Two-phase simulation of nanofluid in a heat exchanger in turbulent flow regime

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1 Euroean Online Journal o Natural and Social Sciences 2014; Vol.3, No.3 Secial Issue on Environmental, Agricultural, and Energy Science ISSN Two-hase simulation o nanoluid in a heat exchanger in turbulent low regime M.Nasiri-Lohesara*, M.Gorji-Bandy Deartment o Mechanical Engineering, Babol University o Technology Babol, Iran * m.nasiri.lohesara@gmail.com Abstract Turbulent orced convection o dierent nanoluids consisting o -Al 2 O 3 /water and CuO/water in a concentric double tube heat exchanger has been investigated numerically using twohase aroach. Nanoluids that are used as coolants lowing in the inner tube while hot ure water lows in outer tube. The study was conducted or Reynolds numbers ranging rom 20,000 to 50,000 and nanoarticles volume ractions o 2, 3, 4 and 6 ercent. The three-dimensional governing equations are discretized using the inite volume aroach. Although, two dierent nanoarticles have almost the same thermal conductivity but using CuO/water nanoluid showing better enhancement in heat transer that roves thermal conductivity is not the only reason o enhancing heat transer. Also, CuO/water showing bigger shear stress in comarison o -Al 2 O 3 /water nanoluid. As a result, nanoluids show higher overall heat transer coeicient in comarison o ure water. Keywords: Turbulent orced convection, Nanoluid, Two-hase aroach, Concentric double tube heat exchanger Introduction With rogresses o technology heat transer augmentation is one o the most challenges or develoing industrial with high technology. There are many techniques or augmenting heat transer that can be classiied in two grous: (Ι Passive techniques that do not need external orce and (ΙΙ Active techniques that need external ower. Passive techniques are included disturbing the boundary layers, imroving the thermohysical roerties or examle, increasing luid thermal conductivity. Alication o additives to liquids is one way o enhancing heat transer. Augmenting o luid thermal conductivity is the main urose in imrovement the heat transer characteristic o liquids. Whereas in solids thermal conductivity is much bigger than liquids. It is exected adding this solid articles to a liquid enhance thermal conductivity o the base luid. More than several decades, adding millimetre or micrometre size articles has been known, but, because o lot roblems or examle: sedimentation, clogging, abrasion and high ressure loss the use o these articles was not eicient (Maxwell, Recently rogress in material engineering and develoing new technologies cause the basis o roducing nano-sized articles. By disersing this nanoarticles to liquid a new class o liquid achieved that irst time. Masuda et al. (1993 introduced the liquid susension o nano-sized articles and then Choi (1995 or the irst time roosed the name o nanoluid. Nanoluids change the thermal and hydraulic eature o base luids and cause enormous heat transer enhancement. Nanoarticles with comaring o millimetre and micrometre articles have more surace contact that can enhance energy transort between luids and articles as well as because o low momentum o this articles revent the erosion and clogging hence nanoluids can be used or small geometries too. Many researchers investigated the thermohysical roerties o nanoluids (Lee, et al, 1999; Li & Peterson, But Research about the orced convection o nanoluids is imortant or the 95

