ORIGINAL_ARTICLE
Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice Boltzmann Method
This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation. A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr = 0.71) and Rayleigh numbers ranging from 103 to 106 at the macroscopic scale (Kn = 10-4). In every case, an appropriate value of the characteristic velocity is chosen using a simple model based on the kinetic theory. By considering the obtained dimensionless velocity and temperature values, the distributions of entropy generation due to heat transfer and fluid friction are determined. It is found that for an enclosure with high value of Rayleigh number (i.e., Ra=105), the total entropy generation due to fluid friction and total Nu number increases with decreasing the aspect ratio.
http://tpnms.usb.ac.ir/article_991_ed33fb88310481a59b7edd67542621f9.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
1
18
10.7508/tpnms.2013.01.001
Entropy generation
Lattice Boltzmann method
Natural Convection
Γ-Shaped enclosure
E.
Fattahi
true
1
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
AUTHOR
M.
Farhadi
true
2
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
LEAD_AUTHOR
K.
Sedighi
true
3
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
Faculty of Mechanical Engineering, Babol University of Technology Babol, Iran
AUTHOR
[1] Y.H Qian., D. d’Humieres, P. Lallemand, LatticeBGK models for Navier–Stokes equation, Europhys.Lett. 17 (6) (1992) 479–484.
1
[2] S. Chen, G.D. Doolen, Lattice Boltzmann methodfor fluid flows, Annu. Rev. Fluid Mech. 30 (1998)329–364.
2
[3] D. Yu, R. Mei, L.S. Luo, W. Shyy, Viscous flowcomputations with the method of lattice Boltzmannequation, Progr. Aerospace Sci. 39 (2003) 329–367.
3
[4] S. Succi, The Lattice Boltzmann Equation for FluidDynamics and Beyond, Clarendon Press, Oxford,2001.
4
[5] X. Shan, Simulation of Rayleigh–Benard convectionusing a lattice Boltzmann method, Phys. Rev. E 55(1997) 2780–2788.
5
[6] X. He, S. Chen, G.D. Doolen, A novel thermalmodel for the lattice Boltzmann method inincompressible limit, J. Comput. Phys. 146 (1998)282–300.
6
[7] Y. Zhou, R. Zhang, I. Staroselsky, H. Chen,Numerical simulation of laminar and turbulentbuoyancy-driven flows using a lattice Boltzmannbased algorithm, Int. J. Heat Mass Transfer 47(2004) 4869–4879.
7
[8] H.N. Dixit, V. Babu, Simulations of high Rayleighnumber natural convection in a square cavity usingthe lattice Boltzmann method, Int. J. Heat MassTransfer 49 (2006) 727–739.
8
[9] P.H. Kao, R.-J. Yang, Simulating oscillatory flowsin Rayleigh– Benard convection using the latticeBoltzmann method, Int. J. Heat Mass Transfer 50(2007) 3315–3328.
9
[10] Y. Peng, C. Shu, Y.T.Chew, Simplified thermallattice Boltzmann model for incompressible thermalflows, Phys. Rev. E 68 (2003) 026701.
10
[11] G. Barrios, R. Rechtman, J. Rojas, Tovar R., Thelattice Boltzmann equation for natural convection ina two-dimensional cavity with a partially heatedwall, J. Fluid Mech. 522 (2005) 91–100.
11
[12] A. Bejan, Heat Transfer, Wiley, New York, 1993.
12
[13] I. Catton, Natural Convection in Enclosures, Proc.the 6th Int. Heat Transfer Conference, 6 (1978) 13-31.
13
[14] S. Ostrach, Natural Convection in Enclosures, J.Heat Transfer 110 (1988) 1175-1190.
14
[15] S. Kakaç, Y. Yener, Convective Heat Transfer, CRCPress, 2nd ed. (1995) 340-350.
15
[16] D. Poilikakos, Natural convection in a confined fluid- filled space driven by a single vertical wall withwarm and cold regions. J. Heat Transfer 107 (1985)867-876.
16
[17] D. Angirasa, M. J. B. M. Pourquié, F. T. M.Nieuwstadt, Numerical study of transient and steadylaminar buoyancy - driven flows and heat transfer ina square open cavity. Numerical Heat Transfer PartA 22 (1992) 223-239.
17
[18] O. Ayhan, A. Ünal, T. Ayhan, Numerical solutionsfor buoyancy - driven flow in a 2-D square enclosureheated from one side and cooled from above,Advanced in Computational Heat Transfer, TR,(1997) 337–394.
18
[19] K. Küblbeck, G. P. Merker, J. Straub, Advancenumerical computation of two – dimensional time -dependent free convection in cavities. Int. J. HeatMass Transfer 23 (1980) 203-217.
19
[20] N. C. Markatos, K. A. Pericleous, Laminer andturbulent natural convection in an enclosed cavity,Int. J. Heat Mass Transfer 27 (1984) 755-772.
20
[21] L. Lage, A. Bejan, The Ra-Pr domain of laminarnatural convection in an enclosure heated from theside. Numerical Heat Transfer Part A 19 (1991) 21-41.
21
[22] A. Bejan, Entropy generation through heat and fluidflow. New York: Wiley; 1982.
22
[23] A. Bejan, Entropy generation minimization. NewYork: CRC Press; 1996
23
[24] A. Bejan, Advanced engineering thermodynamics,2nd ed. New York: Wiley
24
[25] G. de Vahl Davis, Natural convection of air in asquare cavity: a bench mark numerical solution, Int.J. Numer. Methods Fluids. 3 (1983) 249–264.
25
[26] D. Rejane, C. Oliveski, H. Mario Macagnan, B.Jacqueline Copetti, Entropy generation and naturalconvection in rectangular cavities, J. AppliedThermal Engineering
26
[27] M.Y. Ha, M.J. Jung, A numerical study on threedimensionalconjugate heat transfer of naturalconvection and conduction in a differentially heatedcubic enclosure with a heat-generating cubicconducting body, Int. J. Heat and Mass Tran. 43(2000) 4229–4248.
