Performance analysis of non-circular microchannels flooded with CuO-water nanofluid

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1 Performance analysis of non-circular microchannels flooded with CuO-water nanofluid Raesh GAUTAM 1, Avdhesh K. SHARMA 2, Kail D. GUPTA 3 *Corresonding author: Tel.: ++11 (0) ; Fax: ++11 (0) ; avdhesh_sharma35@yahoo.co.in 1: PDM, Bahadurgarh, Haryana, INDIA 2 & 3: Deenbandhu Chhotu Ram University of Science & Technology, Murthal, Soneat, Haryana, INDIA Abstract In this study the erformances of various non-circular microchannel heat sinks (normalized with circular shae) have been comaratively analyzed for CuO-water nanofluid and baseline ure water flow. Nusselt number and Poiseuille number for each microchannel and thermo-hysical roerties of CuO-water nanofluid (viz., thermal conductivity, viscosity, secific heat and density) have been designed either emirically or from literature. Results for traezoidal shae gives highest normalized ressure dros among all cases. Thermal erformances for constant heat flux and constant wall temerature boundary conditions have been assessed in terms of normalized outlet wall temerature and normalized heat exchange rate. Results show that when thermal erformance of any microchannel heat sink (MHS) imroves, the hydraulic erformance deteriorates. Traezoidal microchannel gives best thermal erformance in terms of normalized heat exchange rate secially with CuO-water nanofluids flow. Keywords: CuO-water nanofluids, microchannels, ective thermal conductivity, hydraulic erformance 1. Introduction Faster cooling is crucial for develoment of smaller and comact microscale devices (i.e., microchannels heat sinks). It is well known that solid metals have orders-of-magnitude larger thermal conductivities than liquids. Thus any addition of metallic articles either of microscale or nanoscale may alter the thermo-hysical roerties (viz., thermal conductivity, viscosity, secific heat and density) of resulting fluid. The addition of microscale article is not a ractical reosition, as it shows oor susensions characteristics (unstable), while nonoscale articles shows wonderful susension characteristics leading to higher heat transfer. Furthermore, the recent advancement in nanotechnology has made it ossible to roduce nanometer-sizes articles using inertgas condensation, mechanical grinding rocess, chemical vaor deosition, chemical reciitation, micro emulsions, thermal sray, and sray yrolysis. Eastman et al (1996), have revealed that these nanosize articles (size of less than 100 nm and are oxides of high thermal conductive metals such as CuO, Al 2 O 3 etc.) can have stable susension in industrial heat transfer fluids (i.e. water, ethylene glycol, engine oil) that results in a new class of coolants. These advanced fluids enable to solve the roblems such as sedimentation, clogging, settling of solidarticles, scaling and erosions. The increased interest in microchannels is due to advance manufacturing technologies (etching, vaour deosition, diffusion bonding, extruded aluminum multichannel tubes, ), which made it ossible to construct microchannels in the range of 1 m - 1 mm. These microchannels are most ective for high-flux heat transfer technologies to rovide extremely high heat transfer rates. The alication of nanofluids in microchannels can augment the heat transfer rates further (due to both the high thermal conductivity and convective heat transfer coicient) but at the exense of high ressure dros; it is due to higher values of viscosities of nanofluids. Considerable works have been reorted in ast on roduction and roerties of nanofluids (Keblinski et al 2008, Lee et al 1999, Koo and Kleninstreuer 2004, Jang and Choi 2007, Vaha and Das 2009, Sharma and - 1 -

