Experimental Investigation of Free Convection Heat Transfer from Horizontal Cylinder to Nanoﬂuids

energies

Article Experimental Investigation of Free Convection Heat Transfer from Horizontal Cylinder to Nanoﬂuids

Dorota Sawicka 1, Janusz T. Cie´sli´nski 2,* and Slawomir Smolen 1

1 Faculty of Nature and Engineering, J.R. Mayer–Institute for Energy Engineering, City University of Applied Sciences Bremen, Neustadtswall 30, 28199 Bremen, Germany; [email protected] (D.S.); [email protected] (S.S.) 2 Faculty of Mechanical and Ship Technology, Institute of Energy, Gda´nskUniversity of Technology, Narutowicza 11/12, 80233 Gdansk, Poland * Correspondence: [email protected]

Abstract: The results of free convection heat transfer investigation from a horizontal, uniformly heated tube immersed in a nanofluid are presented. Experiments were performed with five base fluids, i.e., ethylene glycol (EG), distilled water (W) and the mixtures of EG and water with the ratios of 60/40, 50/50, 40/60 by volume, so the Rayleigh (Ra) number range was 3 × 104 ≤ Ra ≤ 1.3 × 106

and the Prandtl (Pr) number varied from 4.4 to 176. Alumina (Al2O3) nanoparticles were tested at the mass concentrations of 0.01, 0.1 and 1%. Enhancement as well as deterioration of heat transfer performance compared to the base ﬂuids were detected depending on the composition of the nanoﬂuid. Based on the experimental results obtained, a correlation equation that describes the dependence of the average Nusselt (Nu) number on the Ra number, Pr number and concentration of

nanoparticles is proposed.

Citation: Sawicka, D.; Cie´sliński,J.T.; Keywords: free convection; horizontal cylinder; nanofluids; correlation equation Smolen, S. Experimental Investigation of Free Convection Heat Transfer from Horizontal Cylinder to Nanofluids. Energies 2021, 14, 2909. 1. Introduction https://doi.org/10.3390/en14102909 Nanofluids have come to be seen as a new generation of coolants, both in single-phase and two-phase systems, e.g., [1–4]. Furthermore, nanofluids or nanocomposites may be Academic Editor: Jose used as a medium in thermal energy storage systems as sensible heat storage [5] and phase A. Almendros-Ibanez change materials [6]. In sensible heat storage systems, the dominating mechanism of the heat transfer is free convection. Contrary to forced convection [7,8], not many studies Received: 29 March 2021 dealing with the free convection of nanofluids exist today. Moreover, the greater part of Accepted: 10 May 2021 them are devoted to the free convection of nanofluids in enclosures of different, sometimes Published: 18 May 2021 very sophisticated, geometries and thermal conditions. A comprehensive review of free convection of nanofluids in cavities is presented in [9]. Publisher’s Note: MDPI stays neutral Relatively few experimental studies have been carried out on free convection around with regard to jurisdictional claims in bodies immersed in nanofluids. Cie´slińskiand Krygier [10] experimentally established published maps and institutional affil- iations. the deterioration of heat transfer during the free convection of water–Al2O3 nanofluid with 0.01% nanoparticle concentration by weight from a horizontal, electrically heated tube covered with a metallic porous coating. Kiran and Babu [11] experimentally studied free convection heat transfer using transformer oil–TiO2 nanofluids with various volume concentrations from 0.05 to 0.2%, as the tested element served as an electrically heated Copyright: © 2021 by the authors. vertical cylinder. It was observed that the addition of nanoparticles up to 0.15% improves Licensee MDPI, Basel, Switzerland. heat transfer. For higher concentrations of TiO nanoparticles, degradation of heat transfer This article is an open access article 2 was observed. The unique, closely related theoretical study to the present paper is the work distributed under the terms and conditions of the Creative Commons by Habibi et al. [12]. Habibi et al. analytically solved the problem of free convection from Attribution (CC BY) license (https:// a horizontal cylinder immersed in an unbounded water–Al2O3 nanofluid. Nanoparticle creativecommons.org/licenses/by/ concentration by volume ranged from 0 to 10%. It was established that the decisive 4.0/). parameter influencing fluid motion and heat transfer around the horizontal cylinder is

Energies 2021, 14, 2909. https://doi.org/10.3390/en14102909 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 14

parameter influencing fluid motion and heat transfer around the horizontal cylinder is viscosity. Following Polidori et al. [13], two formulas were tested: Brinkman model [14] and the Maïga et al. correlation [15]. Results of the calculations show that application of Energies 2021, 14, 2909 2 of 14 the Brinkman model of nanofluid viscosity leads to a moderate increase in the Nu number with increasing nanoparticle concentration (up to 20%). Contradictory results were obtained using the Maïga et al. correlation. In this case, a distinct decrease in Nu number withviscosity. nanoparticle Following increase Polidori was et detected. al. [13], two Building formulas on the were results tested: of the Brinkman parametric model study, [14] twoand thecorrelations Maïga et al.(based correlation on the [15Brinkman]. Results mo ofdel the calculationsand Maïga et show al. correlation that application nanofluid of the viscosityBrinkman formulas) model of nanofluidare proposed viscosity for leadsthe average to a moderate Nu number increase of in thethe Nualumina–water number with nanofluidincreasing in nanoparticle terms of Ra concentrationnumber and nanoparticle (up to 20%). concentration. Contradictory results were obtained usingAs the seen Maïga in the et presented al. correlation. literature In thisreview, case, there a distinct is a lack decrease of experimental in Nu number study deal- with ingnanoparticle with free increaseconvection was heat detected. transfer Building from a on horizontal the results cylinder of the parametric immersed study,in an twoun- boundedcorrelations nanofluid. (based on Geometry the Brinkman of the model experime andntal Maïga container et al. correlation was designed nanofluid such viscositythat the generatedformulas) motion are proposed of the fluid for the was average not significantly Nu number affected of the by alumina–water the free surface nanofluid of the liq- in uid,terms side of walls Ra number and bottom and nanoparticle surface. In order concentration. to avoid influence of axial conduction on heat transferredAs seen from in the the presented cylinder, literature the length-to-di review, thereameter is aratio lack was of experimental made to be study large. dealing In the presentwith free work, convection the results heat of transfer free convection from a horizontal heat transfer cylinder performance immersed from in an a unbounded uniformly heatednanofluid. horizontal Geometry tube of are the discussed. experimental Base container fluids are was ethylene designed glycol such (EG), that water the generated (W) and motion of the fluid was not significantly affected by the free surface of the liquid, side walls mixtures of EG and water at the ratios 60/40, 50/50 and 40/60 by volume. Alumina (Al2O3) and bottom surface. In order to avoid influence of axial conduction on heat transferred nanoparticles were tested at the mass concentrations of 0.01, 0.1 and 1%. from the cylinder, the length-to-diameter ratio was made to be large. In the present work, The literature results show a key role of the effective thermal conductivity and the the results of free convection heat transfer performance from a uniformly heated horizontal effective viscosity of nanofluids in free convection heat transfer. In order to avoid ambi- tube are discussed. Base fluids are ethylene glycol (EG), water (W) and mixtures of EG guity in the interpretation of the present results, the thermal conductivity and the viscos- and water at the ratios 60/40, 50/50 and 40/60 by volume. Alumina (Al O ) nanoparticles ity of the tested nanofluids were determined experimentally. 2 3 were tested at the mass concentrations of 0.01, 0.1 and 1%.