27
[28] A. Mezrhab, H. Bouali, C. Abid, Modelling ofcombined radiative and convective heat transfer inan enclosure with a heat-generating conductingbody, International Journal of ComputationalMethods 2 (3) (2005) 431–450.
28
[29] I. Dagtekin, H.F. Oztop, A. Bahloul., Entropygeneration for natural convection in _-shapedenclosures, Int. Commun. Heat Mass Transf. 34(2007) 502–510.
29
[30] P.H. Kao, Y.H. Chen, R.J. Yang, Simulations of themacroscopic and mesoscopic natural convectionflows within rectangular cavities, J. Heat Mass Tran.51 (2008) 3776–3793.
30
[31] Z. Guo, B. Shi, C. Zheng, A coupled lattice BGKmodel for the Boussinesq equations, Int. J. ofNumerical Methods in Fluids, 39(4) (2002) 325-342.
31
[32] Z.L. Guo, Ch. Zheng, B.C. Shi, An extrapolationmethod for boundary conditions in lattice Boltzmannmethod, Phys. Fluids, 14 (6) (2002) 2007-2010.
32
[33] R. Mei, D. Yu, W. Shyy, L. Sh. Luo, Forceevaluation in the lattice Boltzmann methodinvolving curved geometry, Phys. Rev. E,.65 (2002)1-14.
33
[34] Z.L. Guo, B.C. Shi, Ch. Zheng, A coupled latticeBGK model for the Boussinesq equations, Int. J.Numer. Methods Fluids, 39 (4) (2002), 325-342.
34
[35] E. K. Glapke, C.B. Watkins, J. N. Cannon, Constantheat flux solutions for natural convection betweenconcentric and eccentric horizontal cylinders,Numer. Heat Transfer, 10 (1986), 279-295.
35
[36] X. He, Q. Zou, L.S. Luo, M. Dembo, Analyticsolutions of simple flows and analysis of nonslipboundary condition for the lattice Boltzmann BGKmodel, J. Stat. Phys. 87 (1997), pp. 115–136.
36
[37] H.N. Dixit, Simulation of flow and temperaturefields in enclosures using the lattice Boltzmannmethod. MS Thesis, 2005, Indian Institute ofTechnology Madras, India.
37
[38] Z.L. Guo, Ch. Zheng, B.C. Shi, An extrapolationmethod for boundary conditions in lattice Boltzmannmethod, Phys. Fluids, 14 (6) (2002), 2007-2010.
38
[39] C. Cercignani, Mathematical Methods in KineticTheory, Plenum, New York, 1969.
39
[40] G. Wannier, Statistical Physics, Diver, New York,1966.
40
[41] C. Shu, X.D. Niu, Y.T. Chew, A lattice Boltzmannkinetic model for microflow and heat transfer, J.Stat. Phys. 121 (1–2) (2005) 239–255
41
ORIGINAL_ARTICLE
Modeling of Activated Carbon Preparation from Spanish Anthracite Based on ANFIS Structure
Carbon nanostructures are famous structures which are used in several industries such as separation, treatment, energy storage (i.e. methane and hydrogen storage), etc. A successful modeling of activated carbon preparation is very important in saving time and money. There are some attempts to achieve the appropriate theoretical modeling of activated carbon preparation but most of them were almost unsuccessful due to the complexity between the input and output variables. In this paper the empirical modeling of activated carbon preparation from Spanish anthracite based on adaptive neuro-fuzzy inference system (ANFIS) is investigated. ANFIS model is established to delineate the relationship between the BET surface area of the prepared activated carbon with initial and operational conditions; agent type, agent ratio, activation temperature, activation time and nitrogen flow. The results show that the selected model have a good accuracy with a coefficient of determination values (R2) of 0.9885 and average relative error (ARE) of 0.00268.
http://tpnms.usb.ac.ir/article_992_1e5844e35c4560564226b256369531cd.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
19
25
10.7508/tpnms.2013.01.002
Activated Carbon
ANFIS
Carbon nanostructure
neural network
S.
Rashidi
true
1
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
AUTHOR
M.A.
Fanaei
true
2
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
LEAD_AUTHOR
A.
Ahmadpour
true
3
AUTHOR
[1] J.M. Dias, M.C.M. Alvim-Ferraz, M.F. Almeida,J. Rivera-Utrilla, M. Sánchez-Polo, Wastematerials for activated carbon preparation and itsuse in aqueous-phase treatment: A review, Journalof Environmental Management, 85 (2007) 833-846,.
1
[2] A. Alonso, V. Ruiz, C. Blanco, R. Santamaría, M.Granda, R. Menéndez, S.G.E. de Jager, Activatedcarbon produced from Sasol-Lurgi gasifier pitchand its application as electrodes insupercapacitors, Carbon, 44 (2006) 441-446.
2
[3] I.M.J. Vilella, S.R. de Miguel, O.A. Scelza,Hydrogenation of citral on Pt and PtSn supportedon activated carbon felts (ACF), Latin Americanapplied research, 35 (2005) 51-57.
3
[4] J. Jagiełło, T.J. Bandosz, J.A. Schwarz,Characterization of microporous carbons usingadsorption at near ambient temperatures,Langmuir, 12 (1996) 2837-2842.
4
[5] C.M. Lastoskie, K.E. Gubbins, Characterization ofporous materials using molecular theory andsimulation, in: Advances in ChemicalEngineering, Academic Press, 2001 pp. 203-250,.
5
[6] A. Moussatov, C. Ayrault, B. Castagnède, Porousmaterial characterization - ultrasonic method forestimation of tortuosity and characteristic lengthusing a barometric chamber, Ultrasonics, 39(2001) 195-202.
6
[7] D. Lozano-Castelló, D. Cazorla-Amorós, A.Linares-Solano, D.F. Quinn, Influence of poresize distribution on methane storage at relativelylow pressure: preparation of activated carbon withoptimum pore size, Carbon, 40 (2002) 989-1002.
7
[8] A. Ahmadpour, D.D. Do, The preparation ofactivated carbon from macadamia nutshell bychemical activation, Carbon, 35 (1997) 1723-1732.
8
[9] J. Simitzis, J. Sfyrakis, Activated carbon fromlignocellulosic biomass-phenolic resin, Journal ofApplied Polymer Science, 54 (1994) 2091-2099.