2 Secial Issue on Environmental, Agricultural, and Energy Science ractical alication o nanoluids in heat transer devices. For this urose, dierent aers ocused on the nanoluids convection exerimentally and numerically. Pak and Cho (1998 or the irst time investigated exerimentally the convective heat transer inside a circular tube. They investigated the convective heat transer o -Al 2 O 3 (13 nm/water and TiO 2 (27 nm/water nanoluids in the turbulent low regime. Constant wall heat lux boundary condition was considered in the analysis. It was indicated that the heat transer enhancement obtained with -Al 2 O 3 articles is higher than that obtained with TiO 2 articles. They roosed a new correlation or Nusselt number. Li and Xuan (2002 resented exerimental study to investigate the heat transer coeicient and riction actor o Cu/water nanoluid in both laminar and turbulent low regimes. Constant wall heat lux boundary condition was exosed and observed Nusselt enhancements u to 60%. It was seen that the heat transer coeicient enhancement ratio (heat transer coeicient o nanoluid divided by the heat transer coeicient o base luid increases with increasing Reynolds number. Wen and Ding (2004 investigated exerimentally the convective heat transer o Al 2 O 3 with the base luid o water in laminar low under constant wall heat lux boundary condition. Particle volume raction varied between 0.6% and 1.6%. The result showed increase o 49% Nusselt number or 1.6% volume raction. Also or nanoluid the entrance region length was bigger than the base luid that this length increase with increasing nanoluid article volume raction. Particle migration henomenon that cause disersing non-uniorm thermal conductivity and viscosity and reducing the thermal boundary condition was the reason roosed by them or this anomalous enhancement in heat transer. Desite exerimental investigation, the numerical simulation is ast rogressing. It is seen that there are both single-hase and two-hase models are roosed or the analysis o nanoluids heat transer. Khanaer et al. (2003 were the irst to simulate nanoluid low. They analyzed the natural convection low inside a square enclosure or Cu/Water nanoluid. Their result showed that heat transer and velocity o nanoluid because o enhancement in thermal conductivity and Brownian motion o nanoarticles is higher than base luid. Maiga et al. (2004 numerically studied laminar and turbulent orce convection inside a circular tube under constant wall heat lux boundary condition. They used single-hase assumtion and took the eect o nanoarticles into account only through the substitution o the thermohysical roerties o the nanoluids into the governing equations. They simulated the mixture o Al 2 O 3 /water and Al 2 O 3 /ethylene glycol and showed the wall shear stress and heat transer enhance with increasing volume raction while the latter nanoluid showed better heat transer enhancement in identical Reynolds number and volume raction. Bianco et al. considered the laminar and turbulent low o Al 2 O 3 /Water nanoluid under constant and uniorm heat lux at the wall. They analyzed the roblem by using both single and twohase models. The results showed heat transer enhances with increasing articles volume concentration and Reynolds number and it showed two-hase models or the simulation o nanoluid are satisactory with comaring o exerimental data. In this study, two-hase model o Volume o Fluid (VOF has been used or considering low and heat transer characteristic o nanoluids. CuO/water and -Al 2 O 3 /water nanoluids are used in turbulent low regime in a horizontal concentric double tube heat exchanger. The analyze are conducted or dierent Reynolds numbers and volume ractions ranging rom 20,000 to 50,000 and 2, 3, 4 and 6 ercent resectively. For validation o the numerical solution, the results are comared with exerimental correlation roosed by (Pak and Cho, The aim o this study is to add more contribution to nanoluids convection. Oenly accessible at htt:// 96

3 M.Nasiri-Lohesara, M.Gorji-Bandy Mathematical modelling Geometric coniguration Fig. 1 shows the considered coniguration consisting o the double tube counter-low heat exchanger with a length o 0.65 m and with the inner and the outer diameters o 0.01 m and m resectively. Nanoluids that enter the inner tubes comosed o CuO/water and -Al 2 O 3 /water with article diameter o 20 nm. Table 1 shows the thermohysical roerties o base luid and nanoarticles. Nanoluids roerties Nanoluid thermohysical roerties lay imortant role in accuracy o the results. The eect o nanoarticles can be taken into account by using the thermohysical roerties o the nanoluid in the governing equations. In analyzing nanoluid as a two-hase low the interactions between nanoarticles and liquid are modelled too. The ollowing ormulas are used to comute the thermohysical roerties o the nanoluids under consideration. Pak and Cho (1998 comared the density values were measured exerimentally with hydrometers and those calculated rom (1 at various volume concentrations. The maximum deviation between (1 and exerimental results was 0.6% at volume concentration o 3.16%. Thereore, this equation is aroriate or using nanoluid density: e ( 1 b (1 Also seciic heat o nanoluid are achieved by the ollowing equation: (1 φ(ρc b φ(ρc c e (2 (1 φρb φρ Where subscrits o e, b and indicate the eective roerties, base luid (water in this case and articles resectively. Chon et al. (2005 roosed a correlation or thermal conductivity. This correlation excet the volume raction and articles diameter, considers the temerature and Brownian motion which is deined as: ke d b ( (3 k d k ( Pr Re k where Prandtl and Brownian Reynolds numbers exressed as: kbt Pr,Re (4 2 3 L where is the base luid mean ree ath (0.17 nm or water and is temerature-deendent viscosity o the base luid which is deined as: B T c A10 (5 the constants A, B, C or water are equal to2.414ex ( 5, 247 and 140 resectively. Oenly accessible at htt:// 97

