CuO/ Water Nanofluid Heat Transfer Through Triangular Ducts

Transcription

1 Iranian Journal of Chemical Engineering Vol. 9, No. 1 (Winter), 2012, IAChE CuO/ Water Nanoflui Heat Transfer Through Triangular Ducts S. Zeinali Heris, E. Talaii, S. H. Noie Chemical Engineering Deartment, Engineering Faculty, Ferowsi University of Mashha, Mashha, Iran Abstract In the resent aer laminar flow force convective heat transfer of CuO/water nanoflui in a triangular uct uner constant wall temerature conition is investigate numerically. Sometimes, because of ressure ro limitations the nee for noncircular ucts arises in many heat transfer alications. We use nanoflui instea of ure flui because of its otential to increase heat transfer of system. In this aer, the effect of arameters such as nanoarticles iameter, nanoarticles concentration, tye of nanoarticles an heat transfer comarison between nanoflui an ure flui is stuie. Comarison of convective heat transfer of nanoflui in isosceles triangular ucts with various aex angles is also resente. In this stuy, for the resence of nanoarticles, the isersion moel an for solving ifferential equations, the finite ifference metho is use. merical results inicate an enhancement of heat transfer of flui with changing to the susension of nanometer-size articles in the triangular uct. Results also efine that equilateral triangular uct has a maximum heat transfer in comarison with other tyes of isosceles triangular uct. Keywors: Heat transfer Enhancement, Triangular Duct, CuO/water Nanoflui 1. Introuction Increase effort is being irecte at roucing more efficient heat exchangers to effect savings of energy, material an labor. Because of size an volume constraints in alications to aerosace, nuclear, biomeical engineering an electronics, it may be necessary to use non-circular flowassage geometries, articularly in comact heat exchangers [1]. The otimization of heat exchangers therefore always has to be aime at an increase in the heat transfer simultaneously with a minimum increase of ressure ro[2].consequently, ucts with non-circular cross-section are use in this stuy ue to less ressure ro, although it causes ecreasing heat transfer. As the heat transfer rate through the noncircular ucts (triangle, square, rectangle, etc.) is smaller than that of circular tubes ue to less ressure ro, aing nanoarticles to heat transfer fluis may enhance the heat transfer roerties of noncircular ucts[]. An innovative way of imroving the heat transfer erformance of common fluis is to susen various tyes of small soli Corresoning author: zeinali@ferowsi.um.ac.ir 2

2 CuO/ Water Nanoflui Heat Transfer Through Triangular Ducts articles, such as metallic, nonmetallic an olymeric articles in conventional fluis to form colloial. However, susene articles of the orer of μm or even mm may cause some severe roblems in the flow channels, increasing ressure ro, causing the articles to quicly settle out of susension [4]. Nanofluis ossess better stability, much higher surface area, less clogging an abrasion[5]. So nanoflui was use instea of ure flui because of its otential to increase the heat transfer of the system. Nanofluis are create by isersing nanometer-size articles (< 100 nm) in a base flui such as water, ethylene glycol or roylene glycol [6]. In heat transfer alications, the susension shoul have a sufficiently high volume fraction of susene soli, while avoiing significant increases in viscosity relative to the arent liqui. In aition, the susension shoul remain stable an avoi seimentation or egraation uring use. The most imortant requirement is that susension must be chemically stable, thereby avoiing flocculation, coagulation, or gel formation. Chemical stability can be achieve by use of suitable aitives that moify the surface chemistry of the article liqui system, or rovie a reulsive surface charge, such as that achieve via control of H [7]. Unerstaning the hysical an thermal roerties of nanoflui is essential before using nanofluis in ractical alications [7]. Choi [8] was the first erson to create fluis containing a susension of nanometer-size articles calle nanofluis, an inicate their consierable thermal roerties by measuring the convective heat transfer coefficient of these fluis. Lee an Choi [9] stuie convective heat transfer of laminar flows of an unsecifie nanoflui in microchannels, an observe a reuction in thermal resistance by a factor of 2. Nanofluis were also observe to be able to issiate a heat ower three times more than ure water coul o. Xuan an Rotzel [10] consiere two moels (homogeneous an isersion moel) for investigating force convective heat transfer. Nanofluis boiling rocess has been investigate exerimentally by several researchers. Bang an Chang [11] stuie boiling heat transfer characteristics of nanofluis with alumina nanoarticles susene in water. They foun that the aition of alumina nanoarticles cause a ecrease of ool nucleate boiling heat transfer. There are ifferent an oosite arameters affecting the boiling heat transfer erformance of nanofluis incluing the viscosity of the solution, nanoarticle collision with the heater surface an bubbles, an the bounary layer thicness. Soltani et al investigate Pool boiling heat transfer of non-newtonian nanofluis.the combination of the variations in such arameters causes better erformance for non-newtonain nanofluis in comarison with the non- Newtonian base flui[12]. There are many assive cases about nanofluis that are still unrecognize. Most of the searches are about heat transfer in circular ucts an there is no reort about ucts with a triangular cross-section which causes a lower ressure ro than other forms of ucts. Kays an Lonon [1] showe that a comact heat-exchanger, with a triangular cross-sectional internal flow assage, has a 24 Iranian Journal of Chemical Engineering, Vol. 9, No. 1