9
[10] F. Rezaei, P. Webley, Optimum structuredadsorbents for gas separation processes, ChemicalEngineering Science, 64 (2009) 5182-5191.
10
[11] D. Lozano-Castelló, J. Alcañiz-Monge, M.A. de laCasa-Lillo, D. Cazorla-Amorós, A. Linares-Solano, Advances in the study of methane storagein porous carbonaceous materials, Fuel, 81 (2002)1777-1803.
11
[12] Rashidi, H., and Ahmadpour, A., Investigation theeffect of activating agent on the preparation ofactivated carbon used for methane storage, 12thChemical Engineering National IranianConference, Tabriz, Iran, 2008.
12
[13] M.A. Lillo-Ródenas, D. Lozano-Castelló, D.Cazorla-Amorós, A. Linares-Solano, Preparationof activated carbons from Spanish anthracite: II.Activation by NaOH, Carbon, 39 (2001) 751-759.
13
[14] M.A. Lillo-Ródenas, D. Cazorla-Amorós, A.Linares-Solano, Understanding chemical reactionsbetween carbons and NaOH and KOH: An insightinto the chemical activation mechanism, Carbon,41 (2003) 267-275.
14
[15] D. Lozano-Castelló, M.A. Lillo-Ródenas, D.Cazorla-Amorós, A. Linares-Solano, Preparationof activated carbons from Spanish anthracite: I.Activation by KOH, Carbon, 39 (2001) 741-749.
15
[16] A. Perrin, A. Celzard, A. Albiniak, M. Jasienko-Halat, J.F. Marêché, G. Furdin, NaOH activationof anthracites: effect of hydroxide content on poretextures and methane storage ability, Microporousand Mesoporous Materials, 81(2005) 31-40.
16
[17] M. Kubota, A. Hata, H. Matsuda, Preparation ofactivated carbon from phenolic resin by KOHchemical activation under microwave heating,Carbon, 47 (2009) 2805-2811.
17
[18] S. Jang, Adaptive network-based fuzzy inferencesystem, IEEE, 23 (1993) 665-685.
18
[19] T.M. Nazmy, H. El-Messiry, B. Al-Bokhity,Adaptive Neuro-Fuzzy Inference System forclassification of ECG signals, The 7thInternational Conference on Informatics andSystems (INFOS), 2010 pp. 1-6,.
19
[20] M. Namvar-Asl, M. Soltanieh, A. Rashidi, A.Irandoukht, Modeling and preparation of activatedcarbon for methane storage I. Modeling ofactivated carbon characteristics with neuralnetworks and response surface method, EnergyConversion and Management, 49 (2008) 2471-2477.
20
[21] M. Namvar-Asl, M. Soltanieh, A. Rashidi,Modeling and preparation of activated carbon formethane storage II. Neural network modeling andexperimental studies of the activated carbonpreparation, Energy Conversion and Management,49 (2008) 2478-2482.
21
[22] A. Shahsavand, A. Ahmadpour, Application ofoptimal RBF neural networks for optimization andcharacterization of porous materials, Computersand Chemical Engineering, 29 (2005) 2134-2143.
22
[23] H. Hashemipour, E.l. Jamshidi, S. Baroutian, A.Abazari, Experimental Study and Artificial NeuralNetworks Simulation of Activated CarbonSynthesis in Fluidized Bed Reactor, InternationalJ. of Chemical Reactor Engineering, 7( 2009)1945.
23
ORIGINAL_ARTICLE
Numerical Study of Mixed Convection of Nanofluid in a Concentric Annulus with Rotating Inner Cylinder
In this work, the steady and laminar mixed convection of nanofluid in horizontal concentric annulus withrotating inner cylinder is investigated numerically. The inner and outer cylinders are kept at constanttemperature Ti and To respectively, where Ti>To. The annular space is filled with Alumina-water nanofluid.The governing equations with the corresponded boundary conditions in the polar coordinate are discretizedusing the ﬁnite volume method where pressure-velocity coupling is done by the SIMPLER algorithm.Numerical results have been obtained for Rayleigh number ranging from 102 to 105, Reynolds number from 1 to 300 and nanoparticles volume fraction from 0.01 to 0.06. The effects of the Reynolds and Rayleigh numbers, average diameter of nanoparticles and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the annuli are investigated. According to the results, the average Nusselt number decreases with increasing the Reynolds number. However, the average Nusselt number increases by increasing the Rayleigh number. Moreover, the maximum average Nusselt number occurs for an optimal nanoparticle volume fraction except situations that heat conduction predominates over the heat convection. In these conditions the average Nusselt number is close to unity.
http://tpnms.usb.ac.ir/article_993_6b72c034dcb4abb14c68e9aaea3b1951.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
26
36
10.7508/tpnms.2013.01.003
Concentric Annulus
Finite Volume Method
Mixed convection
Nanofluid
Rotating Inner Cylinder
G. A.
Sheikhzadeh
true
1
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
AUTHOR
H.
Teimouri
true
2
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
LEAD_AUTHOR
M.
Mahmoodi
true
3
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
AUTHOR
[1] H.Q. Yang, K.T. Yang and J.R. Lloyd, Rotationaleffects on natural convection in a horizontalcylinder, AIChE Journal 34 (1988) 1627-1633.
1
[2] H.Q. Yang, Diffusion-controlled mass transfer froma rotating cylinder, Numerical Heat Transfer A 23(1993) 303-318.
2
[3] M. Prudhomme and L. Robillard, Natural convectionin an annular fluid layer rotating at weak angularvelocity. In: Proc. 4th Int. Symp. on TransportPhenomena, Heat and Mass TransferSydney,N.S.W., 1991, p. 38.
3
[4] F. Ladeinde, Studies on thermal convection in selfgravitatingand rotating horizontal cylinders in avertical external gravity field. 1988).
4
[5] T.S. Lee, Numerical computation of fluid convectionwith air enclosed between the annuli of eccentricheated horizontal rotating cylinders, Computers andFluids 21 (1992) 355-368.
