2014
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Effects of coupling on turbulent gasparticle boundary layer flows at borderline volume fractions using kinetic theory
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2
This study is concerned with the prediction of particles’ velocity in a dilute turbulent gassolidboundary layer flow using a fully Eulerian twofluid model. The closures required for equationsdescribing the particulate phase are derived from the kinetic theory of granular flows. Gas phaseturbulence is modeled by oneequation model and solid phase turbulence by MLH theory. Resultsof oneway and twoway coupled approaches are compared with the available experimental andnumerical results. Results show that oneway coupled approach is more efficient for particulatevelocity prediction in dilute flows. But, if the gasphase flow characteristics are desired, the twowaycoupled approach should be used. Effects of free stream velocity on the coupling arediscussed.
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8


Maziar
Dehghan
Mechanical Engineering Department., Amirkabir University of Technology, Tehran, Iran
Mechanical Engineering Department., Amirkabir
Iran(Islamic Republic of Iran)


Hassan
Basirat Tabrizi
Mechanical Engineering Department., Amirkabir University of Technology, Tehran, Iran
Mechanical Engineering Department., Amirkabir
Iran(Islamic Republic of Iran)
hbasirat@aut.ac.ir
Twoway coupled
GasParticle flow
Kinetic theory
Turbulent boundary layer
[[1]. Li J., H. Wang, Z. Liu, S. Chen, C. Zheng, An experimental study on turbulence modification in the nearwall boundary layer of a dilute gasparticle channel flow, Exp Fluids, 53, 1385–1403 (2012). ##[2]. Y. Tsuji, Y. Morikawa, LDV measurements of an airsolid twophase flow in a horizontal pipe, J Fluid Mech., 120, 385–409 (1982). ##[3]. A. Taniere, B. Oesterle, J.C. Monnier, On the behavior of solid particles in a horizontal boundary layer with turbulence and saltation effects. Experiments in Fluids, 23, 463471 (1997). ##[4]. Y. Sato, U. Fukuichi, K. Hishida, Effect of interparticle spacing on turbulence modulation by Lagrangian PIV, Int J Heat Fluid Flow, 21, 554–561 (2000). ##[5]. S.E. Elghobashi, On predicting particleladen turbulent flows. App. Sci. Res., 52, 309329 (1994). ##[6]. F. Li, H. Qi, C. You, Phase Doppler anemometry measurements and analysis of turbulence modulation in dilute gas–solid two phase shear flows, J Fluid Mech., 663, 434–455 (2010). ##[7]. M. Mirzaei, M. Dehghan, Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach, Heat Mass Transfer, 49, 18031811 (2013). ##[8]. M. Di Giacinto, R. Piva, F. Sabetta., Twoway coupling effects in dilute gasparticle flows, ASME Transactions Journal of Fluids Engineering, 104, 304311 (1982). ##[9]. H. Nasr, G. Ahmadi, the effect of twoway coupling and inter particle collisions on turbulence modulation in a vertical channel flow, Int. J. Heat Fluid Flow, 28, 15071517 (2007). ##[10]. H. Nasr, G. Ahmadi, J.B. McLaughin, A DNS study of effects of particleparticle collisions and twoway coupling on particle deposition and phase fluctuations, J. Fluid Mech., 640, p. 507536 (2009). ##[11]. S.A. Slater, A.D. Leeming, J.B. Young, Particle deposition from twodimentional turbulent gas flows. Int. J. Multiphase Flow, 29, 721750 (2003). ##[12]. D. Gidaspow, Multiphase flow and fluidization: continuum and kinetic theory descriptions, Boston: Academic press, (1994). ##[13]. L. Huilin, D. Gidaspow, J. Bouillard, L. Wenti, Hydrodynamics simulation of gassolid flow in a riser using kinetic theory of granular flow. chemical Engineering Journal, 95, 113 (2003). ##[14]. C.K.K. Lun, S.B. Savage, D.J. Jefferey, N. Chepurniy, Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mechanics, 140, 223256 (1984). ##[15]. J.L Sinclair, R. Jackson, Gasparticle flow in a vertical pipe with particleparticle