreading process driven by (a) gravity, and (b) capillary invasion. (c) The

Fig. 5. Experimental system for SBAC on a Cu-HDS/NO3 wicks. (a) Experimental system, (b) a finned copper tube coated with Cu-HDS/NO3 wicks.

Table 1Uncertainties of key parameters.

Name of variables Uncertainties

Length/diameter (L) 0.1 mmWall temperature (Tw) 0.5 KAir temperature (T1) 0.6 KAir velocity (U1) 0.2 m/sWater dripping rate 0.02 ml/minHot water flow rate 30 ml/minThermal load (U) 16.9 WEffective HTC (h) 3.2 W/m2 K

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(Fig. 5(b)). The distilled water, driven with a micropump (GA-X21,Ismatec), is directly dripped on top of fiberglass, and distributedvertically along the fiberglass wicks. The water further spreadshorizontally over the fin surface, which is driven by the capillarypressure within the Cu-HDS/NO3 wicks.

3.2. Data processing and uncertainty analysis

The thermal loads dissipated by SBAC are determined from thethermal balance of hot water that flows through a finned tube,

U ¼ ð1� vÞ _QqCpðTl;in � Tl;outÞ ð5Þwhere U is the effective thermal loads dissipated from exposed sur-faces; v is the heat loss of experiment system, _Q is the volume flowrate of hot water. q, Cp, Tl;in, and Tl;out are the density, thermal capac-ity, inlet and outlet temperatures of hot water, respectively.

The effective HTC of SBAC, hSBAC , is determined as

hSBAC ¼ U=½A TS � T0ð Þ� ð6Þwhere T0 is the air inlet temperature, and T0 ¼ 21:0� 0:5 �C. Ts isthe surface temperature of finned tube, which is determined as alinear function of thermal resistance networks under a 1-Dassumption.

Ts ¼ Tw þUðRCu þ RCu�HDS þ RlÞ ð7Þwhere Tw is the measured wall temperature of finned tube. RCu isthe thermal resistance from the location of thermocouples to thebottom of Cu-HDS wicks, RCu�HDS is the thermal resistance of Cu-HDS/NO3 wicks. Rl is the thermal resistance of the liquid film abovethe coatings (assumed the thickness � 50 mm). The thermal conduc-tivity of Cu-HDS/NO3 is unavailable, herein the thermal conductiv-ity of CuO (kCuO = 21.43 W/(m�K) [40]) is adopted to evaluate thethermal resistance of Cu-HDS/NO3 wicks.

The A in Eq. (6) is the exposed surface area of a finned tube, andit is calculated as

A ¼ Ar þ gf Af ð8Þwhere Ar is the exposed root area of a finned tube, and Af is the totalsurface area of fin. gf is the fin efficiency for a circular fin, which isgiven in terms of the modified Bessel functions [41].

The total thermal resistance of a finned tube coated with Cu-HDS/NO3 wicks, Rtot , is written as

Rtot ¼ DTm=U ð9Þ

where DTm is the log mean temperature difference, and given as

DTm ¼ DTin � DTout

lnðDTin=DToutÞ with DTin ¼ Tl;in � T0;DTout

¼ Tl;out � T0 ð10Þ

The uncertainties of measured parameters are estimated fromthe specifications of instruments, the uncertainties of derivedparameters are calculated using the Kline and McClintock method[42], as listed in Table 1.

3.3. Calibration of experimental system

The biggest uncertainty in evaluating the thermal performanceof SBAC primarily originates from the heat loss of experimentalsystem. To estimate the heat loss, the experimental system is cal-ibrated using forced air convection without evaporation over asmooth copper tube (/st = 14.0 mm). The air velocity ranges from1.0 to 5.0 m/s, corresponding to Reynolds numbers (Re) rangingfrom 806.1 to 3,972.5. Nusselt number (Nu) for the forced airconvection over a circular cylinder can be empirically predictedas [43]

Nu ¼ 0:683Re0:466Pr1=3 for 40 < Re < 4;000 ð11Þ

The factor of heat loss is applied as a correction factor betweenthe experimental and theoretical data. Curve fitting shows an esti-mated heat loss of 14.2%, as illustrated in Fig. 6.

Total thermal resistance (Rtot) 0.15 K/W

Fig. 6. Calibration of the experimental system.

682 P. Wang et al. / International Journal of Heat and Mass Transfer 133 (2019) 677–685

4. Results and discussion

4.1. Effects of water supply

The water supply plays a dominant role in dissipating heat inSBAC because adequate water is required to make up the evapora-tive loss. In our previous study, SBAC was carried out on groovedcopper surfaces coated with CuO wicks, and three wetting condi-tions were identified as dry, partial wetted, and flooded [27]. Anoptimized heat dissipation of SBAC was achieved at the saturatedwetted condition, where the heating surface was fully covered bya thin liquid film. In this research, more effective water supplyon the finned tube is achieved using fiberglass wicks at global level,and water eventually spread locally by superwetting Cu-HDS/NO3

wicks.The global liquid transportation is provided by vertically

mounted fiberglass, where strong water imbibition is driven bygravity and capillary pressure. Various liquid supply routes areachieved by different numbers of fiberglass wicks, and their effectson the thermal performance of SBAC are shown in Fig. 7. Under agiven water supply condition, both the effective HTC of SBAC andthe total thermal resistance of finned tube are linearly improvedwith increasing water consumption until the fin surfaces are fullycovered by water film (i.e., the saturated wetted conditions). Then,a further increase in water supply wouldn’t improve the effective

Fig. 7. The effects of global water transportation on the SBAC. (a) Effective HTC of SBAC, (49.6 ± 0.2 �C, Air velocity: 1.02 ± 0.01 m/s).