2 Singh 2008). Researchers have imroved the formulation for ective thermal conductivity of nanofluids by accounting either the influence of Brownian motion (Lee et al 1999, Koo and Kleninstreuer 2004, Vaha and Das 2009) or the ect of article aggregation and interfacial nanolayer (Murshed et al 2008). Koo and Kleinstruer (2004) roosed that ective thermal conductivity for concentration range of 1 % < < 4 % is comosed of the combination of static and Brownian motion art. Later, Vaha and Das (2009) imroved the model by broad range of 1 % < < 6-10 % for three nanofluids. While the ective thermal conductivity has received much attention in ast, studies on ective viscosity, which influences the fluidity, is relatively less and diverged. However, Masuda et al (2008) and Naguyen et al (2007) have measured the dynamic viscosity of several water based nanofluids for temeratures ranging from room temerature to aroximately 70C. Nguyen et al reorted the most comlete exerimental studies on dynamic viscosities using three cases of waterbased nanofluids: Al 2 O 3 -water with 36 nm and 47 nm articles, and Cuo-water with 29 nm articles. They varied fluid temerature from ambient to 70C. Koo and Kleinstreuer (2005) investigated laminar nanofluid flow in micro heat-sinks using the ective nanofluid thermal conductivity model they had established. For the ective viscosity due to micro-mixing in susensions, they roosed the imact of volume fraction of CuOnanoarticles in laminar flow of water and ethylene glycol on the microchannel ressure gradient, temerature rofile and Nusselt number (Nu). They recommended the use of high Prandtl number (Pr) carrier fluids, high asect ratio channels, high thermal conductivity nanoarticles and treatment of channel surface to avoid nanoarticles accumulation. Numerous works on single hase flow through microchannels have been reorted in ast (Warrier et al. 2002, Morini 2004, Liu and Garimella 2005), the work reorted on nanofluid flow through microchannels is relatively limited. Liu and Garimella (2005) resented interesting comarative study based on five aroximate analytical models to redict convective heat transfer for rectangular microchannel heat sinks. An otimization rocedure is develoed based on minimization of the thermal resistance. Hasan et al. (2009) have erformed numerical simulation on different circular/non-circular microchannel heat exchanger geometries to study the ect of size and shae of channels on the thermal and hydraulic erformance. Kakac and Pramuanaroenki (2009) in his review reorted convective heat transfer enhancement with nanofluid. Li and Kleinstruer (2008) analytically calculate the ect of nanoarticles flow in traezoidal microchannel geometry on the ressure dro and Nusselt number. They observed enhancement in thermal erformance of nanoarticle mixture flow with small increase in uming ower. Wen and Ding (2004) resented exerimental study on convective heat transfer of Al 2 O 3 -deionized water nanofluid flowing through a coer tube. From the literature survey it can be revealed that orts were carried out towards enhancement of thermal conductivity (by using nanofluids) and convective heat transfer coicient for individual microchannels either having triangular, square or rectangular shae. A very few work is focused on microchannels flooded with water based nanofluids. Another hand, the thermal advantage earned due to nanofluid oerated microchannel gives higher skin friction and hence demands more uming ower (or killing this thermal gain). As surface/volume ratio is very large, surface dominant factors become more imortant. Thus, a comarative study to investigate the geometry ect on circular/non-circular microchannels heat sinks on a common latform is needed. In the resent work, therefore, the thermal and hydraulic erformance of various non-circular microchannel heat sinks has been studied for the comarative analysis

3 W h W l H W H H H=W l H W W l (a) Traezoidal (b) (c) (d) (e) Fig. 1 Non-circular shaes 2. Formulation For resent study the thermal and hydraulic erformance of various non-circular microchannel heat sinks designed for various shaes viz., traezoidal and hexagonal, triangular, rectangular and square (refer fig. 1) has been evaluated. For known values of cross-sectional area (A c ), microchannel channel length and shae of each microchannel; the erimeter and hydraulic diameter of each shae can be obtained easily as 2.1 Hydraulic diameter and shae factor For a non-circular microchannel shaes (viz., traezoidal and hexagonal, triangular, rectangular and square), the hydraulic diameter D h can be defined in terms of cross-sectional area, A c, and erimeter,, as 4Ac D, (1) h The erimeter of various microchannels can be written as f shae, A c (2) Here subscrit designate to circular, triangular, rectangular, square, traezoidal and hexagonal shaes resectively. 