interactions. AIChE J., 35, 14731486 (1989). ##[16]. J. Ding, D. Gidaspow, A bubbling fluidization model using kinetic theory of granular flow. AIChE J., 36, 523538 (1990). ##[17]. F. Vejahati, N. Mahinpey, N. Ellis, M.B. Nikoo, CFD simulation of gas–solid bubbling fluidized bed: A new method for adjusting drag law, Canadian J. Chem. Eng., 87 (1), 1930 (2009). ##[18]. M. Dehghan, H. Basirat Tabrizi, On nearwall behavior of particles in a dilute turbulent gas–solid flow using kinetic theory of granular flows, Powder Technology, 224, 273–280 (2012). ##[19]. R. Yusuf, B. Halvorsen, M.C. Melaaen, Computational fluid dynamic simulation of ethylene hydrogenation in a fluidised bed of porous catalyst particles, Canadian J. Chem. Eng., 90 (3), 544557 (2012). ##[20]. J. Wang, E.K. Levy, Particle motions and distributions in turbulent boundary layer of airparticle flow past a vertical flat plate. Experimental Thermal and Fluid science, 27, 845853 (2003). ##[21]. J. Wang, E.K. Levy, Particle behavior in the turbulent boundary layer of a dilute gaspartilce flow past a flat plate. Experimental Thermal and Fluid science, 30, 473483 (2006). ##[22]. M. Dehghan, H. Basirat Tabrizi, Turbulence effects on the granular model of particle motion in a boundary layer flow, Canadian J. Chem. Eng., 92, 189–195 (2014). ##[23]. V.S. Arpaci, P.S. Larsen, Convective heat transfer, PrenticeHall Inc, (1984). ##[24]. S. Dartevelle, Numerical and granulometric approaches to geophysical granular flows, PhD thesis, Department of Geological and Mining Engineering, Michigan Technological University: Houghton, (2003). ##[25]. V.S. Syamlal, W. Rogers, T.J. O'Brien, MFIX documentation: volume I, theory guide: National Technical information service, Springfield, (1993). ##[26]. D. Gidaspow, J. Jung, R.K. Singh, Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 FlourDaniel lecture. Powder Technology, 148, 123141 (2004). ##[27]. Y. Cheng, F. Wei , Y. Guo, Y. Jin, CFD simulation of hydrodynamics in the entrance region of a downer. Chemical Engineering Science, 56(4), 16871696 (2001). ##[28]. A.H. Govan, G.F. Hewitt, C.F. Ngan, Particle motion in the turbulent pipe flow. Int. J. Multiphase Flow, 15, 471481 (1989). ##[29]. M. Dehghan, M. Mirzaei, A. Mohammadzadeh, Numerical formulation and simulation of a nonNewtonian magnetic fluid flow in the boundary layer of a stretching sheet, Journal of Modeling in Engineering 11 (34), 7382 (2013). ##[30]. M. Dehghan, M. Mirzaei, M.S. Valipour, S. Saedodin, Flow of a nonNewtonian fluid over a linearly moving sheet at a transient state; new similarity variable and numerical solution scheme, Journal of Modeling in Engineering, (2014) (accepted manuscript). ##[31]. P.R. Spalart, Direct numerical simulation of turbulent boundary layer up to Reθ=1410. J. Fluid Mechanics, 187, 6198 (1988).##]
Effect of magnetic field on the boundary layer flow, heat, and mass transfer of nanofluids over a stretching cylinder
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The effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. The governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. The obtained ordinarydifferential equations are numerically solved for a range of nondimensional parameters. Resultsshow that the presence of a magnetic field would significantly affects the boundary layer profiles.An increase in magnetic parameter would decrease the reduced Nusselt and Sherwood numbers.
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Aminreza
Noghrehabadi
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid
Iran(Islamic Republic of Iran)
noghrehabadi@scu.ac.ir


Mohammad
Ghalambaz
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid
Iran(Islamic Republic of Iran)
m.ghalambaz@gmail.com


Ehsan
Izadpanahi
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid
Iran(Islamic Republic of Iran)