2.2. Experimental Experimental Setup Setup 2.1.2.1. Experimental Experimental Apparatus Apparatus TheThe main main parts parts of of the the experimental stand stand we werere the the test test container, container, horizontal tube, tube, powerpower system, DAQ-module and and LabVIEW-base LabVIEW-basedd data measuring and data processing system.system. The The test test container made ofof PMMAPMMA hadhad innerinner dimensionsdimensions of of160 160× × 160 × 500500 mm— mm— FigureFigure 11..

t f

FigureFigure 1. 1. SchemeScheme of of the the experimental experimental setup. setup. The container is thermally insulated with Styrodur. In order to fulﬁl the condition of

free convection in an unbounded nanoﬂuid, the geometry of the tested thermal system was carefully designed. The conﬁnement ratios are as follows: HT/D = 20.5, HB/D = 13.5 and SW/D = 7.5. The details of the thermal system are discussed in [16]. Twelve resistance thermometers of type Pt100 and tolerance class B were used to measure liquid temperature. The resistance thermometers were produced by TC Direct (Mönchengladbach, Germany). A stainless steel tube with OD of 10 and 0.6 mm wall thickness was used as a test heater. Energies 2021, 14, x FOR PEER REVIEW 3 of 14

The container is thermally insulated with Styrodur. In order to fulfil the condition of free convection in an unbounded nanofluid, the geometry of the tested thermal system was carefully designed. The confinement ratios are as follows: HT/D = 20.5, HB/D = 13.5 and SW/D = 7.5. The details of the thermal system are discussed in [16]. Twelve resistance thermometers of type Pt100 and tolerance class B were used to measure liquid tempera- Energies 2021, 14, 2909 ture. The resistance thermometers were produced by TC Direct (Mönchengladbach,3 Ger- of 14 many). A stainless steel tube with OD of 10 and 0.6 mm wall thickness was used as a test heater. With L = 15 D, the tube was long enough to neglect influence of side walls on heat transfer [17–19]. The tube was heated by Joule heat. Two resistance thermometers Pt100 With L = 15 D, the tube was long enough to neglect inﬂuence of side walls on heat trans- ferwere [17 used–19]. to The measure tube was inside heated temperature by Joule of heat. the Twoheating resistance tube. Power thermometers supply was Pt100 adjusted were usedby a topanel measure of two inside auto-transformers—Figure temperature of the heating 1. Data tube. recording Power supply and management was adjusted was by adone panel using of two a Texas auto-transformers—Figure Instruments DAQ-module1. Data and recording LabVIEW and 2015 management (National Instruments, was done usingAustin, a TexasTX, USA). Instruments Experiments DAQ-module were conducte and LabVIEWd under 2015 steady (National state Instruments, conditions. Austin,Steady TX,state USA). was assumed Experiments to have were been conducted reached under when steady the temperature state conditions. difference Steady between state was the assumedcylinder’s to wall have and been liquid reached was whenless than the 0.1 temperature K [20]. A successive difference betweensteady state the was cylinder’s estab- walllished and byliquid increasing was lessthe thancurrent 0.1 to K [the20]. heat A successiveing section. steady A new state steady was state established was reached by in- creasingafter 15–20 the currentmin. Maximum to the heating electrical section. power A new supplied steady stateto the was tube reached was after120 15–20W (q min≈ 20. MaximumkW/m2). electrical power supplied to the tube was 120 W (q ≈ 20 kW/m2).

2.2. NanofluidNanofluid Preparation The testedtested fluidsfluids werewere ethylene ethylene glycol, glycol, distilled distilled water water and and mixtures mixtures of of ethylene ethylene glycol- gly- distilledcol-distilled water water (60/40), (60/40), (50/50) (50/50) and and (40/60) (40/60) by by volume. volume. ForFor thethe nanoparticles,nanoparticles, aluminaalumina (Al(Al22O3)) waswas used.used. TheThe nanoparticles nanoparticles had had a sphericala spherical form form and and their their diameter diameter was in was a range in a fromrange 5 from to 250 5 to nm, 250 while nm, while their meantheir mean diameter diameter was 47was nm 47 according nm according to the to manufacturer the manufac- Sigmaturer Sigma Aldrich Aldrich Ltd. (Munich, Ltd. The Germany).nanofluids Thewere nanofluids tested at nanoparticle were tested atmass nanoparticle concentrations mass concentrationsof 0.01, 0.1 and of 1%. 0.01, The 0.1 andnanofluids 1%. The were nanofluids prepared were with prepared the two-step with the method. two-step The method. first Thestep firstwas stepthe preparation was the preparation of the concentrated of the concentrated nanofluid nanofluid in laboratory in laboratory glasses of glasses 250 mL. of 250Then, mL. the Then, nanoparticles the nanoparticles were suspended were suspended in a base in fluid a base and fluid put andinto putan ultrasonic into an ultrasonic bath for bath1 h. The for ultrasonic 1 h. The ultrasonicwasher Elmasonic washer S180H Elmasonic from S180H Elma Schmidbauer from Elma Schmidbauer GmbH (Singen, GmbH Ger- (Singen,many) worked Germany) at a worked frequency at a of frequency 37 Hz and of 37effective Hz and power effective of power200 W. of Next, 200 W.the Next, concen- the concentratedtrated nanofluids nanofluids were mixed were mixed with the with rest the of rest the of base the fluid base fluiduntil untilthe volume the volume of 10 of L 10was L wasprepared. prepared. Finally, Finally, the fluid the fluid was washomogenized homogenized with witha high-speed a high-speed homogenizer homogenizer X1740 X1740 from fromCAT CATGmbH GmbH (Tübingen, (Tübingen, Germany) Germany) with with a speed a speed of rotation of rotation of 12,000 of 12,000 rpm rpm for for1 h. 1 As h. Asan anexample, example, Figure Figure 2 shows2 shows photographs photographs of ofthe the tested tested ethylene ethylene glycol-based glycol-based nanofluids. nanofluids.