2.2 Hydraulic Performance The hydraulic erformance of microchannel in each case can be resented in terms of ressure dro. For given (Re), the ressure dro through the microchannel can be written following Judy et al (2002) as Where 2 P K ent K (3) dev Dh V b f L Vb 2 Re D and K is the Dh h ressure dro arameters and subscrits ent and dev corresonds to entrance and develoing flow, resectively. In the resent work, the ect of develoing flow has been neglected. f is the friction factor for th microchannel, which can be calculated in terms of Poiseuille number ( f Po Re Dh ). ReDh can be defined Vb Dh in terms of ective transort roerties. 2.3 Thermal Performance Circular/non-circular microchannel heat sinks were exosed to constant heat flux and constant wall temerature conditions for evaluating their thermal erformances Constant heat flux Thermal erformance of non-circular microchannel heat sinks with constant heat flux condition has been redicted in terms of outlet wall temerature of the microchannel. Thus, heat transort can be written as Q Vb AcC ( Tbo Tbi ) (4) Here Tb is the bulk temerature and their subscrits i and o denote the inlet and outlet conditions. The wall temerature at the outlet of each microchannel can be calculated holding energy balance in radial direction in terms of outlet bulk temerature and wall temerature, and convective heat transfer coicient as q Two " Tb (5) o h Convective heat transfer coicient for each microchannel is written as h k Nu (6) Dh, - 3 -

4 2.3.2 Constant wall temerature The thermal erformance of circular/noncircular microchannel for constant wall temerature can be redicted in terms of heat transfer rate. The temerature rofile through each microchannel can be written as PL h Tb o Vb AcC (7) Tw e Tw Tb i Here, h is the convective heat transfer coicient, which can be defined by eqn. (6) The heat exchange rate in each microchannel can be simlified as h Vb AcC V A C Tw Tb 1 e (8) Q b c CuO-water Nanofluid flow Thermal erformance of microchannel heat sinks with nanofluids flow either in constant heat flux condition or constant wall temerature conditions cannot be redicted using the conventional exressions for Nu (as alicable for ure water flow). Therefore, for accounting the ect of concentration of CuO nanoarticles, one more term relating to volumetric nanoarticle concentration,, Prandtl number and article Peclet number is needed. Chein and Huang (2005) have already reorted such exression. Therefore, the same has been adated in this work in following form Nu Here Paclet number Pe d and Prandtl number Pr are defined as ubd Ped and Pr (10) Where thermal diffusivity can be defined as k (11) (. C) /3 0.4 NF NuPWF 4.88 Ped Re Pr (9) The roerties of CuO-water nanofluid i.e., viscosity, thermal conductivity, secific heat and density are calculated from different sources as described below. 2.4 Proerties of CuO-water nanofluid Effective secific heat and density The ective secific heat of nanofluids can be obtained from the relation of Xuan and i P L Roetzel (2000), which is based on thermal equilibrium of solid nanoarticles and liquid hase as C 1. C.. C (12) The density of nanofluids is be calculated using the liquid-article mixture theory as. 1. (13) Effective thermal conductivity Since, thermal conductivity of solid metals are much higher than fluids, the high nanoarticle concentration in base fluid (i.e. nanofluids) enables enhancement in thermal conductivity value. There is exerimental evidence that enhancement is much higher than the exectations. The thermal conductivity of nanofluids deends on concentration of nanoarticles, its thermal conductivity and their size, and thermo-hysical roerties of carrier-fluid. For this analysis, thermal conductivity of nanofluids is comuted using the models of Koo and Kleinstreur (2005), and Vaha and Das (2009). It describes the thermal conductivity in terms of article s conventional static