Rashid
Pourrajab
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid
Iran(Islamic Republic of Iran)
Nanofluid
Stretching cylinder
Magnetic field
Brownian motion
Thermophoresis
[[1]. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66, 99105 (1995). ##[2]. H. Masuda and A. Ebata and K. Teramea and N. Hishinuma, Altering the thermal conductivity and viscosity of liquid by dispersing ultrafine particles, Netsu Bussei, 4, 227233 (1993). ##[3]. T. Fang, and A. Aziz, Viscous Flow with SecondOrder Slip Velocity over a Stretching Sheet, Z. Naturforsch., 65a,1087 –1092 (2010). ##[4]. T. Hayat, M. Nawaz, Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets, Z. Naturforsch., 65a, 961 –968 (2010). ##[5]. A. S. Butt, S. Munawar, A. Ali, and A. Mehmood, Entropy Analysis of Mixed Convective Magnetohydrodynamic Flow of a Viscoelastic Fluid over a Stretching Sheet, Z. Naturforsch., 67a, 451–459 (2012). ##[6]. S. Mukhopadhyay, UpperConvected Maxwell Fluid Flow over an Unsteady Stretching Surface Embedded in Porous Medium Subjected to Suction/Blowing, Z. Naturforsch., 67a, 641–646 (2012). ##[7]. A. Ishak and R. Nazar and I. Pop, Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder, Energy Conv. Manag., 49, 32653269 (2008). ##[8]. C.Y. Wang, Fluid flow due to a stretching cylinder, Phys. Fluids, 31, 466468 (1988). ##[9]. A. Ishak and R. Nazar and I. Pop, Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder, Appl. Math. Model, 32, 20592066 (2008). ##[10]. A. Rasekh and D.D. Ganji and S. Tavakoli, numerical solution for a nanofluid past over a stretching circular cylinder with nonunifom heat source, Frontiers Heat. Mass. Transf. (FHMT), 3, 043003 (2012). ##[11]. R. Subba and R. Gorla and A. Chamkha and E. AlMeshaiei, melting heat transfer in a nanofluid boundary layer on a stretching circular cylinder, J. Naval Arch. Marin. Eng., 9, 110 (2012). ##[12]. M. Subhas Abel and P.G. Siddheshwar and N. Mahesha, Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a nonuniform property micropolar liquid, Appl. Math. Comp., 217, 5895–5909 (2011). ##[13]. W.A. Khan and I. Pop, Boundarylayer flow of a nanofluid past a stretching sheet, Int. J. Heat. Mass. Transf., 53, 2477–2483 (2010). ##[14]. R. Kandasamy and P. Loganathan and P. Puvi Arasu, Scaling group transformation for MHD boundarylayer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection, Nuclear Eng. Design, 241, 20532059 (2011). ##[15]. N. Bachok and A. Ishak and I. Pop, Unsteady boundarylayer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet, Int. J. Heat. Mass. Transf., 55, 21022109 (2012). ##[16]. J. Buongiorno, Convective Transport in Nanofluids, J. Heat. Transf., 128, 240245 (2006).##]
An experimental investigation of rheological characteristics of non Newtonian nanofluids
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Rheological characteristics of Al2O3, CuO and TiO2 nano particles were investigated in oil asthe base fluid at 1 and 2 wt.%. Constitutive relations for nonNewtonian fluid were discussedbased on the powerlaw model. Measured viscosities of each nanofluid were used to evaluatethe powerlaw and consistency index. Results indicated that the nanofluid viscosity decreasedby increasing the concentration. Oil showed shear thickening behavior while nanofluids showedshear thinning behavior. An increase in nanoparticle concentration caused a decrease in thepowerlaw index beside an increase in the consistency index. Moreover, the present studyshowed that the effective viscosity of fluids would be decreased by nanoparticle addition atsome wt.% and some shear rates. Furthermore, results showed that the classic models fornanofluid viscosity couldn’t predict their real values of nano fluid viscosity, as the measuredvalues are less than the predicted ones.
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23


Milad
Tajik JamalAbad
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
Faculty of Mechanical Engineering, Semnan
Iran(Islamic Republic of Iran)


Maziar
Dehghan
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
Faculty of Mechanical Engineering, Semnan
Iran(Islamic Republic of Iran)


Seyfolah
Saedodin
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
Faculty of Mechanical Engineering, Semnan
Iran(Islamic Republic of Iran)