5
[6] E. Abu-Nada, Z. Masoud and A. Hijazi, Naturalconvection heat transfer enhancement in horizontalconcentric annuli using nanofluids, InternationalCommunications in Heat and Mass Transfer 35(2008) 657-665.
6
[7] H.C. Brinkman, The viscosity of concentratedsuspensions and solutions, Journal of ChemicalPhysics 20 (1952).
7
[8] R.L. Hamilton and O.K. Crosser, Thermalconductivity of heterogeneous two-componentsystem, I&EC Fundamentals 1 (1962) 187-191.
8
[9] E. Abu-Nada, Effects of variable viscosity andthermal conductivity of Al2O3-water nanofluid onheat transfer enhancement in natural convection,International Journal of Heat and Fluid Flow 30(2009) 679-690.
9
[10] M. Izadi, A. Behzadmehr and D. Jalali-Vahida,Numerical study of developing laminar forcedconvection of a nanofluid in an annulus,International Journal of Thermal Sciences 48 (2009)2119-2129.
10
[11] M. Izadi, A. Behzadmehr and D. Jalali-Vahida,Numerical study of developing laminar forcedconvection of a nanofluid in an annulus,International Journal of Thermal Sciences 48 (2009)2119-2129.
11
[12] N. Masoumi, N. Sohrabi and A. Behzadmehr, A newmodel for calculating the effective viscosity ofnanofluids, Journal of Physics D: Applied Physics42 (2009) 055501.
12
[13] C.H. Chon, K.D. Kihm, S.P. Lee and S.U.S. Choi,Empirical correlation finding the role of temperatureand particle size for nanofluid (Al2O3) thermalconductivity enhancement, Applied Physics Letters87 (2005) 1-3.
13
[14] E.E. Feldman, R.W. Hornbeck and J.F. Osterle, Anumerical solution of developing temperature forlaminar developing flow in eccentric annular ducts,International Journal of Heat and Mass Transfer 25(1982) 243-253.
14
[15] N.H. Abu-Sitta, K. Khanafer, K. Vafai and A.M. Al-Amiri, Combined forced- and natural-convectionheat transfer in horizontally counterrotatingeccentric and concentric cylinders, Numerical HeatTransfer; Part A: Applications 51 (2007) 1167-1186.
15
[16] M.I. Char and Y.H. Hsu, Computation of buoyancydrivenflow in an eccentric centrifugal annulus witha non-orthogonal collocated finite volume algorithm,International Journal for Numerical Methods inFluids 26 (1998) 323-343.
16
[17] J. Buongiorno, Convective transport in nanofluids,Journal of Heat Transfer 128 (2006) 240-250.
17
[18] S. Maiga, S.J. Palm, C.T. Nguyen, G. Roy and N.Galanis, Heat transfer enhancement by usingnanofluids in forced convection flows, InternationalJournal of Heat and Fluid Flow 26 (2005) 530-546.
18
[19] C.T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T.Mare, S. Boucher and H. Angue Mintsa,Temperature and particle-size dependent viscositydata for water-based nanofluids - Hysteresisphenomenon, International Journal of Heat and FluidFlow 28 (2007) 1492-1506.
19
[20] K. Khanafer and K. Vafai, A critical synthesis ofthermophysical characteristics of nanofluids,International Journal of Heat and Mass Transfer 54(2011) 4410-4428.
20
[21] A. Bejan, Convection Heat Transfer, John Wiley &Sons, 2003.
21
[22] T.H. Kuehn and R.J. Goldstein, An experimentaland theoretical study of natural convection in theannulus between horizontal concentric cylinders,Journal of Fluid Mechanics 74 (1976) 695-719.
22
[23] J.S. Yoo, Mixed convection of air between twohorizontal concentric cylinders with a cooledrotating outer cylinder, International Journal of Heatand Mass Transfer 41 (1998) 293-302.
23
ORIGINAL_ARTICLE
Numerical Analysis of Inlet Gas-Mixture Flow Rate Effects on Carbon Nanotube Growth Rate
The growth rate and uniformity of Carbon Nano Tubes (CNTs) based on Chemical Vapor Deposition (CVD) technique is investigated by using a numerical model. In this reactor, inlet gas mixture, including xylene as carbon source and mixture of argon and hydrogen as carrier gas enters into a horizontal CVD reactor at atmospheric pressure. Based on the gas phase and surface reactions, released carbon atoms are grown as CNTs on the iron catalysts at the reactor hot walls. The effect of inlet gas-mixture flow rate, on CNTs growth rate and its uniformity is discussed. In addition the velocity and temperature profile and also species concentrations throughout the reactor are presented.
http://tpnms.usb.ac.ir/article_994_52a54eb2f90863cb821e6c9896191495.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
37
44
10.7508/tpnms.2013.01.004
Chemical Vapor Deposition
Numerical Analysis
Carbon Nanotube
B.
Zahed
true
1
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
AUTHOR
T.
Fanaei S.
true
2
Electrical and Electronic Department, University of Sistan and Baluchestan, Zahedan, I.R.Iran
Electrical and Electronic Department, University of Sistan and Baluchestan, Zahedan, I.R.Iran
Electrical and Electronic Department, University of Sistan and Baluchestan, Zahedan, I.R.Iran
LEAD_AUTHOR
H.
Ateshi
true
3
Chemical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Chemical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Chemical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
AUTHOR
[1] S. Iijima, Helical microtubules of graphitic carbon,Nature 354 (1991) 56.
1
[2] Y.X. Liang, T.H. Wang, A double-walled carbonnanotube field-effect transistor using the inner shellas its gate, Physica E 23 (2004) 232.
2
[3] C. Klinke, A. Afzali, Interaction of solid organicacids with carbon nanotube field effect transistors,Chemical Physics Letters 430 (2006) 75.
3
[4] T.W. Odom, J.L. Huang, P. Kim, C.M. Lieber,Atomic structure and electronic properties ofsingle-walled carbon nanotubes, Nature 391(1998) 62–64.
4
[5] M. Grujicic, G. Cao, B. Gersten, Reactor lengthscalemodeling of chemical vapor deposition ofcarbon nanotubes, J. Mater. Sci. 38(8) (2003)1819–30.