and Brownian motion contribution. The static art is exressed as k k 2k 2k k static k (14) k k 2k k k While, Brownian contribution is written as k k T b brownian C f (15) d Where β and f were introduced to consider the hydraulic interaction among the Brownian motion induced fluid arcels and the article interaction due to the article interaction otential to encasulate the strong temerature deendence for CuO-water nanofluid in the range of 1 % φ 6 % and 298 T 363 K (Vaha and Das 2009) (16) f ( T ) 273 (17) Thus, the ective thermal conductivity of the nanofluid (k ) can be obtained by combining the conventional static art (based on Maxwells Model) and Brownian motion contribution as k k k (18) static brownian - 4 -

5 2.4.3 Effective Viscosity: For the resent analysis, a theoretical or emirical correlation for viscosity of CuOwater nanofluid is required that can reflect the ect of article size, volume fraction and temerature. In fact, a very few exerimental data on viscosity for CuO-water nanofluid, is available in the oen literature which show diverging trends. Therefore, in the resent work, a reliable exerimental data of Nguyen et al (2007) for CuO-water nanofluid with article diameter of 29 nm, has been used to correlate the ective viscosity in terms of fluid temerature and article volume concentration as (19) 2 2 T T T Since the values of constants in eqn. (19) are derived emirically, the validity of the above exression is limited within the temerature range of C and article volume concentration range of 0-9%, resectively. Predicted data are found within the maximum error range of 5 %. The viscosity of base fluid (i.e., distilled water) is obtained following the exression as reorted by Nguyen et al (2007) T T 10 e (20) 3. Results and discussion The hydraulic and thermal erformance of various non-circular microchannel heat sinks for constant heat flux and constant wall temerature conditions and flooded with CuOwater nanofluid, have been normalized with circular geometry for better corresondence of results. Performance is resented based on single channel. Thermal erformance of circular/non-circular microchannel heat sink for constant heat flux and constant wall temerature condition is resented in terms of normalized heat exchange rate and normalized outlet wall temerature through the microchannel, which is normalized by dividing by the result of circular microchannel. The flow through the microchannel is studied in laminar regime ( ) with fully develoed flow (i.e., thermally as well as hydraulically). The roerties of working fluid are assumed to be constant. The cross-section area and length of microchannel are fixed at 27 mm and 4.28e-8 m 2 resectively. 3.1 Hydraulic erformance The hydraulic erformance of different microchannel geometry (viz. triangular, rectangular, square, traezoidal and hexagonal) is obtained in normalized form of ressure dro with circular geometry. Normalized ressure dro Nanofluid: CuO-water Traezoidal Fig. 2 Effect of geometry on normalized ressure dro (CuO-water nanofluid). Normalized ressure dro Pure water flow Traezoidal Fig. 3 Effect of non-circular geometries on normalized ressure dro for ure water flow. The trends of normalized ressure dros through non-circular microchannel for ure water flow and CuO-water nanofluid flow are lotted against in figs From both cases, it is clear that normalized ressure dro in each microchannel geometry is not sensitive to. It should be noted here that the ressure dro through each microchannel is sensitive to Reynolds number. Furthermore, traezoidal geometry - 5 -