Mohammad Sadegh
Valipour
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
Faculty of Mechanical Engineering, Semnan
Iran(Islamic Republic of Iran)
msvalipour@semnan.ac.ir


Amirhossein
Zamzamian
Materials and Energy Research Center (MERC), Karaj, Iran
Materials and Energy Research Center (MERC),
Iran(Islamic Republic of Iran)
nanofluids
Viscosity
Rheological characteristics
Powerlaw index
Consistency index
[[1]. B.C. Pak, Y.I. Cho, “Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles,” Experimental Heat Transfer, 11 (2), 151170 (1998). ##[2]. S.K. Das, N. Putra, W. Roetzel, “Pool Boiling Characteristics of Nano fluids,” International Journal of Heat and Mass Transfer, 46 (5), 851862 (2003). ##[3]. M. Mirzaei, M. Dehghan, “Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach”, Heat Mass Transfer, 49, 18031811 (2013). ##[4]. S.Z. Heris, S.G. Etemad, M.N. Esfahany, “Experimental Investigation of Oxide Nanofluids Laminar Flow Convective Heat Transfer,” Int. Comm. Heat Mass Trans., 33(4), 529535 (2006). ##[5]. D.P. Kulkarni, D.K. Das, G.A. Chukwu, “Temperature Dependent Rheological Property of Copper Oxide Nanoparticles Suspension (Nanofluid),” J. Nanoscience Nanotechnology, 6(4), 11501154 (2006). ##[6]. T. Phuoc, M. Massoudi, R. Chen., “Viscosity and thermal conductivity of nanofluids containing multiwalled carbon nanotubes stabilized by chitosan,” International Journal of Thermal Sciences, 50, 1218 (2011). ##[7]. A. Einstein, “Eine neue Bestimmung der Molekuldimension,” Annalen der Physik, 19, 289306 (1906). ##[8]. J. Yang, F. Li, W. Zhou, Y. He, B. Jiang , “Experimental investigation on the thermal conductivity and shear viscosity of viscoelasticfluidbased nanofluids”, International Journal of Heat and Mass Transfer, 55, 31603166 (2012). ##[9]. P. Ravi, S. David, W. Jinlin, “Measurement of nanofluid viscosity and its implications for thermal applications”. Applied Phys. Lett., 89 (13), 133108 1331083 (2006). ##[10]. S. Lee, S. Park, S. Kang, I. Bang, J. Kim , “Investigation of viscosity and thermal conductivity of SiC nanofluids for heat transfer applications,” International Journal of Heat and Mass Transfer, 54, 433438 (2011). ##[11]. A.Utomo, H. Poth, P. Robbins, A. Pacek , “Experimental and theoretical studies of thermal conductivity, viscosity and heat transfer coefficient of titania and alumina nanofluids” ,International Journal of Heat and Mass Transfer, 55, 7772–7781 (2012). ##[12]. H. Chen, Y. Ding, Y. He, C. Tan, “Rheological behavior of ethylene glycol based titania nanofluids”, Chem. Phys. Lett. 444, 333–337 (2007). ##[13]. H. Chen, S. Witharana, Y. Jin, C. Kimd, Y. Ding, “Predicting thermal conductivity of liquid suspensions of nanoparticles based on rheology”, Particuology 7, 151–157 (2009). ##[14]. M. Kole, T.K. Dey, “Viscosity of alumina nanoparticles dispersed in car engine coolant,” Experimental Thermal and Fluid Science, 34, 677–683 (2010). ##[15]. M. Nabeel Rashin, J. Hemalatha, “Viscosity studies on novel copper oxide–coconut oil nanofluid,” Experimental Thermal and Fluid Science, 48, 67–72 (2013). ##[16]. M. Hojjat, S.Gh. Etemad, R. Bagheri, J. Thibault, “Rheological characteristics of nonNewtonian nanofluids: Experimental investigation”, International Communications in Heat and Mass Transfer, 38, 144–148 (2011). ##[17]. M. Kole, T.K. Dey, “Thermophysical and pool boiling characteristics of ZnOethylene glycol nanofluids”, International