5
[6] H. Endo, K. Kuwana, K. Saito, D. Qian, R. AndrewsE.A. Grulke, CFD prediction of carbon nanotubeproduction rate in a CVD reactor, Chem.Phys. Lett.387 (2004) 307–311.
6
[7] K. Kuwana, K. Saito, Modeling CVD synthesisof carbon nanotubes: nanoparticle formation fromferrocene, Carbon 43(10) (2005) 2088–95.
7
[8] A.A. Puretzky, D.B. Geohegan, S. Jesse, I.N.Ivanov, G. Eres, In situ measurements andmodeling of carbon nanotube array growthkinetics during chemical vapor deposition, Appl.Phys. A 81(2) (2005) 223–40.
8
[9] C.L. Andrew, W.K.S. Chui, Modeling of the carbonnanotube chemical vapor deposition process usingmethane and acetylene precursor gases,Nanotechnology, 19(16) (2008) 165607–14.
9
[10] L. Pan, Y. Nakayama, H. Ma, Modelling the growthof carbon nanotubes produced by chemical vapordeposition, Carbon 49 (2011) 854-861.
10
[11] C.L. Yaws, Chemical Properties Handbook,McGraw-Hill,Newyork 1999.
11
ORIGINAL_ARTICLE
Preparation of γ-Al2O3 and Prioritization of Affecting Factors on the Crystallite Size Using Taguchi Method
In this work, boehmite sol was prepared by a previously applied and validated method; hydrolysis of aluminum chloride hexa-hydrate. In order to obtain precise results, the effect of pH after adding precipitating agent, aging time, peptizing temperature and ultrasonic vibration time on the crystallite size of final precipitate were investigated in a narrow range. The preparation conditions applied in the production step of nanocrystalline boehmite affected on the desired alumina phase. Experiments were set based on the statistical design of experiments (Taguchi method). Furthermore the influence of calcination on crystallization and phase transformation of the precipitate was investigated using X-ray diffractometry (XRD) and simultaneous thermal analysis (STA) techniques. To evaluate the results, the obtained data were statistically analyzed. Considering the statisti cal analysis of experiments, the pH after adding precipitating agent is the major parameter affecting crystallite size. In contrast, aging time has the smallest effect on the crystallite size. In addition, Transmission electron microscopy (TEM) of the samples revealed that the particle size of the powders was well distributed in the nano-size range. Taguchi prediction on the crystallite size was 2.096±0.139 nm (with confidence interval of 95%) which confirmed by a verification experiment (2.064 nm).
http://tpnms.usb.ac.ir/article_995_e336e2525dd3abae3cac0ffda37cb23a.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
45
52
10.7508/tpnms.2013.01.005
Boehmite
γ-alumina
Precipitation
aging time
ultrasonic vibration
Experimental design
M.
Shayesteh
true
1
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
LEAD_AUTHOR
M.
Shafiee Afarani
true
2
Department of Materials Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Department of Materials Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Department of Materials Engineering, University of Sistan and Bluchestan, Zahedan, Iran
AUTHOR
A.
Samimi
true
3
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
AUTHOR
M.
Khorram
true
4
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
Deparetment of Chemical Engineering, University of Sistan and Bluchestan, Zahedan, Iran
AUTHOR
[1] R.R. Bhave, Inorganic Membranes:Characterizationand application, New York, van Nostrand Reinhold(1991) 1- 24.
1
[2] K.A. DeFriend, M.R. Wiesner, A.R. Barron,Alumina and aluminate ultrafiltration membranesderived from alumina nanoparticles, J. MembrSci. vol. 224 (2003) 11-28.
2
[3] Y. Cho, K. Han, K. Lee, separation of CO2 bymodified _-Al2O3 membranes at high temperature, J.Membr Sci. 104 (1995) 219.
3
[4] X. Changrong, W. Feng, M. Zhaojing, L.Fanqing , P. Dingkun, M. Guangyao, Boehmite solproperties and preparation of two-layer aluminamembrane by a sol-gel process, J. Membr Sci. 116(1996) 9-16.
4
[5] M.L. Panchula, J.Y. Ying , Mechanical Synthesisof Nanocrystalline _-Al2O3 Seeds for EnhancedTransformation Kinetics, Nanostruct Mater. 9(1997) 161.
5
[6] K. Kamata, T. Mochizuki, S. Matsumoto, A.Yamada, K. Miyokawa, Preparation ofsubmicrometer Al2O3 powder by gas-phaseoxidation of tris(acetylacetonato) alumina (III), J.Am Ceram Soc. 68 (8) (1985) C-193–C-194.
6
[7] J.G. Li, X.D. Sun. Synthesis and sintering behaviorof a nanocrystalline _-Al2O3 powder, Acta Mater. 48(2000) 3103-3112.
7
[8] J.J. Kingsley, K.C. Patil, A novel combustionprocess for the synthesis of fine particle _- aluminaand related oxide materials, Mater Lett. 6 (1988)427–432.
8
[9] S.A. Hassanzadeh-Tabrizi, E. Taheri-Nassaj,H. Sarpoolaky, Synthesis of an alumina–YAGnanopowder via Sol-Gel method, J Alloy Compd.456 (2008) 282-285.
9
[10] R. Tipakontitikul, A. Niyompan, K. Srisurat, N.Kanchanarat, T. Tunkasiri, Effect of pH onPhase Formation and Morpholo of theNanocrystalline Boehmite Powder Prepared by aPrecipitation Method, Journal of Micros copySociety of Thailand 22 (2008) 20-22.
10
[11] W. Tsunenori, M. Yoshihisa, M. Takeo, K.Hiroyoshi, H. Saburo, W. Kenji, I. Masashi,Pore structure of c-Ga2O3–Al2O3 particlesprepared by spray pyrolysis, Micropor MesoporMat. 145 (2011) 131-140.
11
[12] R. Brace, E. Matijevic, Aluminium hydrousoxide sols: I, J. Inorg Nucl Chem. 35 (1973)3691–3705.