2 3 Figure 2. Tested EG–AlEG–Al2O3 nanofluids.nanoﬂuids.

2.3. NanofluidNanofluid Properties The literature results showshow aa keykey rolerole ofof thethe effectiveeffective thermalthermal conductivityconductivity andand thethe effective viscosity of nanofluidsnanofluids inin freefree convectionconvection heatheat transfer.transfer. Therefore,Therefore, inin orderorder toto avoid ambiguity in the interpretation of the present results, the thermal conductivity and the viscosity of the tested nanofluids were determined experimentally [21]. The developed present correlations for the thermal conductivity and the effective viscosity of the tested nanofluids are listed in Tables1 and2, respectively. Energies 2021, 14, 2909 4 of 14

Table 1. Correlations for the thermal conductivity of the tested nanoﬂuids.

Liquid Correlation Equation Number

−3 0.2388 3.14·10 Water kn f = kb f (1 + 0.1046ϕm 100/dp ) Equation (1) −3 6.15·10 −5 EG kp 0.0738 9.76·10 Equation (2) k = k (1 + 0.0193 ϕm 100/dp ) n f b f kb f −3 Water/EG (60:40) kn f = kb f = 1.428·10 T Equation (3) −3 Water/EG (50:50) kn f = kb f = 1.334·10 T Equation (4) −3 Water/EG (40:60) kn f = kb f = 1.166·10 T Equation (5)

Table 2. Correlations for the dynamic viscosity of the tested nanoﬂuids.

Liquid Correlation Equation Number 0.0151 0.0236µ1.939 Water µn f = 664.06ϕm t b f Equation (6) 0.0061µ1.017 EG µn f = 1.11ϕm b f Equation (7) 0.0106µ1.003 Water/EG (60:40) µn f = 1.13ϕm b f Equation (8) µ0.9906 Water/EG (50:50) µn f = 1.14 b f Equation (9) 0.0094 0.279µ1.3237 Water/EG (40:60) µn f = 2.83ϕm t b f Equation (10)

Density and speciﬁc heat of the tested nanoﬂuids were determined by use of the Equations (11) and (12) proposed by Pak and Cho [22], respectively

ρn f = ϕvρp + (1 − ϕv)ρb f (11)

cp,n f = ϕvcp,p + (1 − ϕv)cp,b f (12) The thermal expansion coefﬁcient was determined from the equation proposed by Khanafer et al. [23] (1 − ϕv)βb f ρb f + ϕvρpβp βn f = (13) ρn f Thermophysical properties of the base ﬂuids were obtained from the data provided in the ASHRAE Handbook [24]. The appropriate correlations are shown in Table3.

Table 3. Correlations for the thermophysical properties of the base ﬂuids.

Parameter Water EG −3 −4 Thermal conductivity [W/(mK)] kb f = 1.974·10 ·T kb f = 8.49·10 ·T −5 1226.8 −7 3440 Viscosity [Pa s] µb f = 1.435·10 ·e T µb f = 1.6·10 ·e T 3 Density [kg/m ] ρb f = 1107.6 − 0.3708·T ρb f = 1331.2 − 0.732·T 2 Speciﬁc heat [J/(kgK)] cpb f = 5603 − 9.2129·T + 0.0149·T cpb f = 1062.3 + 4.507·T Thermal expansion coefﬁcient [1/K] = · −3 − 4.7211 · −3 β = 0.00065 βb f 9.3158 10 t t2 10 b f

The properties of alumina (Al2O3) nanoparticles are shown in Table4.

Table 4. Properties of Al2O3 nanoparticles.

Thermal Thermal Expansion Density [26] ρ Speciﬁc Heat [26] c Conductivity [25] k p pp Coefﬁcient [27] β p [kg/m3] [J/(kg K)] p [W/(mK)] [1/K] 35 3600 765 8.46 × 10−6

2.4. Stability of the Tested Nanofluids Stability of the nanofluids is a critical factor in the application of nanofluids that can alter not only the thermo-physical properties of nanofluids but also the thermal character- Energies 2021, 14, x FOR PEER REVIEW 5 of 14

Table 4. Properties of Al2O3 nanoparticles.

Thermal Conductivity [25] kp Density [26] ρp Specific Heat [26] cpp Thermal Expansion Co- [W/(mK)] [kg/m3] [J/(kg K)] efficient [27] βp [1/K] 35 3600 765 8.46 × 10−6

Energies 2021, 14, 2909 2.4. Stability of the Tested Nanofluids 5 of 14 Stability of the nanofluids is a critical factor in the application of nanofluids that can alter not only the thermo-physical properties of nanofluids but also the thermal charac- isticsteristics of theof the heating heating surface surface [28 [28–30].–30]. For For this this study, study, the the stability stability of of the the tested tested nanofluids nanofluids waswas estimated estimated by by the the turbidity turbidity measurement measurement using using WTW WTW device device Turb Turb 430 IR430 from IR from Xylem— Xy- WTWlem—WTW (Weilheim (Weilheim in Oberbayern, in Oberba Bavaria,yern, Bavaria, Germany). Germany). The measurement The measurement principle principle of this of devicethis device is based is based onthe on the spectrophotometry spectrophotometry method. method. The The nephelometric nephelometric turbidity turbidity units units (NTUs)(NTUs) werewere recordedrecorded andand foundfound toto be be slightly slightly changed changed over over the the period period of of performed performed testing—atesting—a period period exceeding exceeding 14 14 days. days. A A single single NTU NTU value value of theof the turbidity turbidity was was calculated calculated as anas averagean average of three of three measurements. measurements. Figure Figure3 shows 3 shows the turbiditythe turbidity of EG-based of EG-based nanofluids nanofluids as aas function a function of time. of time. For For these these nanofluids, nanofluids, the th turbiditye turbidity was was measured measured for for a period a period of 11 of to11 13to days.13 days. It was It was found found that that the the stability stability of the of testedthe tested EG-based EG-based nanofluids nanofluids is satisfactory is satisfactory for thefor testedthe tested period. period. After After 13 days, 13 days, the maximumthe maximum turbidity turbidity change change of 26% of 26% was was observed observed for thefor nanoparticlethe nanoparticle concentration concentration of 0.01%. of 0.01%.