4 Secial Issue on Environmental, Agricultural, and Energy Science Figure 1. Schematic o considering coniguration Table 1. Thermohysical roerties o materials under consideration. Material Density (Kg/ Thermal conductivity (W/m k Seciic heat (J/Kg K Water Al2O CuO One equation or dynamic viscosity o nanoluid is deined as: n (6 b Equation (6 was obtained by Maiga et al (2007 with curve itting based on exerimental data o Wang et al. (1999. And, this equation was successully used by Maiga et al (2007 or simulating o single-hase nanoluid consist o -Al 2 O 3 /water nanoluid. In the resent study (6 is used or simulating two-hase o -Al 2 O 3 /water nanoluid. Another equation or eective dynamic viscosity o nanoluid which consider the eects o density, diameter o articles and volume raction was roosed by Masoumi et al. (2009 as ollows: 2 VBd n b, 3 d (7 72c kbT where VB, is the Brownian velocity o nanoarticles. In (7 the d d 1 c d c c d c c, are obtained rom exerimental data and are exressed as: c , c c , c In the resent study, (7 is used or calculating o CuO/water nanoluid eective dynamic viscosity. Governing equations In VOF model the two dierent hases do not interenetrate. For each additional hase the volume raction o that hase is added in the comutational cell. I volume raction o nanoarticles hase is indicated as, then the ollowing three conditions are ossible: Oenly accessible at htt:// 98

5 M.Nasiri-Lohesara, M.Gorji-Bandy ϕ =0 (The cell just contains base luid ϕ =1 (The cell just contains nanoarticles 0<<1 (The cell contains the interace between the nanoarticles and base luid hase resectively. The tracking o the interace between the hases is accomlished by the solution o continuity equation or secondary hase (8 and then inding the volume raction o rimary hase conducts by the (9:.( V 0 (8 k 1 (9 The conservation o momentum and energy equations are given as (10 and (11 resectively: T V V P.( ( V V (10.( V( E P.( kt (11 Turbulence modelling In order to close the governing equations the standard k- two-equation eddy-viscosity model is used. This model roosed by Launder and Salding (1972 and it is based on the solution o equations or turbulent kinetic energy k and the turbulent dissiation rate. Their equations can be exressed as ollows: t, mix.( mixvmixk.( k Gk, mix mix (12 k t,mix.( mixv mix.( (c1 Gk,mix c2mix (13 k where 2 c k t, mix mix (14 T Gk, mix t, mix ( Vmix ( Vmix (15 With constant values o = 1.44, = 1.92, = 0.09 and =1.3, =1 Boundary conditions Above equations are solved or the ollowing boundary equations. At the inner tube inlet, uniorm temerature roile with T in 298 K are assumed. Pure water enters in the annulus with m uniorm and constant velocity and temerature V in, an and T in, an 360 K resectively. The s inner tube is without thickness and outer tube is thermally insulated. At tubes outlet ully develoed conditions and on the walls, the non-sli conditions are considered. Moreover, a constant turbulent intensity equal to 1% is imosed or both sides. Oenly accessible at htt:// 99