12
[13] S.A. Hassanzadeh-Tabrizi, E. Taheri-Nassaj,Economical synthesis of Al2O3 nanopowderusing a precipitation method”, Mater Lett.63 (2009) 2274-2276.
13
[14] H. Kwang-Taek, L. Hee-Soo, L. Shi-Hee, C.Koo-Chun, P. Shin-Seo, L. Jae-Hoon, Synthesis ofaluminum hydrates by a precipitation method andtheir use in coatings for ceramic membranes, J EurCeram Soc. 21 (2001) 375-380.
14
[15] V. Francetic, P. Bukovec, Peptization and Al-Keggin Species in Alumina Sol, Acta ChimSlov. 55 (2008) 904- 908.
15
[16] H. Beygi, M. Zare, S.A. Sajjadi, Fabrication ofFeNi–Al2O3, nanocomposites and optimizationof mechanical properties using Taguchi method,Powder Technology 232 (2012) 49–57.
16
[17] S. H. Sadeghi, V. Moosavi, A. Karami, N.Behnia, Soil erosion assessment and prioritization ofaffecting factors at plot scale using the Taguchimethod, Journal of Hydrology, 448–449 (2012) 174–180.
17
[18] X. Bokhimi, J.A. Toledo-Antonio, M.L.Guzman-Castillo, B. Mar-Mar, F. Hernandez-Beltran, J. Navarette, Dependence of BoehmiteThermal Evolution on Its Atom Bond Lengths andCrystallite Size, J. Solid State Chem. 161 (2001)319-326.
18
[19] K. Okada, T. Nagashima, Y. Kameshima, A.Yasumori, T. Tsukada, Relationship betweenFormation Conditions, Properties, and CrystalliteSize of Boehmite, J Colloid Interf Sci. 253 (2002)308–314.
19
[20] J.M. Rousseaux, P. Weisbecker, H. Muhr, E.Plasari, Aging of Precipitated Amorphous AluminaGel, Ind Eng Chem Res. 41 (2002) 6059-6069.
20
[21] Y. Raghvendra, M. Priya, P. Avinash, Growthmechanism and optical property of ZnOnanoparticles synthesized by sonochemical method,Ultrason Sonochem 15(2008) 863–868
21
ORIGINAL_ARTICLE
Study on Thermal and Hydrodynamic Indexes of a Nanofluid Flow in a Micro Heat Sink
The paper numerically presents laminar forced convection of a nanofluid flowing in a duct at microscale. Results were compared with both analytical and experimental data and observed good concordance with previous studies available in the literature. Influences of Brinkman and Reynolds number on thermal and hydrodynamic indexes have been investigated. For a given nanofluid, no change in efficiency (heat dissipation to pumping power) was observed with an increasing in Reynolds number. It was shown that the pressure was decrease with an increase in Brinkman number. Dependency of Nu increment changes with substrate material.
http://tpnms.usb.ac.ir/article_996_bc15214e1358cf5ff5b5df0d67140891.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
53
63
10.7508/tpnms.2013.01.006
Microchannel heat sink
Nanofluid
Viscous dissipation effect
M.
Izadi
true
1
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
LEAD_AUTHOR
M. M.
Shahmardan
true
2
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran
AUTHOR
A. M.
Rashidi
true
3
Nanotechnology Research Center, Research Institute of Petroleum Industry (R.I.P.I)
Nanotechnology Research Center, Research Institute of Petroleum Industry (R.I.P.I)
Nanotechnology Research Center, Research Institute of Petroleum Industry (R.I.P.I)
AUTHOR
[1] D.B. Tuckerman, R.F.W. Pease, Highperformance heat sinking for VLSI, IEEEElectron. Devices Lett. EDL-2 (5) (1981) 126–129.
1
[2] B.C. Pak, Y.I. Cho, Hydrodynamic and heattransfer study of dispersed fluids with submicronmetallic oxide particles, Exp. Heat Transfer 11(1998) 151–170.
2
[3] S. Lee, S.U.S. Choi, Applications of metallicnanoparticle suspensions in advanced coolingsystem, in: Y Kwon, D.C. Davis, H.H. Chung(Eds.), Recent Advances in Solid/Structures andApplication of Metallic Materials, PVP-vol.342/MD-vol. 72, ASME, New York, 1996, pp.227–234.
3
[4] Y. Xuan, Q. Li, Investigation on convective heattransfer and flow features of nanofluids, ASME J.Heat Transfer 125 (2003) 151–155.
4
[5] D. Wen, Y. Ding, Experimental investigation intoconvective heat transfer of nanofluids at theentrance region under laminar flow conditions,Int. J. Heat Mass Transfer 47 (2004) 5181–5188.
5
[6] J. Buongiorno, Convective transport in nanofluids,ASME J. Heat Transfer 128 (2006) 240–250.
6
[7] Mirmasoumi, S., Behzadmehr, A., Numericalstudy of laminar mixed convection of a nanofluidin a horizontal tube using two-phase mixturemodel, Applied Applied Thermal Engineering 282008; 717–727.
7
[8] Izadi, M., Behzadmehr A., Jalali-Vahid, D.,Numerical study of developing laminar forcedconvection of a nanofluid in an annulus,International Journal of Thermal Sciences 482009; 2119–2129.
8
[9] R. Chein, J. Chuang,Experimental microchannelheat sink performance studies using nanofluids,International Journal of Thermal Sciences 46(2007) 57–66.
9
[10] R. Chein, J. Chuang, Experimental microchannelheat sink performance studies using nanofluids,International Journal of Thermal Sciences 46(2007) 57–66.
10
[11] J. Y. Jung, H. S. Oh, H.Y. Kwak, Forcedconvective heat transfer of nanofluids inmicrochannels, International Journal of Heat andMass Transfer 52 (2009) 466–472.
11
[12] C.J. Ho, L.C. We, Z.W. Li, An experimentalinvestigation of forced convective coolingperformance of a microchannel heat sink withAl2O3/water nanofluid, Applied ThermalEngineering 30 (2010) 96-103.
12
[13] M. D. Byrne, R. A. Hart, A. K. da Silva,Experimental thermal–hydraulic evaluation ofCuO nanofluids in microchannels at variousconcentrations with and without suspensionenhancers, International Journal of Heat and MassTransfer 55 (2012) 2684-2692.