HTC or even slightly deteriorate it. Although the actual wettingconditions within wicks are challenging to recognize, the curvesof effective HTCs vs. water consumption clearly indicate that theevolution of surface wetting conditions from partial wetted toflooded, which are identical to those on grooved flat surfaces inour previous research [26,27].

The performance of SBAC is significantly enhanced when thenumber of fiberglass wicks increases from 1 to 2. The effectiveHTCs are 41.0 ± 0.5 and 56.9 ± 0.5 W/(m2 K) at the saturated wet-ted conditions, the thermal loads are 164.5 ± 14.6 and202.2 ± 13.2 W, and the water consumptions are 6 and 8 ml/minfor finned tubes with 1 and 2 fiberglass wicks, respectively. Thethermal performance is slightly improved with 3 fiberglass wicksbut deteriorates a bit with 4 wicks. A relatively stable performanceof SBAC is achieved with an effective HTC about 37.4 W/(m2 K) andthe thermal loads about 210.0 W at surface temperature49.6 ± 0.2 �C and air velocity 1.02 ± 0.01 m/s. In practical applica-tion, more fiberglass wicks require additional costs of fabricationand maintains, herein the number of fiberglass wicks is recom-mended as 2 in this research.

The effects of local liquid transportation provided by the wickstructures of surface coatings, including microscale Cu-HDS/NO3

wicks and nanoscale CuO wicks, are shown in Fig. 8. The convectiveheat transfer (i.e., dry cooling without sweating boosted) on theCuO wicks, at wall temperature of 60.0 �C and air velocity of1.0 m/s, is adopted as a baseline for comparison. The SBAC dramat-ically improves the air-side heat transfer rates, the effective HTCsof SBAC are enhanced by 379.9% and 138.1%, and the total thermalresistances are reduced by 76.1% and 52.1% on the Cu-HDS/NO3

wicks and the CuO wicks, respectively. The effective HTC of SBACis improved by 84.0%, and the total thermal resistance is reducedby 46.5%, when the liquid wicking rate increases from 0.68 ml/s,for the CuO wicks, to 2.16 ml/s, for the Cu-HDS/NO3 wicks. The rea-son is that thinner liquid films can be formed on the superwettingCu-HDS/NO3 wicks, resulting in a smaller thermal resistance of liq-uid film [44]. Moreover, liquid meniscuses formed within themicrostructures of Cu-HDS/NO3 greatly extend effective evapora-tion area and intensifies local evaporation [45].

This study also shows that the thermal performance of SBACcan be further improved by increasing the air velocity owing toimproved liquid spreading over the fin surfaces by a higher shearforce. The effective HTC of SBAC is further increased by 247.5%owing to the CuO wicks; while only by 86.1% owning to the Cu-HDS/NO3, when the air velocity increases from 1.0 to 2.0 m/s. Itindicates that the super wicking capacity well complements SBACat low air velocity, making the superwetting Cu-HDS/NO3 wicks

b) total thermal resistance of finned tubes coated with wicks. (Surface temperature:

Fig. 8. Effects of surface coatings on the SBAC. (a) Effective HTC of SBAC, (b) total thermal resistance of finned tubes coated with wicks. (Number of fiberglass wicks: 2, Surfacetemperature: 59.5 ± 0.3 �C).

P. Wang et al. / International Journal of Heat and Mass Transfer 133 (2019) 677–685 683

more attractive in the practical applications of SBAC. Since higherair velocity accompanies with dramatically increased pressuredrop and higher operating costs of ACS [46].

4.2. Effects of surface temperature

As a typical convective heat and mass transfer process, theeffective HTC of SBAC in Eq. (6) can be rewritten as

hSBAC ¼ hconv þ hevap ¼ hconv þm00hfg=½A Ts � T0ð Þ� ð12Þwhere hconv and hevap are HTCs for the convective and the evapora-tive heat transfer, respectively. The thermal load dissipated in theevaporative heat transfer is related to the latent heat, hfg , and theevaporation rate (i.e., the convective mass transfer rate),m00, whichis driven by the vapor mass fraction between the water film andthe air [47], given as

m00 ¼ hmass YsðTsÞ � Y0ðT0;RHÞð Þ ¼ � qD1� Ys

dYdn

����n¼0

ð13Þ

where hmass is the mass transfer coefficient, Ys is the vapor massfraction at the surface of liquid film. Y0 is the vapor mass fractionin the air, which is related to the temperature and RH. D is thewater–vapor mass diffusion coefficient, which is related to the tem-perature at the liquid–vapor interface. By taking the mean free pathand average velocity for water molecules in an ideal gas from theMaxwell-Boltzmann distributions, the diffusion coefficient can beempirically expressed as [48]

Fig. 9. The effects of surface temperature on the SBAC. (a) Effective HTC of SBAC, (b) totalAir velocity: 1.01 ± 0.01 m/s).