Journal of Thermal Sciences 62, 6170 (2012). ##[18]. M.T. JamalAbad, A. Zamzamian, M. Dehghan, Experimental studies on the heat transfer and pressure drop characteristics of Cuwater and Alwater nanofluids in a spiral coil, Experimental Thermal and Fluid Science, 47, 206–212 (2013). ##[19]. F.M. White, “Viscous Fluid Flow”, third ed. McGrawHill, New York, 2006. ##[20]. M. Dehghan, H. Basirat Tabrizi, On nearwall behavior of particles in a dilute turbulent gas–solid flow using kinetic theory of granular flows, Powder Technology, 224, 273–280 (2012). ##[21]. M. Dehghan, H. Basirat Tabrizi, Turbulence effects on the granular model of particle motion in a boundary layer flow, Canadian Journal of Chemical Engineering, 92, 189–195 (2014). ##[22]. M. Dehghan, H. B. Tabrizi, Effects of coupling on turbulent gasparticle boundary layer flows at borderline volume fractions using kinetic theory, Journal of Heat and Mass Transfer Research, 1, 18 (2014). ##[23]. M. Dehghan, M. Mirzaei, A. Mohammadzadeh, Numerical formulation and simulation of a nonNewtonian magnetic fluid flow in the boundary layer of a stretching sheet, Journal of Modeling in Engineering, 11 (34), 7382 (2013). ##[24]. G. Astarita and G. Marrucci, “Principles of NonNewtonian Fluid Mechanics”, McGrawHill (UK), (1974). ##[25]. D.C. Leigh, “NonNewtonian fluids and the second law of thermodynamics”, Physics of Fluids, 5, 501–502 (1962). ##[26]. B.D. Coleman, H. Markovitz, W. Noll, “Viscometric Flows of NonNewtonian Fluids”, SpringerVerlag, (1966). ##[27]. H.C. Brinkman, “The Viscosity of Concentrated Suspensions and Solution”, J. Chem. Phys. 20, 571581(1952). ##[28]. D.A. Drew, D.A. Passman, “Theory of Multicomponent Fluids”, Springer, Berlin, (1999). ##[29]. H.I. Andersson, B.S. Dandapat, “Flows of a power law fluid over a stretching sheet”. Stability Appl Anal Continuous Media,1, 339–347 (1991). ##[30]. M. Dehghan, M. Mirzaei, M.S. Valipour, S. Saedodin, Flow of a nonNewtonian fluid over a linearly moving sheet at a transient state; new similarity variable and numerical solution scheme, Journal of Modeling in Engineering, (2014) (accepted in press).##]
Entropy generation calculation for laminar fully developed forced flow and heat transfer of nanofluids inside annuli
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In this paper, second law analysis for calculations of the entropy generation due to the flow andheat transfer of waterAl2O3 and ethylene glycolAl2O3 nanofluids inside annuli is presented. Thephysical properties of the nanofluids are calculated using empirical correlations. Constant heatfluxes at inner surface of the annuli are considered and fully developed condition for fluid flowand heat transfer is assumed. The control volume approach is selected for calculation of theentropy generation. Total entropy generation for different values of the nanoparticles volumefractions at different geometrical ratios is obtained and compared with those of the base fluid.Also, the geometrical ratios at which the minimum entropy generation is achieved are presented.The results show that when the ratio of the annuli length to its hydraulic diameter (L/Dh) exceedssome critical values, adding of the nanoparticles is not efficient. For each value of thenanoparticles concentration, there is a length ratio (L/Dh) at which the entropy generation isminimized.
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33