3 Zeinali Heris, Talaii, Noie high ratio of heat-transfer area to flowassage volume. Shah an Lonon [14] stuie the heat transfer characteristics of laminar flow in a wie variety of channel shaes, incluing for equilateral triangular with roune corners, isosceles triangular, right triangular an arbitrary triangular crosssection ucts, for an extensive range of thermal bounary conitions. As can be seen, investigations are about ure fluis, so stuying the laminar flow force convective heat transfer of nanoflui in a triangular uct with constant wall temerature using the isersion moel is the aim of this aer. 2. Mathematical moeling Laminar flow force convection of CuO/water nanoflui in a triangular uct is stuie numerically. The uct coigurations an coorinate system are shown in Fig U = b Y 2 b 2 + a YX ( b Y + a X ) b 27 (1) The energy equation for constant roerty flow is efine as: eff ρ. c eff T x x + T T = u y y z (2) in the above equation is effective thermal conuctivity of nanoflui an may tae the following form[15]: = + eff () is the isersion thermal conuctivity an the following formula has been roose to calculate [15-16 ]: = C( ρ.c ).u m. ν..a (4) In which (C) is an unnown constant an shoul be etermine by matching exerimental ata. At the en, the energy equation for laminar flow in an equilateral triangular uct is: Figure 1. Geometry of a triangular uct. For the hyroynamically eveloe an thermally eveloing flow, there is only one nonzero comonent of velocity (u), an the imensionless velocity for triangular ucts using imensionless arameters incluing u y U = (u m is average velocity), Y = 2b an u m x X = is efine as follows [14]: 2a 2 θ C.( ρ.c ). ν..a θ 2aU = + Z ( ρ.c 2 ) u m ( ρ.c ) X 2 C.(.c )...a 2 a ρ ν θ + + b (.c ) u (.c ) 2 ρ ρ m Y (5) In Eq. (5), Peclet number can be use to simlify the equation e ( ρ ) 2a.u..c m = (6) Iranian Journal of Chemical Engineering, Vol.9, No. 1 25