Figure 3. Turbidity of EG–Al2O3 nanofluids; nanoparticle concentration: - 0.01%, - 0.1%, ∆ - 1%. Figure 3. Turbidity of EG–Al2O3 nanofluids; nanoparticle concentration:# ○ - 0.01%, - 0.1%, ∆ - The change in water-based nanofluids’ turbidity is substantial for lower▫ nanoparticle 1%. concentrations (Figure4). The turbidity decreased during the first 3 days by 73 and 72% for nanoparticleThe change mass in concentrations water-based nanofluids’ of 0.1 and 0.01%, turbidity respectively, is substantial a decrease for lower in the nanoparticle turbidity results from the sedimentation process. Surprisingly, the turbidity of the nanofluid with concentrations (Figure 4). The turbidity decreased during the first 3 days by 73 and 72% 1% nanoparticle concentration is almost constant over the period of 7 days. for nanoparticle mass concentrations of 0.1 and 0.01%, respectively, a decrease in the tur- 2.5.bidity Data results Reduction from and the Measurementsedimentation Uncertainty process. Surprisingly, the turbidity of the nanofluid with 1% nanoparticle concentration is almost constant over the period of 7 days. The algorithm of the data reduction as well as the procedure of measurement uncertainty estimation were the same as in the case presented in [16]. According to the calculations shown in [16], the maximum errors for the heat flux and heat transfer coefficient were estimated to be ±4.2 and ±5.5%, respectively.

EnergiesEnergies2021 2021, ,14 14,, 2909 x FOR PEER REVIEW 66 ofof 1414

Figure 4. Turbidity of water–Al2O3 nanofluids; nanoparticle concentration: - 0.01%, - 0.1%, ∆ - 1%. Figure 4. Turbidity of water–Al2O3 nanofluids; nanoparticle concentration:# ○ - 0.01%, - 0.1%, ∆ - 3. Results ▫ 1%. 3.1. Validation of the Research Methods 2.5. DataA number Reduction of experimental and Measurement tests Uncertainty using base fluids, i.e., water, EG and water/EG mixtures, were conducted in order to validate the present experimental setup and procedure. The algorithm of the data reduction as well as the procedure of measurement uncer- The present experimental results are compared with the recognized Churchill and Chu tainty estimation were the same as in the case presented in [16]. According to the calcula- correlation recommended for uniformly heated, isolated horizontal cylinders immersed in tions shown in [16], the maximum errors for the heat flux and heat transfer coefficient unbounded fluid [31]. were estimated to be ±4.2 and ±5.5%, respectively. 2  1/6  3. Results  0.387(Raq/Nu)  Nu = 0.6 + 8  (14) 3.1. Validation of the Research Methods 9 27   1 + 0.559 16  A number of experimental tests using base fluids,Pr i.e., water, EG and water/EG mixtures,As were an example, conducted Figure in order5 shows to validate comparison the present of the predictionsexperimental from setup the and present procedure. devel- opedThe present empirical experimental correlation forresults water are [16 compared] with the recognized Churchill and Chu correlation recommended for uniformly heated, isolated horizontal cylinders immersed 0.2109 0.166 in unbounded fluid [31]. Nu = 0.4017 Raq Pr (15) and the predictions obtained from the Churchill and Chu correlation (Equation (14)). The Churchill and Chu correlation underestimates⎛ predictions from⎞ the developed Equation (15) 0.387(Ra /Nu)/ with a satisfactory maximum deviation⎜ of 3.4%. ⎟ Nu = ⎜0.6 + ⎟ (14) ⎜ ⎟ 0.559 3.2. Influence of Nanoparticle Concentration on1 Heat + Transfer Pr The experimental investigation⎝ on EG-based nanofluids was⎠ performed for heat flux from 2000 to 14,000 W/m2. The corresponding temperature difference ranged from 8 to As an example, Figure 5 shows comparison of the predictions from the present de- 38 K. veloped empirical correlation for water [16] Experimental results (Figure6) revealed that the addition of nanoparticles results . . in an increase or decrease in theNu Nu = numbers 0.4017 Ra depending Pr on nanoparticle concentration(15) compared to pure EG. A slight increase in Nu number was recorded for nanoparticle mass and the predictions obtained from the Churchill and Chu correlation (Equation (14)). The concentration of 0.1%. For the nanoparticle concentrations of 0.01 and 1%, a decrease in Churchill and Chu correlation underestimates predictions from the developed Equation Nu number was noted. The highest decrease in the Nu number was observed for the (15) with a satisfactory maximum deviation of 3.4%. nanoparticle concentration of 1% and amounted 12% in comparison to pure EG. The red line in Figure6 represents the developed empirical correlation for pure EG.

Nu = 0.4673 Ra0.231Pr0.096 (16)

Energies 2021, 14, x FOR PEER REVIEW 7 of 14

Energies 2021, 14, x FOR PEER REVIEW 7 of 14 Energies 2021, 14, 2909 7 of 14

Figure 5. Present data compared to predictions from the literature correlation.

3.2. Influence of Nanoparticle Concentration on Heat Transfer The experimental investigation on EG-based nanofluids was performed for heat flux from 2000 to 14,000 W/m. The corresponding temperature difference ranged from 8 to 38 K. Experimental results (Figure 6) revealed that the addition of nanoparticles results in an increase or decrease in the Nu numbers depending on nanoparticle concentration compared to pure EG. A slight increase in Nu number was recorded for nanoparticle mass concentration of 0.1%. For the nanoparticle concentrations of 0.01 and 1%, a decrease in Nu number was noted. The highest decrease in the Nu number was observed for the nanoparticle concentration of 1% and amounted 12% in comparison to pure EG. The red line in Figure 6 represents the developed empirical correlation for pure EG.

Figure 5. Present data compared to predictionsNu = 0.4673 from Ra the. literaturePr. correlation. (16) Figure 5. Present data compared to predictions from the literature correlation.

Figure 6. Nu–RaNu–Ra relationship relationship for ethylene glycol-based nanofluids. nanoﬂuids.

An experimental investigation of water-based nanoﬂuids has been performed for heat ﬂux from 2000 to 22,000 W/m2. The corresponding temperature difference ranged from 3 to 25 K.