Roohollah
Rafee
Faculty of mechanical engineering, Semnan University, Semnan, Iran
Faculty of mechanical engineering, Semnan
Iran(Islamic Republic of Iran)
rafee@semnan.ac.ir
Second law of thermodynamics
Entropy generation
nanofluids
Heat transfer
Annuli
Laminar flow
[[1]. Y.M. Xuan, Q. Li, Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow, 21, 58–64 (2000). ##[2]. B.X. Wang, L.P. Zhou, X.F. Peng. A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int. J. Heat Mass Transfer, 46, 2665–2672 (2003). ##[3]. H. Xie, M. Fujii, X. Zhang, Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticlefluid mixture. Int. J. Heat Mass Transfer, 48, 2926–2932 (2005). ##[4]. N. Masoumi, N. Sohrabi, A. Behzadmehr, A new model for calculating the effective viscosity of nanofluids. J. Phys. D: Appl. Phys, 42, 055501 (2009). ##[5]. C.T. Nguyen, F. Desgranges, N. Galanis, G. Roy, T. Maré, S. Boucher, H. Angue Mintsa, Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer enhancement using nanofluids reliable? Int. J. Thermal Sci., 47, 103–111 (2008). ##[6]. E. AbuNada, Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection, Int. J. Heat Fluid Flow, 30, 679–690 (2009). ##[7]. M. Izadi, A. Behzadmehr, D. JalaliVahida, Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Thermal Sci., 48, 2119–2129 (2009). ##[8]. E. AbuNada, Z. Masoud, A. Hijazi, Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids, Int. Comm. Heat Mass Transfer, 35, 657–665 (2008). ##[9]. J.H. Lee, K.S. Hwang, S.P. Jang, B.H. Lee, J.H. Kim, S.U.S. Choi, Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of AI2O3 nanoparticles, Int. J. Heat Mass Transfer, 51(1112), 26512656 (2008). ##[10]. W. Yu, D.M. France, S.U.S. Choi, J.L. Routbort, Review and assessment of nanofluid technology for transportation and other applications, Energy Systems Division, Argonne National Laboratory, (2007). ##[11]. V. Vasu, K. Rama Krishna, A.C.S. Kumar, Heat transfer with nanofluids for electronic cooling, Int. J. Mater. Prod. Technol., 34(1J2), 158171 (2009). ##[12]. M.N. Pantzali, A.A. Mouza, S.V. Paras, Investigating the efficacy of nanofluids as coolants in plate heat exchangers (PHE), Chem. Eng. Sci., 64, 3290 300 (2009). ##[13]. P.K. Singh, K.B. Anoop, T. Sundarajan, S.K. Das, Entropy generation due to flow and heat transfer in nanofluids, Int. J. Heat Mass Transfer, 53, 4757–4767 (2010). ##[14]. M. Moghaddami, A. Mohammadzade, S. Alem Varzane Esfehani, Second law analysis of nanofluid flow, Energ. Convers. Manage., 52, 1397–1405 (2011). ##[15]. A. Ijam, R. Saidur, Nanofluid as a coolant for electronic devices (cooling of electronic devices), Appl. Therm. Eng., 32, 7682 (2012). ##[16]. A. Bejan, Entropy generation minimization, CRC Press, Boca Raton, (1996). ##[17]. T.H. Ko, K. Ting, Entropy generation and thermodynamic optimization of fully developed laminar convection in a helical coil, Int. Commun. Heat Mass Transfer, 32, 214223 (2005). ##[18]. T.H. Ko, Thermodynamic analysis of optimal mass flow rate for fully developed laminar forced convection in a helical coiled tube based on minimal entropy generation principle. Energ. Convers. Manag., 47, 30943104 (2006). ##[19]. P.K. Nag, K. Naresh, Second law optimization of convection heat transfer through a duct with constant heat flux, Int. J. Energy