13
[14] S. A. Fazeli, S. M. Hosseini Hashemi, H.Zirakzadeh, M. Ashjaee, Experimental andnumerical investigation of heat transfer in aminiature heat sink utilizing silica nanofluid,Superlattices and Microstructures 51 (2012) 247–264.
14
[15] M. Kalteh, A. Abbassi , M Saffar-Avval, A.Frijns, A. Darhuber, J. Harting, Experimental andnumerical investigation of nanofluid forcedconvection inside a wide microchannel heat sink,Applied Thermal Engineering 36 (2012) 260-268.
15
[16] Kosar, Effect of substrate thickness and materialon heat transfer in microchannel heat sinks,International Journal of Thermal Sciences 49(2010) 635-642.
16
[17] M. Kalteh, A. Abbassi, M Saffar-Avval, JensHarting, Eulerian–Eulerian two-phase numericalsimulation of nanofluid laminar forced convectionin a microchannel, International Journal of Heatand Fluid Flow 32 (2011) 107-116.
17
[18] M. Hojjat , S.Gh. Etemad , R. Bagheri , J.Thibault, Rheological characteristics of non-Newtonian nanofluids: Experimentalinvestigation, International Communications inHeat and Mass Transfer 38 (2011) 144–148.
18
[19] A.G. Fedorov, R. Viskanta, Three dimensionalconjugate heat transfer in the microchannel heatsink for electronic packaging. InternationalJournal of Heat
19
[20] and Mass Transfer 43 (2000) 399e415.
20
[21] G. Tunc, Y. Bayazitoglu, Heat transfer inmicrotubes with viscous dissipation, Int. J. HeatMass Transfer 44 (2001) 2395–2403.
21
[22] H.-E. Jeong, J.-T. Jeong, Extended Graetzproblem including streamwise conduction andviscous dissipation in microchannel, InternationalJournal of Heat and Mass Transfer 49 (2006)2151–2157.
22
[23] P.M. Coelho, F.T. Pinho, Fully-developed heattransfer in annuli with viscous dissipation, Int. J.Heat Mass Transfer 49 (2006) 3349–3359.
23
[24] S. Del Giudice, C. Nonino, S. Savino, Effects ofviscous dissipation and temperature dependentviscosity in thermally and simultaneouslydeveloping laminar flows in microchannels, Int. J.Heat Fluid Flow 28 (2007) 15–27.
24
[25] O. Aydin, M. Avci, Analysis of laminar heattransfer in micro-Poiseuille flow, InternationalJournal of Thermal Sciences 46 (2007) 30–37.
25
[26] K. Hooman, Entropy generation for microscaleforced convection: Effects of different thermalboundary conditions, velocity slip, temperaturejump, viscous dissipation, and duct geometry,International Communications in Heat and MassTransfer 34 (2007) 945–957.
26
[27] M. Corcione, Empirical correlating equations forpredicting the effective thermal conductivity anddynamic viscosity of nanofluids, EnergyConversion and Management 52 (2011) 789-793.
27
[28] T. X. Phuoc, M. Massoudi, R. Chen, Viscosityand thermal conductivity of nanofluids containingmulti-walled carbon nanotubes stabilized bychitosan, International Journal of ThermalSciences 50 (2011) 12-18.
28
[29] Ebadian, M.A., Dong, Z.F., 1998. Forcedconvection, internal flow in ducts. In: Rohsenow,W.M., Hartnett, J.P., Cho, Y.I. (Eds.), Handbookof Heat Transfer.McGraw-Hill, New York, pp.5.1–5.137.
29
[30] M. Kalteh, A. Abbassi , M Saffar-Avval, A.Frijns, A. Darhuber, J. Harting, Experimental andnumerical investigation of nanofluid forced convection inside a wide microchannel heat sink,Applied Thermal Engineering 36 (2012) 260-268.
30
[31] M.B. Abbott and D.R. Basco, Computational fluiddynamics: An introduction for engineers,Longman Scientific & Technical, 1989.
31
ORIGINAL_ARTICLE
Investigation of the Effect of Nanoparticles Mean Diameter on Turbulent Mixed Convection of a Nanofluid in a Horizontal Curved tube Using a Two Phase Approach
Turbulent mixed convection of a nanofluid (water/Al2O3, Φ=.02) has been studied numerically. Two-phase mixture model has been used to investigate the effects of nanoparticles mean diameter on the flow parameters. Nanoparticles distribution at the tube cross section shows that the particles are uniformly dispersed. The non-uniformity of the particles distribution occurs in the case of large nanoparticles and/or high value of the Grashof numbers. The study of particle size effect showed that the effective Nusselt number and turbulent intensity increases with the decreased of particle size.
http://tpnms.usb.ac.ir/article_997_d472c32290701d713a0453f8ff4f880f.pdf
2013-01-01T11:23:20
2017-10-24T11:23:20
64
74
10.7508/tpnms.2013.01.007
Nanofluid
Turbulent Mixed Convection
Two phase
Curved tube
nanoparticles mean diameter
Pressure drop
O.
Ghaffari
true
1
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
AUTHOR
A.
Behzadmehr
behzadmehr@hamoon.usb.ac.ir
true
2
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
Mechanical Engineering Department, University of Sistan and Baluchestan, Zahedan, I.R. Iran
LEAD_AUTHOR
[1] S.U.S. Choi, Enhancing thermal conductivity offluid with nanoparticles, developments andapplications of non-Newtonian flow, ASME FED231/MD 66(1995) 99–105.
1
[2] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E.Lockwood, and E. A.Grulke, Anomalous thermalconductivity enhancement in nanotubesuspensionsAppl. Phys. Lett79,(2001) 2252 -2255
2
[3] H. Zhu, C. Zhang, S. Liu, Y. Tang, and Y. Yin,Effects of nanoparticle clustering and alignmenton thermal conductivities of Fe3O4 aqueousnanofluids.Appl. Phys.Lett. 89, (2006) 023123
3
[4] S. M. S. Murshed, K. C. Leong, and C. Yang,Investigations of thermal conductivity andviscosity of nanofluids Int. J. Therm.Sci. 47,(2008) 560-568
4
[5] C.H. Chon, K.D. Kihm, S.P. Lee, S.U.S. Choi,Empirical correlation finding the role oftemperature and particle size for nanofluid (Al2O3)thermal conductivity enhancement, Appl. Phys.Lett. 87 (2005) 1–3.