6 gives the highest value, while hexagonal shae gives lowest value of normalized ressure dro trends for both ure water as well as CuOwater nanofluid flow. It is also observed that nanofluid offers more resistance to flow through the microchannels of any shae. It is exected due to higher viscosity values of CuO-water nanofluid secially at higher article concentrations. 3.2 Thermal erformance In this section, the thermal characteristics of microchannel using ure water and nanofluid flow (CuO-water) were studied in laminar regime. The characteristics of microchannels (excet traezoidal) were studied for two different boundary conditions, namely constant wall temerature and constant heat flux. The inlet temerature of cold streams for all cases is ket constant at 20 C Constant Heat flux For constant heat flux condition, the thermal erformance of non-circular microchannel heat sinks were evaluated in terms of outlet wall temerature, which is normalized with circular geometry and referred as normalized outlet wall temerature in subsequent discussions. At this end, a constant heat flux of kW/m 2 is sulied externally to each microchannel heat sinks following Li et al, (2008). The cases for triangular, rectangular, square and hexagonal microchannel shaes have been simulated. The influence on normalized outlet wall temerature each microchannel against is comared for baseline ure water flow and CuO-water nanofluid flow as shown in fig Normalize wall outlet temerature Pure water flow water flow) on the normalized outlet wall temerature for constant heat flux condition. Normalized wall outlet temerature Nanofluid flow: CuO-water 0.95 Fig. 5 Effect of non-circular shaes (for CuOwater nanofluid flow) on normalized outlet wall temerature for constant heat flux conditions. The results of ure water flow (refer fig. 4) show that normalized outlet wall temerature of microchannel heat sinks increases with Re. For triangular microchannel, the highest value of normalized outlet wall temerature is observed, while for hexagonal and rectangular cases, there are lowest trends. Unlike ure water flow, the normalized outlet wall temerature for CuO-water nanofluid flow decreases with Re. microchannel gives lowest values of normalized outlet wall temerature, while hexagonal shae tends to highest (refer fig. 5). The lowest value of normalized outlet wall temerature in case of triangular shae is exected. For constant heat flux, the erimeter of triangular microchannel is highest while hydraulic diameter is lowest (cf. table 1) which gives high heat transfer coicient for nanofluids flow. The variation of wall temeratures among the microchannel is found to be relatively small in contrast to ure water flow. It may be exected due to significant role of nanoarticle concentration on convective heat transfer. Table 1. Perimeter and Hydraulic diameter of different Geometries 0.95 Fig. 4 Effect of non-circular shaes (for ure - 6 -

7 3.2.2 Constant wall temerature For this case, thermal erformance of the microchannel heat sinks is assessed in terms of the heat exchange rate, which is normalized by baseline circular shae. The wall temerature of microchannel has been fixed at 70C. Fig. 6 for ure water flow reveals that normalized heat exchange rate imroves marginally with for these shaes. Among all cases, the traezoidal microchannel is found to be marginally sensitive with and also shows highest normalized heat exchange rate, while hexagonal microchannel gives the lowest value with ure water flow. Normlized heat exchange rate Pure water flow Traezoidal Fig. 6 Effect of non-circular shaes (for ure water flow) on the normalized heat exchanged rate at constant wall temerature. Normalized heat exchange rate Geometry P (mm) D h (mm) Circle Rectangle Traezoidal Hexagon Nanofluid flow: CuO-water Traezoidal Fig. 7 Effect of non-circular shaes (for CuOwater nanofluid) on the normalized heat exchanged rate at constant wall temerature. Fig. 7 gives the influence of variation in on normalized heat exchange rate with CuO-water nanofluid at volumetric concentration of 4%. The case of traezoidal microchannel shows strong function of normalized heat exchange rate, while hexagonal geometry gives lowest value showing hardy any relation with Reynolds number. For traezoidal microchannel, the hydraulic diameter is minimum, thus heat transfer must be maximum for both ure water and CuO-water nanofluid. Furthermore, Nu for rectangular shae microchannel is higher than that of triangular shae leading to high heat transfer. Moreover, for CuO-water nanofluid, the Nu for both the cases (rectangular and triangular) become marginal, and heat transfer coicient for convection strongly dominated by hydraulic diameter (refer eqn. 1). Since the hydraulic diameter of the triangular case is less than that of rectangular, the heat exchange rate of triangular microchannel will be much higher than that of rectangular microchannel. 