Res., 13, 537543 (1989). ##[20]. M. Rafati, A.A. Hamidi, M. Shariati Niaser, Application of nanofluids in computer cooling systems (heat transfer performance of nanofluids), Appl. Therm. Eng., 45, 914 (2012). ##[21]. O. Mahian, A. Kianifar, C. Kleinstreuer, M. A. AlNimr, I. Pop, A. Z. Sahin, S. Wongwises, A review of entropy generation in nanofluid flow, Int. J. Heat Mass Transfer, 65, 514532 (2013). ##[22]. O. Mahian, H. Oztop, I. Pop, Sh. Mahmud, S. Wongwises, Entropy generation between two vertical cylinders in the presence of MHD flow subjected to constant wall temperature, Int. Commun. Heat Mass Transfer, 44, 87–92 (2013). ##[23]. M. Torabi, A. Aziz, Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling. Int. Commun. Heat Mass Transfer, 39, 14871495 (2012). ##[24]. O. Mahian, Sh. Mahmud, S. Zeinali Heris, Analysis of entropy generation between corotating cylinders using nanofluids. Energy, 44, 438446 (2012). ##[25]. E. AbuNada, Z. Masoud, A. Hijazi, Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids, Int. Commun. Heat Mass Transfer, 35, 657–665 (2008). ##[26]. R. Mokhtari Moghari, A. Akbarinia, M. Shariat, F. Talebi, R. Laur, Two phase mixed convection Al2O3–water nanofluid flow n an annulus, Int. J. Multiphase Flow, 37(6), 585595 (2011). ##[27]. C. Yang, W. Li, A. Nakayama, Convective heat transfer of nanofluids in a concentric annulus. Int. J. Thermal Sci., 71, 249257 (2013). ##[28]. J. Buongiomo, Convective transport in nanofluids. J. Heat Transfer, 128, 240250 (2006). ##[29]. B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer, 11, 151170 (1998). ##[30]. Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer, 43, 37013707 (2000). ##[31]. X. Wang, X. Xu and S.U.S. Choi, Thermal conductivity of nanoparticlefluid mixture, J. Thermo physics Heat Transfer, 13, 474480 (1999). ##[32]. M.A. Ebadian and Z.F. Dong, Forced convection internal flow in ducts, in W.M. Rohsenow, J.P. Hartnet and Y.I. Cho (Eds), Handbook of Heat Transfer, McGrawHill, New York, 13715 (1998). ##[33]. I.H. Shames, Mechanics of Fluids, 4th ed., McGraw Hill, (2003).##]
The optimization of inlet and outlet port locations of a vented square cavity
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2
In this study, mixed convection heat transfer and local and global entropy generation in aventilated square cavity have been investigated numerically. The natural convection effect isachieved by a constant heat flux imposed at the bottom wall and cooled by injecting a coldfollow. In order to investigate the effect of port location, four different placementconfigurations of the inlet and outlet ports are studied. In each case, external flow enters intothe cavity through an inlet port in the left side of the cavity and exits from the opposite side.The other boundaries are assumed adiabatic. The cavity is subjected to laminar flow of water.The investigation has been carried out for the Re=1000, and the Richardson number with therange of 0.0001(Global Entropy Generation), Heat Transfer Irreversibility (HTI) and Fluid FrictionIrreversibility (FFI) are calculated and compared. Then, the optimum inlet/outlet configurationhas been selected based on the minimum GEG and the maximum heat transfer.
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45