Similar to the EG–Al2O3 (0.1%) nanofluid, the water–Al2O3 mixture with a nanoparticle mass concentration of 0.1% exhibits an increase in Nu number compared to pure water. The maximum increase in Nu number was about 7% for the minimum Ra number— Figure7. A decrease in the Nu numbers was observed for the water–Al 2O3 mixture with a nanoparticle mass concentration of 0.01% compared to pure water. No influence of nanoparticles on the Nu numbers was observed for the water–Al2O3 nanofluid with a nanoparticle mass concentration of 1%—the measurement points overlap the red line representing a developed empirical correlation for pure water.

Nu = 0.374 Ra0.2613Pr0.16. (17) Figure 6. Nu–Ra relationship for ethylene glycol-based nanofluids.

Energies 2021, 14, x FOR PEER REVIEW 8 of 14 Energies 2021, 14, x FOR PEER REVIEW 8 of 14

An experimental investigation of water-based nanofluids has been performed for heat fluxAn fromexperimental 2000 to 22,000investigation W/m. ofThe water- correspondingbased nanofluids temperature has been difference performed ranged for fromheat 3flux to 25 from K. 2000 to 22,000 W/m . The corresponding temperature difference ranged fromSimilar 3 to 25 to K. the EG–Al2O3 (0.1%) nanofluid, the water–Al2O3 mixture with a nanoparticle massSimilar concentration to the EG–Al of 20.1%O3 (0.1%) exhibits nanofluid, an increase the water–Alin Nu number2O3 mixture compared with to a pure nanopar- wa- ter.ticle The mass maximum concentration increase of 0.1%in Nu exhibits number an was increase about in 7% Nu for number the minimum compared Ra tonumber— pure wa- Figureter. The 7. maximumA decrease increase in the Nu in numbersNu number was was observed about 7%for forthe the water–Al minimum2O3 mixture Ra number— with aFigure nanoparticle 7. A decrease mass concentration in the Nu numbers of 0.01% was compared observed to for pure the water. water–Al No 2influenceO3 mixture of withna- noparticlesa nanoparticle on the mass Nu concentration numbers was ofobserved 0.01% compared for the water–Al to pure2 Owater.3 nanofluid No influence with a nano- of na- particlenoparticles mass on concentration the Nu numbers of 1%—the was observed measurement for the water–Al points overlap2O3 nanofluid the red with line arepre- nano- sentingparticle a massdeveloped concentration empirical of correlation 1%—the meas for pureurement water. points overlap the red line representing a developed empirical correlation for pure water. Energies 2021, 14, 2909 Nu = 0.374 Ra.Pr. 8(17) of 14 Nu = 0.374 Ra.Pr. (17)

. . Figure 7. Nu–Ra relationship for water based nanofluids. FigureFigure 7. 7. Nu–RaNu–Ra relationship relationship for for water water based based nanofluids. nanofluids. TheThe experimental experimental investigation investigation of of EG/water EG/water (60/40) (60/40) mixture-based mixture-based nanofluids nanofluids was was The experimental investigation of EG/water (60/40) mixture-based nanofluids was performedperformed for for heat heat flux flux from from 2000 2000 to 21,000 to 21,000 W/mW/m. The2. corresponding The corresponding temperature temperature dif- performed for heat flux from 2000 to 21,000 W/m. The corresponding temperature dif- ferencedifference ranged ranged from from 4 to 435 to K. 35 K. ference ranged from 4 to 35 K. ExperimentalExperimental results results show show that that the additionaddition ofof nanoparticlesnanoparticles with with a a mass mass concentration concentra- Experimental results show that the addition of nanoparticles with a mass concentra- tionof 0.1%of 0.1% leads leads toan to increasean increase in the in the Nu Nu numbers numbers within within the the whole whole range range of Ra of numbersRa numbers with tion of 0.1% leads to an increase in the Nu numbers within the whole range of Ra numbers witha maximum a maximum of 15% of 15% for thefor minimumthe minimum Ra number—FigureRa number—Figure8. 8. with a maximum of 15% for the minimum Ra number—Figure 8.

Figure 8. Nu–Ra relationship for EG/water (60/40) mixture-based nanoﬂuids.

The red line in Figure8 represents the developed empirical correlation for the EG/water (60/40) mixture.

Nu = 1.110Ra0.194 (18) A distinct decrease in the Nu numbers compared to the base fluid was noted for the nanofluid with 0.01% nanoparticle concentration with the average difference of about 8%. For the nanofluid with a nanoparticle mass concentration of 1%, the Nu numbers are higher than for the base fluid with Ra < 500,000. For higher Ra numbers, the Nu numbers are lower than for the base fluid with a maximum of 5% difference. The experimental investigation of EG/water (50/50) mixture-based nanofluids was performed for heat flux from 2000 to 20,000 W/m2. The corresponding temperature difference ranged from 4 to 30 K. Experimental investigations show an increase in the Nu numbers within the whole range of the Ra number for the nanoparticle concentration of 0.01 and 0.1%—Figure9. For Energies 2021, 14, x FOR PEER REVIEW 9 of 14

Figure 8. Nu–Ra relationship for EG/water (60/40) mixture-based nanofluids.

The red line in Figure 8 represents the developed empirical correlation for the EG/water (60/40) mixture. Nu = 1.110Ra. (18) A distinct decrease in the Nu numbers compared to the base fluid was noted for the nanofluid with 0.01% nanoparticle concentration with the average difference of about 8%. For the nanofluid with a nanoparticle mass concentration of 1%, the Nu numbers are higher than for the base fluid with Ra < 500,000. For higher Ra numbers, the Nu numbers are lower than for the base fluid with a maximum of 5% difference. The experimental investigation of EG/water (50/50) mixture-based nanofluids was performed for heat flux from 2000 to 20,000 W/m. The corresponding temperature difference ranged from 4 to 30 K. Energies 2021, 14, 2909 9 of 14 Experimental investigations show an increase in the Nu numbers within the whole range of the Ra number for the nanoparticle concentration of 0.01 and 0.1%—Figure 9. For the nanoparticle mass concentration of 1%, a decrease in the Nu numbers in comparison tothe pure nanoparticle EG/water mass (50/50) concentration mixture was of observed 1%, a decrease with a maximum in the Nu numbersof 6% for inthe comparison highest Ra number.to pure EG/water The red line (50/50) in Figure mixture 9 represents was observed the developed with a maximum empirical of 6%correlation for the highestfor the EG/waterRa number. (50/50) The red mixture. line in Figure9 represents the developed empirical correlation for the EG/water (50/50) mixture. . NuNu = =1.7053 1.7053 Ra Ra0.1626 (19)

Figure 9. Nu–Ra relationship for EG/wat EG/waterer (50/50)-based (50/50)-based nanofluids. nanoﬂuids.