6 Secial Issue on Environmental, Agricultural, and Energy Science Comutational rocedure and validation In the numerical solution, inite volume method is utilized or solving the above equations. PRESTO and QUICK Scheme is used or ressure correction and volume raction resectively. For other equations second order uwind is adoted or numerical solution. The SIMPLE algorithm is used or ressure-velocity couling. Dierent non-uniorm grids or heat exchanger inner and outer tubes are tested to insure indeendency o solution Fig and cells or the inner and the outer tube is suicient or the resent study resectively. Finer mesh is used near the wall because o higher velocity and temerature gradient. Mean Nusselt number is calculated as ollows: haved Nu (16 ke Also overall heat transer coeicient based on the inner tube heat transer coeicient ( h in and the outer tube heat transer coeicient ( h out can be exressed as ollows : 1 U ( h in h out The outer heat transer coeicient ( h out is constant and equal to or boundary conditions as mentioned beore. In Fig. 3 validation takes lace with a correlation roosed by Dittus and Boelter(1930 or ure luid in turbulent ie low. The average and maximum error or the inner tube is 2% and 3.6% resectively. Also comarison with resect to overall heat transer coeicient is conducted by the correlation roosed by Pak and Cho (1998 or nanoluid heat transer Fig. 4. Results and discussion Results o numerical solution o convective heat transer o dierent nanoluids in concentric heat exchanger with two-hase model (VOF and dierent volume concentration (Maxwell, 1881; Masuda et al, 1993; Choi, 1995; Pak and Cho, 1998 at turbulent low regime are resented. The mean diameter o CuO and -Al 2 O 3 nanoarticles are assumed to be 20 nm. Fully develoed (hydrodynamically and thermally turbulent low is assumed or the outer and the inner tube or L ( 130 and L ( 65 resectively (Incroera & Bergman, Constant uniorm velocity inlet D h D h and turbulent intensity or ure water equal to m/s and 1% are assumed in the annulus or all runs. Thereore, heat transer coeicient o outer tube ( h out is constant and equal to Comarison with exerimental correlation roosed by Pak and Cho (1998 or nanoluid in term o U ave also has taken lace. Figure 4 deict overall heat transer enhancement by increasing volume ractions o nanoarticles or dierent Reynolds numbers. As shown in Figs. 4, overall heat transer enhances by augmenting o nanoarticle concentration and also Reynolds number. Eect o Reynolds number is more ronounced on heat transer enhancement when comared to nanoarticles volume concentration. For examle or CuO/water nanoluid or a ixed volume concentration o 2 %, or Re=20,000 to 50,000 overall heat transer enhanced rom to On the other hand, or Re=20,000 and volume concentration varying rom 0 to 6% the enhancement is to But with combination o these two arameters simultaneously overall heat transer as high Oenly accessible at htt:// 100

7 M.Nasiri-Lohesara, M.Gorji-Bandy as can be achieved in comarison o the value or Re=20,000 and 0. The maximum and average deviation or Re=50,000 in comarison o exerimental data are 3.8% and 3.1% or -Al 2 O 3 /water nanoluid and 4.5% and 3.5% or CuO/water nanoluid resectively. It is obvious that numerical rediction o -Al 2 O 3 /water nanoluid is closer to exerimental data. One o this reason is dynamic viscosity o -Al 2 O 3 /water nanoluid which is urely exerimental. Also Pak and Cho (1998 s exerimental study was carried out or -Al 2 O 3 /water and TiO 2 /water nanoluids. It should be mentioned that this exerimental correlation is valid or volume concentration ranges between 0 to 3% and other nanoarticles volume concentration is just showing the trends. Hence, using enhanced models or thermal conductivity and viscosity which considering more heat transer mechanisms o nanoluids can romote the numerical solution inner tube, cells inner tube, cells inner tube, cells inner tube, cells outer tube, cells outer tube, cells outer tube, cells Re Figure 2. Dierent grids or indeendency o solution inner tube, Dittus-Boelter inner tube, resent study outer tube, Dittus-boelter outer tube, resent study Re Figure 3. Grid validation or inner tube and annulus by correlation roosed by Dittus and Boelter (1930 Oenly accessible at htt:// 101