4 CuO/ Water Nanoflui Heat Transfer Through Triangular Ducts Consequently the temerature istribution equation is in the form of: 2 θ 2a θ 2aU = + C. υ..a Z e 2 X 2 2 a 2a θ + + C. υ..a b e 2 Y (7). Thermo hysical roerties of nanofluis It is execte that the heat transfer coefficient of the nanoflui will een on the thermal conuctivity an the heat caacity of the base flui an nanomaterials, flow attern, Reynols an Prantl numbers, temerature, the volume fraction of the susene articles, the imensions an shae of the articles [17]. So, some of the thermohysical roerties use in this aer are efine as: Density of nanoflui [10, 15, 18]: ρ ( ν ) ρ bf = ν. ρ + 1 (8) Secific heat caacity of nanoflui [10,15,18]: C ( 1 ν) νρc + ρbf C bf = (9) ρ Thermal conuctivity is an imortant arameter in the fiel of nanoflui heat transfer[19].various moels for Conuctive heat transfer coefficient of nanofluis are roose. In absence of exerimental ata, Yu an Choi correlation [20] was use for etermination of nanoflui effective thermal conuctivity: + 2bf = + 2 bf + 2( bf )(1 + β ) ν bf ( bf )(1 + β ) ν (10) In equation (10) β is the ratio of the nanolayer thicness to the original article raius an β = 0. 1 was use to calculate the nanoflui effective thermal conuctivity. All the thermohysical roerties iscusse above were incororate in the resent numerical analysis to comute the laminar heat transfer for three ifferent tyes of nanofluis which are summarize in Table 1. Table 1. Thermohysical roerties of the nanoarticles use in the numerical comutations at inlet temerature of 2 K Nanoarticle AL 2 O Cuo Cu g m ρ C J gk W mk Valiation of the simulation In this aer, the finite ifference metho is use for numerical solution. Fig. 2 shows the gri istribution of the triangular uct that was use. The iscretization in the hysical sace (x, y) is erforme by iviing the flow omain in equal triangular elements. The gri is constructe by rawing insie the triangular cross section, three grous of arallel lines. The lines of each grou are equally istance an arallel to one of the three sies of the triangle. The benefits of such a iscretization is obvious since the bounaries of the comutational omain are ientical to the bounaries of the triangular cross section of 26 Iranian Journal of Chemical Engineering, Vol. 9, No. 1

5 Zeinali Heris, Talaii, Noie the channel, roviing goo accuracy in the numerical solution[21]. Figure. Comarison between moel reictions an results efine by Lonon [14] Figure 2. Physical lattice with its triangular elements Of course, the involve comutational effort is significant since solving for the unnown istribution function, in a general-geometry roblem, woul require a six-imensional hase sace gri (three variables in the hysical sace an three variables in the molecular velocity sace), which imoses severe emans on comuter resources (time an memory) [22]. The gri use in the resent analysis is (56 in x, y irection,100 in z irection). In orer to ensure gri ineenence, the solution is teste for , which gave similar values. Therefore, was accete as the otimal gri size. In orer to valiate the comutational moel, the numerical results were comare with the theoretical ata available for the conventional fluis in triangular uct by Lonon [14]. Fig. islays the comarison of sselt number comute by Lonon an comute values from the resent simulations. 5. Results an iscussion The numerical coe eveloe is use to investigate the effect of arameters such as nanoarticles concentration (ν), nanoarticle iameter (), an Reynols number on the heat transfer of nanofluis. It is also use for Heat transfer comarison between isosceles triangular ucts with various aex angles. Consiering the laminar flow regime, the range of Reynols number is between Fig. 4 shows the average sselt number versus Re for ure water an water/ CuO nanoflui. As shown in Fig. 4, the sloe of versus Re is greater for water/ CuO comare to ure water, which means a consierable enhancement of heat transfer by aing nanoarticles to the base flui. The actual mechanism behin this enhancement remains unclear [2]. For examle, at Re=2065, sselt number of water is increase from.79 to 5.8 by aing nanoarticles of CuO (.01 volume concentration, iameter of 10 nm). Fig. 5 shows the average sselt number versus Reynols at various concentration of CuO for 10nm-40nm nanoarticles. The effects of nanoarticle size an article concentration on the thermal conuctivity are shown in this figure.this figure inicates that Iranian Journal of Chemical Engineering, Vol.9, No. 1 27

6 CuO/ Water Nanoflui Heat Transfer Through Triangular Ducts Figure 4. Comarison between nanoflui an ure flui heat transfer the average sselt number increases with nanoarticles concentration, an better enhancement is seen at lower article iameters. This henomenon can be relate to nanoarticles interactions [24]. Essentially, aing more nanoarticles to the base flui resulte in the further enhancement of the thermal roerties of the base flui. For examle, at =10 an Re=424, by increasing nanoarticles concentration from 0.01 to 0.04, the average sselt number increases from 2.72 to.49 or at higher Reynols number (Re=212), the sselt number changes from 5.46 to It can be seen that the sselt number enhancement by nanoarticles concentration is negligible at high nanoarticles iameters.but Fotuian an Nasr Esfahany [25] showe that in turbulent regime, increasing the nanoarticles concentration i not show much of an effect on heat transfer enhancement in the range of concentrations stuie in that wor. Figure 5. The iluence of CuO nanoarticles volume concentration on the sselt number over a range of Reynols numbers with nm iameter nanoarticles 28 Iranian Journal of Chemical Engineering, Vol. 9, No. 1