The experimental investigationinvestigation onon EG/waterEG/water (40/60) mixture-based mixture-based nanofluids nanoﬂuids was 2 performed for for heat heat flux ﬂux from from 2000 2000 to to 22,000 22,000 W/mW/m. The. The corresponding corresponding temperature temperature dif- ferencedifference ranged ranged from from 4 to 4 31 to 31K. K. Experimental results show an increase in the Nu numbers for the nanoparticle mass Energies 2021, 14, x FOR PEER REVIEW Experimental results show an increase in the Nu numbers for the nanoparticle10 mass of 14

concentration of 0.1% within the whole rang rangee of the Ra numbers tested with a maximum of 5% for the maximum Ra number—Figure 10. of 5% for the maximum Ra number—Figure 10.

Figure 10. Nu–Ra relationship for EG/waterEG/water (40/60)-based (40/60)-based nanofluids. nanoﬂuids.

The red line in Figure 10 representsrepresents thethe developeddeveloped empiricalempirical correlationcorrelation for thethe EG/water (40/60) (40/60) mixture. mixture. Nu = 1.309Ra0.185 (20) Nu = 1.309Ra. (20) For the nanoparticle mass concentration of 0.01%, experimental points for the nanoﬂuid almostFor overlap the nanoparticle the data for amass pure EG/waterconcentration (40/60) of mixture0.01%, experimental represented by points the red for line the in nanofluid almost overlap the data for a pure EG/water (40/60) mixture represented by the red line in Figure 10. For the nanofluid with a nanoparticle mass concentration of 1%, the Nu numbers are higher than for the base fluid for Ra < 400,000. For higher Ra numbers, the Nu numbers are lower than for the base fluid. Figure 11 illustrates the impact of nanoparticle concentration on the Nu numbers for water-based (Figure 11a) and EG-based (Figure 11b) nanofluids for selected heat fluxes. As expected, the Nu numbers increase with heat flux increase for all tested nanofluids. Experimental data show that independent on heat flux and base fluid, the Nu numbers reach a kind of optimum for the nanoparticle mass concentration of 0.1%.

(a)

Energies 2021, 14, x FOR PEER REVIEW 10 of 14

Figure 10. Nu–Ra relationship for EG/water (40/60)-based nanofluids.

The red line in Figure 10 represents the developed empirical correlation for the EG/water (40/60) mixture.

. Energies 2021, 14, 2909 Nu = 1.309Ra 10 of(20) 14 For the nanoparticle mass concentration of 0.01%, experimental points for the nanofluid almost overlap the data for a pure EG/water (40/60) mixture represented by the Figurered line 10 in. ForFigure the nanofluid10. For the with nanofluid a nanoparticle with a nanoparticle mass concentration mass concentration of 1%, the Nu of numbers 1%, the areNu highernumbers than are for higher the base than fluid for for the Ra base < 400,000. fluid for For Ra higher < 400,000. Ra numbers, For higher the Ra Nu numbers, numbers arethe lowerNu numbers than for are the lower base fluid.than for the base fluid. Figure 11 illustrates the impact ofof nanoparticlenanoparticle concentrationconcentration onon thethe NuNu numbersnumbers forfor water-basedwater-based (Figure 1111a)a) and EG-based (Figure 1111b)b) nanofluidsnanofluids for selected heat fluxes.fluxes. AsAs expected,expected, the Nu numbers increase with heatheat fluxflux increase for all tested nanofluids.nanofluids. Experimental data show that independent on heat fluxflux andand basebase fluid,fluid, thethe NuNu numbersnumbers reach aa kindkind ofof optimumoptimum forfor thethe nanoparticlenanoparticle massmass concentrationconcentration ofof 0.1%.0.1%.

Energies 2021, 14, x FOR PEER REVIEW 11 of 14

(a)

(b)

Figure 11. InfluenceInﬂuence of nanoparticle concentration on Nu number for selected heat fluxes ﬂuxes for EG (a) (anda) and water water (b). (b).

3.3. Present Present Correlation Putra et al. [32] [32] correlated correlated their experiment experimentalal results of water-based nanofluids nanoﬂuids using an Nu-type Nu-type correlation correlation in in the the form form NuNu == CRaCRa. However,n. However, as it as was it was shown shown in [17], in[ 17Nu], numberNu number is a function is a function of Ra number of Ra number as well asas wellPr number. as Pr number.Xuan and Xuan Roetzel and [33] Roetzel suggested [33] that the correlation equation for nanofluids should include a concentration of the nanoparticles. A multidimensional regression analysis based on the least squares method was used to develop a correlation equation for the Nu numbers for free convection of water–Al2O3, EG–Al2O3 and the mixtures of water and EG at the ratios of 60/40, 50/50, 40/60 by volume of nanofluids of different nanoparticle concentration from horizontal cylinder in an unbounded fluid.

. . . Nu = 0.63Ra Pr (1−𝜑) (21) Figure 12 shows the comparison of the experimental results for all tested nanofluids with the predictions made from the developed correlation (Equation (21)). For 85% of points, the difference between experimental data and corresponding predictions is lower than ±10%. Considering the complexity of the examined process, the obtained agreement is satisfactory. The developed correlation is valid for the Ra number range 3 × 104 ≤ Ra ≤ 1.3 × 106, the Pr number range 4.4 < Pr < 176 and the mass concentrations of alumina na- ≤ ≤ noparticles 0.01% 𝜑 1%.

Energies 2021, 14, 2909 11 of 14

suggested that the correlation equation for nanofluids should include a concentration of the nanoparticles. A multidimensional regression analysis based on the least squares method was used to develop a correlation equation for the Nu numbers for free convection of water–Al2O3, EG–Al2O3 and the mixtures of water and EG at the ratios of 60/40, 50/50, 40/60 by volume of nanofluids of different nanoparticle concentration from horizontal cylinder in an unbounded fluid. 0.23 0.053 2.64 Nucorr = 0.63Ra Pr (1 − ϕ) (21) Figure 12 shows the comparison of the experimental results for all tested nanofluids with the predictions made from the developed correlation (Equation (21)). For 85% of points, the difference between experimental data and corresponding predictions is lower than ±10%. Considering the complexity of the examined process, the obtained agreement is satisfactory. The developed correlation is valid for the Ra number range 3 × 104 ≤ Ra Energies 2021, 14, x FOR PEER REVIEW 6 12 of 14 ≤ 1.3 × 10 , the Pr number range 4.4 < Pr < 176 and the mass concentrations of alumina nanoparticles 0.01% ≤ ϕm ≤ 1%.