8 Secial Issue on Environmental, Agricultural, and Energy Science a c CuO(ak and cho Al2O3(Pak and Cho CuO(Pak and Cho Al2O3(Pak and Cho b d CuO(Pak and Cho Al2O3(Pak and Cho 6800 CuO(Pak and Cho Al2O3(Pak andcho Figure 4. Overall heat transer coeicient enhancement or (a Re=20,000 (b Re=30,000 (c Re=40,000 and (d Re=50,000 As a result o Fig. 4, heat transer enhancement using CuO/water is more than -Al 2 O 3 /water nanoluid, however the thermal conductivity o -Al 2 O 3 nanoarticle is almost bigger than CuO one. Consequently, thermal conductivity o nanoarticles is not the dominant arameter that seciies the convection heat transer enhancement o the nanoluid. Average wall shear stress o dierent nanoluids by augmenting volume concentration o nanoarticles with dierent Reynolds numbers are shown in Fig. 5. As a result, wall shear stress increase with increasing o Reynolds number and volume concentration o nanoarticles. Although CuO/water nanoluids redicts more enhancement in heat convection than -Al 2 O 3 /water, but wall shear stress o ormer is much bigger than the latter as deict in Fig. 5. For examle or volume raction o 2% and Reynolds number o 30,000 the average wall shear stress o -Al 2 O 3 /water and CuO/water nanoluids are 36.7 and resectively. As shown in Fig. 5(a to Fig. 5(d the eect o Reynolds number on increasing the wall shear stress is more than volume raction o nanoarticles. For Re=20,000 and 0 to 6 % or examle or CuO/water nanoluid the wall shear stress increases rom 15.6 to On the other hand, or a ixed value o 2 % and Re=20,000 to Re=50,000 the wall shear stress varying rom 57.9 to that the eect o increasing Reynolds number on average wall shear stress is more ronounced. Conclusion In the resent aer, turbulent orced convection o -Al 2 O 3 /water and CuO/water nanoluids inside a double tube concentric heat exchanger was numerically investigated using two-hase aroach (VOF. Oenly accessible at htt:// 102

9 M.Nasiri-Lohesara, M.Gorji-Bandy Two-hase aroach underestimates the overall heat transer coeicient but a comarison with exerimental correlation roosed by Pak and Cho (1998 showed that the numerical results are at good agreement o this correlation. Results showed or a ixed Reynolds number o 20,000, or CuO/water and just 6 % overall heat transer enhancement about 17% achieved in comarison o ure water ( 0. Also using simultaneously Reynolds number and, or Re=50,000 and 6 % overall heat transer enhancement about 37% was achieved in comarison o Re=20,000 and 0. Then nanoluid can be good substitution or ure water in heat transer devices or otimizing the energy. a c Shear stress shear stress shear stress b Figure 5. Average wall shear stress rediction or (a Re=20,000 (b Re=30,000 (c Re=40,000 and (d Re=50,000 shear stress Reerences Bianco, V.,&F. Chiacchio, O. Manca, S. Nardini (2009. Numerical investigation o nanoluids orced convection in circular tubes. Alied Thermal Engineering, 29, Choi, S. U. S. (1995. Enhancing Thermal Conductivity o Fluids with Nanoarticles. Develoments and Alications o Non-Newtonian Flows. The American Society o Mechanical Engineers, New York, Chon, C.H., K.D. Kihm, S.P. Lee, & S.U.S. Choi (2005. Emirical correlation inding the role o temerature and article size or nanoluid (Al2O3 thermal conductivity enhancement. Journal o Physics, 87, 1 3. Dittus, F.W. & L.M.K. Boelter (1930. Heat Transer in Automobile Radiators o the Tubular Tye. Uniu. Cali. Publ. in Eng., d Oenly accessible at htt:// 103

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