7 Zeinali Heris, Talaii, Noie As an examle, by increasing nanoarticle size from 10 to 50nm in 0.02 concentration at Re=1744, the average sselt numbers ecrease from 5.2 to Also, at Reynols number 2050 in 0.02 susensions, increasing nanoarticle size from 10 to 50nm leas to a ecrease in from 5.68 to This figure inicates that the better enhancement is seen at higher Reynols numbers. The results illustrate that by increasing nanoarticle concentration from 0.01 to 0.04 at Re = 500, the average sselt number increases from 2.88 to.6; while at Re= 2000, the sselt number changes from 5. to 6.2. But it was shown that in turbulent regime, the ratio of convective heat transfer coefficient of nanoflui to that of ure water ecrease with Reynols number[25]. In orer to comare the heat transfer enhancement using ifferent in of soli nano-aitive, Fig. 6 inicates the sselt number versus Reynols of nanofluis at various volume fraction for 10nm nanoarticles. As shown in Fig. 6, at =10nm an Re=2000, by increasing nanoarticles concentration from 0.01 to 0.04, the average sselt number of water/cu, water/cuo an water/al 2 O increases from 5.79 to 6.51,5.29 to 6.2 an 4.8 to 5.95, resectively. So water/cu nanoflui with 0.04 volume concentration of 10nm Cu nanoarticles has a maximum heat transfer in comarison with the 2 other tyes of nanoflui mentione reviously. It has long been nown that the layere molecules are in an intermeiate hysical state between a bul liqui an a soli [26], the soli-lie nanolayer of liqui molecules Figure 6. Comarison of sselt number versus Reynols number for three ifferent nanofluis at 0.02,0.04 volume fraction of 10nm nanoarticles. woul be execte to lea to a higher thermal conuctivity than that of the bul liqui [27]. Because heat transfer between the articles an the flui tae lace at the articles an flui interface [16], equation (10) consiers the interface between nanoarticles an liqui (orere nanolayer at soli/liqui interface) as a arameter for calculating nanoflui thermal conuctivity uner the static conition. By taing into account the increase in thermal conuctivity of nanoflui, other factors such as isersion an chaotic movement of nanoarticles, Brownian motion an article migration must be consiere in the interretation of heat transfer erformance of nanofluis. Moghaassi et al. [19] stuie a moel for the reiction of the effective thermal conuctivity of nanofluis base on imensionless grous. They foun that the moele effective thermal conuctivity increases as article size is reuce. This henomenon is ue to the relative effects of nanoarticle motion mechanisms of ilute susensions such as Brownian motion, thermohoresis an osmohoresis, incluing Iranian Journal of Chemical Engineering, Vol.9, No. 1 29