Figure 12. Experimental results vs. predictions from the developed correlation.

4. Discussion and Conclusions Free convection convection heat heat transfer transfer from from a horizo a horizontalntal cylinder cylinder immersed immersed in nanofluids in nanofluids was wasstudied. studied. The experimental The experimental setup setup was designed was designed in order in order to fulfil to fulfilrequirements requirements of free of con- free vectionconvection in an in unbounded an unbounded fluid. fluid. In order to ensure wide range of Ra numbers, five five base fluids fluids were investigated, i.e., water, EGEG andand water–EGwater–EG mixtures:mixtures: (60/40),(60/40), (50/50)(50/50) andand (40/60)(40/60) byby volume.volume. AluminaAlumina (Al2O3) nanoparticles were tested at the mass concentrations of 0.01, 0.1 and 1%. (Al2O3) nanoparticles were tested at the mass concentrations of 0.01, 0.1 and 1%. Stability of the tested nanofluids as a fundamental issue of the potential application of Stability of the tested nanofluids as a fundamental issue of the potential application the nanofluids was studied very carefully. of the nanofluids was studied very carefully. As it was established in [12,13,23,34], evaluation of the impact of nanoparticles on As it was established in [12,13,23,34], evaluation of the impact of nanoparticles on free convective heat transfer depends on the determination of the thermophysical prop- free convective heat transfer depends on the determination of the thermophysical properties of the analyzed nanofluids. Depending on the formulas adopted to calculate major erties of the analyzed nanofluids. Depending on the formulas adopted to calculate major properties, such as thermal conductivity and viscosity, contradictory results regarding the properties, such as thermal conductivity and viscosity, contradictory results regarding the influence of nanoparticles were found. Therefore, the present study’s correlations for the calculation of thermal conductivity and viscosity of the tested nanofluids are based on actual measurements. Present experimental data show that the addition of alumina nanoparticles to water, EG and mixtures of water and EG results in an increase or decrease in the Nu numbers depending on the nanoparticle concentration. An optimum of the Nu numbers was observed for the nanoparticle mass concentration of 0.1%. A heat transfer correlation equation for the nanofluids has been developed and verified for various Ra numbers, Pr numbers and nanoparticle mass concentrations.

Author Contributions: Conceptualization, J.T.C.; methodology, J.T.C. and S.S.; software, D.S.; validation, J.T.C. and S.S.; formal analysis, J.T.C.; investigation, D.S.; data curation, D.S.; writing—original draft preparation, J.T.C.; writing—review and editing, J.T.C. and S.S.; funding acquisition, J.T.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding.

Institutional Review Board Statement: Not applicable.

Energies 2021, 14, 2909 12 of 14

influence of nanoparticles were found. Therefore, the present study’s correlations for the calculation of thermal conductivity and viscosity of the tested nanofluids are based on actual measurements. Present experimental data show that the addition of alumina nanoparticles to water, EG and mixtures of water and EG results in an increase or decrease in the Nu numbers depending on the nanoparticle concentration. An optimum of the Nu numbers was observed for the nanoparticle mass concentration of 0.1%. A heat transfer correlation equation for the nanofluids has been developed and verified for various Ra numbers, Pr numbers and nanoparticle mass concentrations.

Author Contributions: Conceptualization, J.T.C.; methodology, J.T.C. and S.S.; software, D.S.; validation, J.T.C. and S.S.; formal analysis, J.T.C.; investigation, D.S.; data curation, D.S.; writing—original draft preparation, J.T.C.; writing—review and editing, J.T.C. and S.S.; funding acquisition, J.T.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Acknowledgments: The authors thank Albrecht Eicke (City University of Applied Sciences Bremen) for kind cooperation during figures preparation. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

a Thermal diffusivity (m2/s) cp Specific heat (J/(kg K)) D Outer diameter of heated cylinder (m) g Gravitational acceleration (m/s2) h Heat transfer coefficient (W/(m2 K)) HB Distance between periphery of cylinder and bottom wall (m) HT Submersion depth (m) k Thermal conductivity (W/(m K)) hD Nu= k Nu number (-) Pr Pr number (-) q Heat flux (W/m2) 3 gβ(Tw−Tf)D Ra= νa Ra number related to temperature difference (-) gβqD4 Raq= kνa Ra number related to heat flux (-) SW Distance between periphery of cylinder and side wall (m) t Temperature (◦C) T Temperature (K) ∆T Temperature difference (K) Greek Symbols β Thermal expansion coefficient (1/K) µ Dynamic viscosity (Pa s) ν Kinematic viscosity (m2/s) ϕ Nanoparticle concentration (-) ρ Density (kg/m3) Subscripts bf Base fluid f Fluid m Mass nf Nanofluid p Particle v Volume w Wall Energies 2021, 14, 2909 13 of 14