D � T1:685s 0 �C < TS < 100 �C ð14Þ

Eqs. (13) and (14) indicate that the evaporation rate is related tothe mass diffusion coefficient and the gradient of mass fraction atthe water-air interface.

The effects of surface temperature on the performance of SBACat air velocity of 1.0 m/s are shown in Fig. 9. It shows that the heatdissipation performance is continuously improved with anincrease in surface temperature, indicating that the evaporativeheat transfer plays a dominant role in heat dissipation. The contri-bution of surface temperature is limited for convective heat trans-fer because its effects are in terms of thermal properties of air nearthe heating surfaces, while high surface temperature directly leadsto intense water-vapor transportation for evaporative heat trans-fer, as indicated by Eq. (14). As a result, the effective HTC of SBACincreases from 38.5 to 52.6 W/(m2 K), and the total thermal resis-tance decreases from 0.348 to 0.193 K/Wwhen the surface temper-ature increases from 40 to 60 �C. Moreover, the thermal loadssignificantly increase from 92.7 to 263.1 W due to a larger temper-ature difference established between the heating surface and air.

4.3. Effects of air velocity

The effects of air velocity on the performance of SBAC areshown in Fig. 10. The effective HTC of SBAC is substantiallyenhanced from 22.9 to 84.4 W/(m2 K) and the total thermal resis-tance decreases from 0.459 to 0.157 K/W with an increase of airvelocity from 0.5 to 2.5 m/s. This is consistent with the empirical

thermal resistance of finned tubes coated with wicks. (Number of fiberglass wicks: 2,

Fig. 10. The effects of air velocity on the SBAC. (a) Effective HTC of SBAC, (b) total thermal resistance of finned tubes coated with wicks. (Number of fiberglass wicks: 2, Surfacetemperature: 49.6 ± 0.2 �C).

684 P. Wang et al. / International Journal of Heat and Mass Transfer 133 (2019) 677–685

correlations for the convective heat and mass transfer, which statesthat the Nusselt number (Nu) and the Sherwood number (Sh)under a forced air convection are proportional to the Reynoldsnumber (Re). At a higher air velocity, the gradient of mass fractionat the water-air interface increases due to the effective transporta-tion of evaporated vapors, which results in an improved evapora-tion process as described by Eq. (13). The curves of the overallHTC related to the air velocities are similar to those of HTC of SBACbecause of a fixed wall temperature (Tw = 49.6 ± 0.2 �C).

As a summary, the performance of SBAC can be significantlyimproved by increasing the surface temperature and the air veloc-ity. In practical applications, thermal load on each finned tube isgiven, and the surface temperature can be passively changed bythe air velocity, i.e., a lower surface temperature accompanies witha higher air velocity. Therefore, an optimal operational conditionexists in terms of the evaporative heat transfer in SBAC. An opti-mized air velocity needs to be identified in any specific applica-tions of SBAC.

5. Conclusions

Sweating-boost air cooling (SBAC) is promising to dramaticallyenhance the air-side heat transfer with a high water-efficiency. Asuperwetting copper hydroxyl nitrate (Cu-HDS/NO3) wicks wasdeveloped to improve the thermal performance of SBAC. Cu-HDS/NO3 crystals are directly synthesized on copper substrates usingwet chemical oxidization and exhibit a superior wicking rate of2.16 ml/s and a high thermal stability up to 225 �C. SBAC on a finnedtube coated with the developed wicks has been experimentallyevaluated. We show that Cu-HDS/NO3 wicks enables dramaticallyenhanced HTCs of SBAC up to 379.9%. Increasing surface tempera-tures and air velocities can enhance the thermal performance ofSBAC, but the effects of air velocities are more significant. Thewicking capacity of micro/nanostructures plays a dominant rolein determining SBAC performance. We also found that an optimaloperation condition exists in terms of the evaporative heat transferin SBAC. An optimized air velocity needs to be identified in anyspecific applications of SBAC.

Conflict of interest

None declared.

Acknowledgements

This work is supported by National Science Foundation (NSF)and Electric Power Research Institute (EPRI) joint program ‘‘Waterfor Energy” under Grant No. 1357920 (Program Manager: Dr. JoséLage). The authors greatly appreciate the generous support fromDr. Nansheng Xu and Prof. Kevin Huang (Department of Mechani-cal Engineering, University of South Carolina (USC)) in XRD analy-sis, from Dr. Julia G. Pribyl and Prof. Brian C. Benicewicz(Department of Chemistry and Biochemistry, USC) in the TGAanalysis.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.109.

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