8 CuO/ Water Nanoflui Heat Transfer Through Triangular Ducts size eenence, on the thermal conuctivity. Also, it may be ue to the effect of effective surface increasing with article size ecreasing.this is achieve using the isersion moel to analyze heat transfer enhancement of nanofluis. Fig. 7 shows the average sselt number as a function of half aex angle of isosceles triangular uct of this stuy. As shown in Fig. 7, by increasing the aex angle from 10 to 60, for.01 volume concentration an 10nm CuO articles iameter, sselt number an Reynols number increase from 1.64 to 5.46 an 22 to 212, resectively. Consequently for laminar flow, nanofluis through equilateral triangular cross-section ucts have a maximum sselt number in comarison with other tyes of isosceles triangles. flui change the structure of the flow fiel an lea to heat transfer enhancement. This is achieve using the isersion moel to analyze heat transfer enhancement of nanofluis. The results obtaine by numerical solution show that ecreasing the nanoarticles size increases the sselt number at a secific concentration an increasing the nanoarticles concentration increases the sselt number at constant article size. Secifically, the increase in thermal conuctivity is relatively ineenent of article interaction for low concentrations, while it is strongly eenent on the article interaction for high concentrations. Results also show that equilateral triangular ucts cause higher heat transfer coefficient than other tyes of isosceles triangular uct a (half aex angle) Figure 7. Heat transfer comarison between isosceles triangular ucts with various aex angles 6. Conclusions In this aer, Laminar flow force convection of CuO/water nanoflui in a triangular uct is stuie numerically. Results inicate that aing nanoarticles to the base flui increases the heat transfer coefficient of the flui. Disersion an ranom movement of nanoarticles insie the Nomenclature C Secific heat of flui [J/g K] Pbf C Secific heat of nanoflui [J/g K] P C Secific heat of nanoarticles [J/g K] P Nanoarticles iameter [m] bf Thermal conuctivity of flui [W/m K] Thermal conuctivity of nanoflui [W/m K] Thermal conuctivity of nanoarticle [W/m K] Disersion thermal conuctivity [W/mK] eff Effective thermal conuctivity [W/mK] Re Reynols number of nanoflui T Nanoflui local temerature [K] T i Inlet temerature of nanoflui [K] 0 Iranian Journal of Chemical Engineering, Vol. 9, No. 1

9 Zeinali Heris, Talaii, Noie T w u u m U θ Triangle wall temerature [K] Local axial velocity[m/s] Average axial velocity [m/s] Dimensionless velocity [m/s] Dimensionless temerature ρ Density of nanoflui [ g / m ] ρ Density of flui [ g / m ] bf ρ Density of nanoarticles [ g / m ] ν Volume fraction of nanoarticles References [1] Rebay, M. an Paet, J., "Parametric stuy of unsteay force convection with ressure graient", Int. J. Eng. Sci., 4: (2005). [2] Ahmet, Z. S., "Irreversibilities in various uct geometries with constant wall heat flux an laminar flow", Energy 2(6), 465 (1998). [] Tauscher, R. an Mayinger, F., "Heat transfer enhancement in a late heat exchanger with rib-roughene surfaces", Lehrstuhl afur Thermoynami Technische universitat muchen Garching Germany, [4] Nassan, T. H., Zeinali Heris, S. an Noie, S. H. "A comarison of exerimental heat transfer characteristics for Al2O/water an CuO/ water nanofluis in square cross-section uct", International Communications in Heat an Mass Transfer, 7, (2010). [5] Duangthongsu, W., an Wongwises, S., "Effect of thermohysical roerties moels on the reicting of the convective heat transfer coefficient for low concentration nanoflui", International Communications in Heat an Mass Transfer, , 5 (2008). [6] Fotuian, S.M. an Nasr Esfahany, M., "Exerimental stuy of turbulent convective heat transfer an ressure ro of ilute CuO/water nanoflui insie a circular tube", International Communications in Heat an Mass Transfer, 7, (2010). [7] Namburu, P. K., Das, D. K., Tanguturi, K. M. an Vajjha, R. S., "merical stuy of turbulent flow an heat transfer characteristics of nanofluis consi-ering variable roerties", Int. J. Thermal Sciences, accete January (2008). [8] Chung, S. J., Leonar, J. P., Nettleshi, I., Lee, J.K., Soong, Y., Martello, D.V. an Chyu, M.K., "Characterization of ZnO nanoarticle susension in water: Effectiveness of ultrasonic isersion", Power Technology, 75 80, 194 (2009). [9] Choi, S.U.S., "Enhancing thermal conuctivity of flui with nanoarticles", Develoments an Alication of non-newtonian flows, D.A. Siginer an H.P. Wanges., FED, V.21/MD, 66, 99 (1995). [10] Lee, S. an Choi, S.U.S., "Alication of metallic nanoarticle susensions in avance cooling systems", in: 1996 International Mechanical Engineering Congress an Exosition, Atlanta, USA, (1996). [11] Xuan, Y. an Rotzel, W., "Concetion for heat transfer correlation of nanoflui", Int J. Heat & Mass Transfer, 4, , (2000). [12] Bang, C. an Chang, S. H., "Boiling heat transfer erformance an henomena of Al 2 O water nano-fluis Iranian Journal of Chemical Engineering, Vol.9, No. 1 1

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