References 1. Choi, S. Enhancing Thermal Conductivity of Fluids with Nanoparticles. In Developments and Applications of Non-Newtonian Flows; ASME: New York, NY, USA, 1995; Volume 231/MD, pp. 99–105. 2. Taylor, R.; Coulombe, S.; Otanicar, T.; Phelan, P.; Gunawan, A.; Lv, W.; Rosengarten, G.; Prasher, R.; Tyagi, H. Small particles, big impacts. A review of the diverse applications of nanofluids. J. Appl. Phys. 2013, 113, 011301. [CrossRef] 3. Sajid, M.U.; Ali, H.M. Recent advances in application of nanofluids in heat transfer devices: A critical review. Renew. Sustain. Energy Rev. 2019, 103, 556–592. [CrossRef] 4. Mahian, O.; Kolsi, L.; Amani, M.; Estellé, P.; Ahmadi, G.; Kleinstreuer, C.; Marshall, J.S.; Taylor, R.A.; Abu-Nada, E.; Rashidi, S.; et al. Recent advances in modeling and simulation of nanofluid flows-Part II: Applications. Phys. Rep. 2019, 791, 1–59. [CrossRef] 5. El-Kaddadi, L.; Asbik, M.; Zari, N.; Zeghmati, B. Experimental study of the sensible heat storage in the water/TiO2 nanofluid enclosed in an annular space. Appl. Therm. Eng. 2017, 122, 673–684. [CrossRef] 6. Cie´sliński,J.T.; Fabrykiewicz, M. Thermal energy storage using stearic acid as PCM material. J. Mech. Energy Eng. 2018, 2, 217–224. 7. Hussein, A.M.; Sharma, K.V.; Bakar, R.A.; Kadirgama, K. A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid. Renew. Sustain. Energy Rev. 2014, 29, 734–743. [CrossRef] 8. Mahian, O.; Kolsi, L.; Amani, M.; Estellé, P.; Ahmadi, G.; Kleinstreuer, C.; Marshall, J.S.; Siavashi, M.; Taylor, R.A.; Niazmand, H.; et al. Recent advances in modeling and simulation of nanofluid flows-Part I: Fundamentals and theory. Phys. Rep. 2019, 790, 1–48. [CrossRef] 9. Haddad, Z.; Oztop, H.F.; Abu-Nada, E.; Mataoui, A. A review on natural convective heat transfer of nanofluids. Renew. Sust. Energ. Rev. 2012, 16, 5363–5378. [CrossRef] 10. Cie´sliński,J.T.; Krygier, K. Free convection of water-Al2O3 nanofluid from horizontal porous coated tube. Key Eng. Mater. 2014, 597, 15–20. [CrossRef] 11. Kiran, M.R.; Babu, S.R. Experimental investigation on natural convection heat transfer enhancement using transformer oil-TiO2 nano fluid. Int. Res. J. Eng. Technol. (IRJET) 2018, 5, 1412–1418. 12. Habibi, M.R.; Amini, M.; Arefmanesh, A.; Ghasemikafrudi, E. Effects of viscosity variations on buoyancy-driven flow from a horizontal circular cylinder immersed in Al2O3-water nanofluid. Iran. J. Chem. Eng. 2019, 38, 213–232. 13. Polidori, G.; Fohanno, S.; Nguyen, C.T. A note on heat transfer modelling of Newtonian nanofluids in laminar free convection. Int. J. Thermal Sci. 2007, 46, 739–744. [CrossRef] 14. Brinkman, H.C. The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 1952, 20, 571. [CrossRef] 15. Maïga, S.E.B.; Palm, S.J.; Nguyen, C.T.; Roy, G.; Galanis, N. Heat transfer enhancement by using nanofluids in forced convection flows. Int. J. Heat Fluid Flow 2005, 26, 530–546. [CrossRef] 16. Cie´sliński,J.T.; Smolen, S.; Sawicka, D. Free convection heat transfer from horizontal cylinders. Energies 2021, 14, 559. [CrossRef] 17. Fand, R.M.; Morris, E.W.; Lum, M. Natural convection heat transfer from horizontal cylinders to air, water and silicone oils for Rayleigh numbers between 3 × 102 to 2 × 107. Int. J. Heat Mass Transf. 1997, 20, 1173–1184. [CrossRef] 18. Ashjaee, M.; Yazdani, S.; Bigham, S.; Yousefi, T. Experimental and numerical investigation on free convection from a horizontal cylinder located above an adiabatic surface. Heat Transf. Eng. 2012, 33, 213–224. [CrossRef] 19. Atayılmaz, ¸S.Ö.;Teke, I.˙ Experimental and numerical study of the natural convection from a heated horizontal cylinder. Int. Commun. Heat Mass Transf. 2009, 36, 731–738. [CrossRef] 20. Cie´sliński, J.T.; Pudlik, W. Laminar free-convection from spherical segments. Int. J. Heat Fluid Flow. 1988, 9, 405–409. [CrossRef] 21. Sawicka, D.; Cie´sliński,J.T.; Smoleń,S. A comparison of empirical correlations of viscosity and thermal conductivity of water- ethylene glycol-Al2O3 nanofluids. Nanomaterials 2020, 10, 1487. [CrossRef] 22. Pak, B.C.; Cho, Y.I. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transf. 1998, 11, 151–170. [CrossRef] 23. Khanafer, K.; Vafai, K.; Lightstone, M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 2003, 46, 3639–3653. [CrossRef] 24. ASHRAE. American Society of Heating, Refrigerating and Air-Conditioning Engineers. In ASHRAE Handbook—Fundamentals; ASHRAE: Atlanta, GA, USA, 2005. 25. Buongiorno, J.; Venerus, D.C.; Prabhat, N.; McKrell, T.J.; Townsend, J.; Christianson, R.J.; Tolmachev, Y.V.; Keblinski, P.; Hu, L.-W.; Alvarado, J.L.; et al. A benchmark study on the thermal conductivity of nanofluids. J. Appl. Phys. 2009, 106, 094312. [CrossRef] 26. Vajjha, R.S.; Das, D.K. Specific heat measurement of three nanofluids and development of new correlations. ASME J. Heat Transf. 2009, 131, 071601. [CrossRef] 27. Ho, C.J.; Liu, W.K.; Chang, Y.S.; Lin, C.C. Natural convection heat transfer of alumina–water nanofluid in vertical square enclosures: An experimental study. Int. J. Therm. Sci. 2010, 49, 1345–1353. [CrossRef] 28. Yu, W.; Xie, H. A Review on nanofluids: Preparation, stability mechanisms, and applications. J. Nanomater. 2012, 2012, 435873. [CrossRef] 29. Kouloulias, K.; Sergis, A.; Hardalupas, Y. Sedimentation in nanofluids during a natural convection experiment. Int. J. Heat Mass Transf. 2016, 101, 1193–1203. [CrossRef] Energies 2021, 14, 2909 14 of 14

30. Fuskele, V.; Sarviya, R.M. Recent developments in nanoparticles synthesis, preparation and stability of nanofluids. Mater. Today: Proc. 2017, 4, 4049–4060. [CrossRef] 31. Churchill, S.; Chu, H. Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int. J. Heat Mass Transf. 1975, 18, 1049–1053. [CrossRef] 32. Putra, N.; Roetzel, W.; Das, S.K. Natural convection of nanofluids. Heat Mass Transf. 2003, 39, 775–784. [CrossRef] 33. Xuan, Y.; Roetzel, W. Conceptions for heat transfer correlations of nanofluids. Int. J. Heat Mass Transf. 2000, 43, 3701–3707. [CrossRef] 34. Ho, C.J.; Chen, M.W.; Li, Z.W. Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity. Int. J. Heat Mass Transf. 2008, 51, 4506–4516. [CrossRef]