5
[6] J. Koo and C. Kleinstreuer,A new thermalconductivity model for nanofluids,Journal ofNanoparticle Research 6 (2004),577–588
6
[7] N. Sohrabi, N. Masoumi, A. Behzadmehr, andS.M.H. Sarvari, A Simple Analytical Model forCalculating the Effective Thermal Conductivity ofNanofluids, Heat Transfer Asian Research, 39(2010) 141-150.
7
[8] K. Khanafer, K. Vafai, M. Lightstone, Buoyancydrivenheat transfer enhancement in a twodimensional enclosure utilizing nanofluids. Int. J.Heat Mass Transfer 46 (2003) 3639–3653.
8
[9] M. Akbari, A. Behzadmehr, Developing laminarmixed convection of a nanofluid in a horizontaltube with uniform heat flux. Int. J. Heat FluidFlow 29 (2007) 566–586.
9
[10] M.Izadi, A.Behzadmehr, D.Jalali-Vahida,Numerical study of developing laminar forcedconvection of a nanofluid in an annulus,Int.J.Thermal sciences 48 (2009)2119-2129.
10
[11] Y.M. Xuan , W. Roetzel, Conceptions for heattransfer correlation of nanofluids. Int. J. HeatMass Transfer 43 (2000) 3701–3707.
11
[12] A. Mokmeli, M. Saffar-Avval, Prediction ofnanofluid convective heat transfer using thedispersion model. Int. J. Therm. Sci. 49 (2010)471–478.
12
[13] S. Kumar, S. Kumar Prasad, J. Banerjee, Analysisof flow and thermal field in nanofluid using asingle phase thermal dispersion model. AppliedMathematical Modelling 34 (2010) 573–592.
13
[14] Y.M. Xuan, Q. Li, Investigation on convectiveheat transfer and flow features of nanofluids. J.Heat Transfer 125 (2003) 151–155.
14
[15] J.Bungirno, convective transport in nanofluid , J.of Heat Transfer 128 (2006),240-250
15
[16] A. Behzadmehr, M. Saffar-Avval, N. Galanis,Prediction of turbulent forced convection of ananofluid in a tube with uniform heat flux using atwo-phase approach. Int. J. Heat Fluid Flow 28(2007) 211–219.
16
[17] R. Lotfi, Y. Saboohi, A.M. Rashidi, Numericalstudy of forced convective heat transfer ofNanofluids: Comparison of different approaches.Int. Com. Heat Mass Transfer 37 (2010) 74–78.
17
[18] V. Bianco, O. Manca, S. Nardini, Numericalinvestigation on nanofluids turbulent convectionheat transfer inside a circular tube. Int. J. Thermal.Sci. 50(2011)341-349
18
[19] S.Kondaraju, E. K. Jin, and J. S. Lee.Investigation of heat transfer in turbulentnanofluids using direct numerical simulations,Physical Review E 81, (2010) 016304.
19
[20] Mirmasomi and behzadmehr, Effect ofnanoparticles mean diameter on laminar mixedconvection heat transfer of a nanofluid Int. J. ofHeat and Fluid Flow 29 (2008) 557–566.
20
[21] A. Akbarinia, R. Laur Investigating the diameterof solid particles effects on a laminar nanofluidflowin a curved tube using a two phase approach.Int.J.of Heat and Fluid Flow 30 (2009) 706–714
21
[22] S.Vashisth,V.Kumar,Kirishna D.P.Nigam.AReviewon potential applications of curvedgeometries in process industry .Ind. Eng .Chem.Res. 47 (2008), 3291-3337
22
[23] S.A.Berger, L.Talbot, SL.Yao, Flow in curvedpipes Annual Review of Fluid Mechanics15(1983) 461-512.
23
[24] RK.Shah, SD.Joshi. Convective heat transfer incurved ducts. Handbook of single phaseconvective heat transfer. New York: John Wileyand Sons (1987).
24
[25] GW .Hogg, The effect of secondary flow on pointheat transfer coefficients for turbulent flow insidecurved tubes. PhD Thesis, University ofIdaho(1968).
25
[26] SV.Patankar, VS. Pratap, DB.Spalding,Predictionof turbulent flow in curved pipes. J Fluid Mech57(1975)583-95.
26
[27] L. J. Li,C. X. Lin, M. A. Ebadian. Turbulentmixed convective heat transfer in the entranceregion of a curved pipe with uniform walltemperature.Int. Journal of Heat and MassTransfer 41(1998)3793-3805.
27
[28] O.Ghaffari, A.Behzadmehr, H.Ajam,. Turbulentmixed convection of a nanofluid in a Horizontalcurved tube using a two phase approach. Int.J.Com. Heat Mass Transfer37 (2010) 1551–1558
28
[29] M.Manninen,V.Taivassalo,S. Kallio,On theMixture Model for Multiphase Flow, VTTPublications 288(1996). Technical ResearchCenter of Finland.
29
[30] L.Schiller, A. Naumann, A drag coefficientcorrelation. Z. Ver. Deutsch. Ing. 77(1935), 318–320.
30
[31] D.Gidaspow, Multiphase Flow and Fluidization.Academic Press(1994).
31
[32] B.E.Launder,D.B.Spalding, Lectures inMathematical Models of Turbulence.AcademicPress(1972), London, England.
32
[33] N. Masoumi, N. Sohrabi, A. Behzadmehr, A newmodel for calculating the effective viscosity ofnanofluids, J. Phys. D Appl. Phys. 42 (2009)055501.
33
[34] H.Gao, L. Guo, X. Zhang. Liquid–solid separationphenomena of two-phase Turbulent flow in curvedpipes. Int.J. of Heat and Mass Transfer 45 (2002)4995–5005
34