4. Conclusion Hydraulic and thermal erformances (normalized with circular geometry) of noncircular microchannel heat sinks have been comared for ure water flow and CuO-water nanofluid flow. Results of normalized ressure dro through traezoidal microchannel for ure water and CuO-water nanofluid flow for constant heat flux are found to be sensitive with. For constant heat flux, normalized wall temerature is found to be decreased with for cases investigated (excet traezoidal shae). These results are more sensitive for nanofluid flow. Moreover, triangular shae gives lowest trends allowing scoe for more heat transort. For ure water flow, the trends are ust oosite. For constant wall temerature, in ure water flow, traezoidal channel shows clear domination for normalized heat exchange rate, while hexagonal shae gives lowest trends for - 7 -

8 same range. When thermal erformance of microchannel heat sink imroves, the hydraulic erformance deteriorates and vice versa. Therefore, the thermal and hydraulic erformance of traezoidal microchannel heat sink must be otimized to develo advance Microscale cooling devices for current and future heat removal alications References Chein R., Huang G., Analysis of microchannel heat sink erformance using nanofluids. Alied Thermal Engg.; 25, Eastman J.A., Choi U.S., Lee S.,Thoson L.J., Lee A.S., Enhanced Thermal Conductivity through the develoment of nanofluids. Conference: 1996 Fall meeting of the Materials Research Society (MRS), Boston, MA (United States), 2-6 Dec Hasan M.I., Rageb A.A., Yaghoubi M., Homayoni H., Influence of channel geometry on the erformance of a counter flow microchannel heat exchanger. Int. J. of Thermal Sciences, 48, Jang S.P., Choi S.U.S., Effect of various arameters on nanofluids thermal conductivity. J. of Heat Transfer, 129, Judy J., Maynes D., Webb B.W., 2002 Characterization of frictional ressure dro for liquid flows through microchannels. Int. J. of Heat and Mass Transfer; 45, Kakac S., Pramuanaroenki A., Review of convective heat transfer enhancement with nanofluids, Int. J. of Heat and Mass Transfer, Keblinski P., Prasher R., Eaen J., Thermal conductance of nanofluids: is the controversy over? J. of Nanoarticles Research, 10, Koo J. and Kleninstreuer C., A new thermal conductive model for nanofluids. J. of Nanoarticles Research, 6, Koo, J. Kleinstreuer C., Laminar nanofluid flow in microsheet-shinks. Int. J. Nanoarticle Res., 48, Lee S., Choi S.U.S., Li S., Eastman J.A., Measuring thermal conductivity of fluids containing oxide nanoarticles. Journal of Heat Transfer, 121, Li J., Kleinstreuer C., Thermal erformance of nanofluids flow in microchannels. Int. Journal of Heat and Fluid Flow, 29, Liu D., Garimella S.V., Analysis and Otimization of the thermal erformance of microchannel heat sinks. Int. J. of Numerical Methods for Heat Fluid Flow, 15, Morini G.L., Single hase convective heat transfer in microchannels: a review of exerimental results, Int. J. of thermal sciences, 43, Murshed S.M.S, Leong K.C., Yang C., 2008, Investigation of thermal conductivity and viscosity of nanofluids. Int. J. of Thermal Science, 47, Nguyen C.T., Desgranges F., Roy G.,Gallanis N., Mare T., Boucher S., Mintsa H. A., Temerature and article- size deendent viscosity data for water- based nanofluids- Hysteresis henomenon. Int. J. of Heat and Fluid Flow, 28, Pak and Cho Sharma A.K., Singh A.K., Model develoment for ective thermal conductivity and dynamic viscosity of alumina-water nanofluids. Proceeding of the 1 st Euroean conf. on Microfluidics; Vaha R.S., Das D.K., Exerimental determination of thermal conductivity of three nanofluids and develoment of new correlation. Int. J. of Heat & Mass transfer, Warrier GR, Dhir VK, Mamoda LA, Heat transfer and ressure dro in narrow rectangular channels. Ex. Thermal and Fluid Science, 26, Wen D., Ding Y., Exerimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. Int. J. of Heat and Mass Transfer, Xuan Y, Roetzel W., Concetion for heat transfer correlation of nanofluids. Int. J. Heat Mass Transfer, 43,