Taher
Armaghani
Islamic azad university Mahdishahr branch, Department of engineering, Mahdishahr, Iran.
Islamic azad university Mahdishahr branch,
Iran(Islamic Republic of Iran)
taherarmaghani@yahoo.com


Farhad
Talebi
Department of mechanical engineering, Semnan University, Semnan, Iran
Department of mechanical engineering, Semnan
Iran(Islamic Republic of Iran)
ftalebi@semnan.ac.ir


Amir Houshang
Mahmoudi
Department of mechanical engineering, Semnan University, Semnan, Iran
Department of mechanical engineering, Semnan
Iran(Islamic Republic of Iran)
amirhoshangm@gmail.com


M
Farzaneh Gord
Department of mechanical engineering, Shahrood University of Technology, Shahrood, Iran
Department of mechanical engineering, Shahrood
Iran(Islamic Republic of Iran)
Vented square cavity
Entropy generation
Heat transfer
Irreversibility
Fluid friction irreversibility
[[1]. K.J. Kennedy, A. Zebib, Combined free and forced convection between horizontal parallel planes: some case studies, Int. J. Heat Mass Transf., 26, 471–474 (1983). ##[2]. T. Basak, S. Roy, P.K. Sharma, I. Pop, Analysis of mixed convection flows within a square cavity with uniform and nonuniform heating of bottom wall, Int. J. Therm. Sci., 48, 891–912 (2009). ##[3]. G. Guo, M.A.R. Sharif, Mixed convection in rectangular cavities at various aspect ratios with moving isothermal sidewalls and constant flux heat source on the bottom wall, Int. J. Therm. Sci., 43, 465–475 (2004). ##[4]. K.M. Khanafer, A.M. AlAmiri, I. Pop, Numerical simulation of unsteady mixed convection in a driven cavity using an externally excited sliding lid, Eur. J. Mech. B/Fluids, 26, 669–687 (2007). ##[5]. S. Saha, G. Saha, M. Ali, Md.Q. Islam, Combined free and forced convection inside a twodimensional multiple ventilated rectangular enclosure, ARPN J. Eng. Appl. Sci., 1 (3), 23–35 (2006). ##[6]. M.D.M. Rahman, M.A. Alim, S. Saha, M.K. Chowdhury, A numerical study of mixed convection in a square cavity with a heat conducting square cylinder at different locations, J. Mech. Eng., ME39 (2), 78–85 (2008). ##[7]. B. Ghasemi, S.M. Aminossadati, Numerical simulation of mixed convection in a rectangular enclosure with different numbers and arrangements of discrete heat sources, Arab. J. Sci. Eng., 33 (1B), 189–207 (2008). ##[8]. S. Saha, G. Saha, M. Ali, Md.Q. Islam, Combined free and forced convection inside a twodimensional multiple ventilated rectangular enclosure, ARPN J. Eng. Appl. Sci., 2 (2), 25–36 (2007). ##[9]. A. H. Mahmoudi, M. Shahi, F. Talebi, Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid, Int. Comm. Heat Mass Transfer, 37, 11581173 (2010). ##[10]. A. Bejan, A study of entropy generation in fundamental convective heat transfer, J. Heat Transfer, 101, 718725 (1979). ##[11]. A. Bejan, Secondlaw analysis in heat and thermal design, Adv. Heat Transfer, 15, 158 (1982). ##[12]. A. Bejan, Entropy Generation Minimization, CRC press, Boca Raton, NY, (1996). ##[13]. N. Kasagi, M. Nishimura, DNS of combined forced and natural convection in a vertical plane channel, Int. J. Heat Mass Transfer, 18, 8899 (1997). ##[14]. A.C. Baytas, Entropy generation for natural convection in an inclined porous cavity, Int. J. Heat Mass Transfer, 43, 42254232 (2000). ##[15]. S. Mahmud, R. A. Fraser, The secondlaw analysis in fundamental convective heat transfer problem, Int. J. Thermal Sciences, 42, 177186 (2003). ##[16]. A. Andreozzi, A. Auletta, O. Manca, Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel, int. J. Heat Mass Transfer, 49, 32213228 (2006). ##[17]. A.Omri, and S.B. Nasrallah, Control volume finite element numerical simulation of mixed convection in an aircooled cavity, Numerical Heat Transfer, Part A, 36, 615637 (1999). ##[18]. S. Singh, and M.A.R. Sharif, Mixed Convection cooling of a rectangular cavity with inlet and exit openings ondifferentially heated side walls. Numerical Heat Transfer, Part A, 44, 233253(2003). ##[19]. Md. Mustafizur Rahman, M. A. Alim and Sumon Saha, mixed convection in a square cavity with a heatconducting horizontal square cylinder, Suranaree J. Sci. Technol., 17,139153 (2010). ##[20]. C. Balaji, M. Holling, H. Herwing, Entropy generation minimization in turbulent mixed convection flows, Int. Comm. Heat Mass Transfer, 34, 544552 (2007). ##[21]. I. Zahmatkesh, on the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure, Int. J. Thermal Sciences, 47, 339346 (2008). ##[22]. M. shahi, A.H. Mahmoudi, A. Honarbakhsh Rauof, entropy generation due to a natural convection cooling of nanofluid, Int Comm. Heat Mass Transfer, 38, 972983 (2011). ##[23]. A. H. Mahmoudi, I. Pop, M. Shahi, F. Talebi, MHD natural convection and entropy generation in a trapezoidal enclosure using nanofluid, computer and fluids, 72, 4662 (2013). ##[24]. J.H. Ferziger, M. Peric, Computational Method for Fluid Dynamic, SpringerVerlag, NY, (1999). ##[25]. S.V. Patankar, Numerical heat transfer and fluid flow, hemisphere, NY, (1980). ##[26]. G. De Vahl Davis, Natural convection of air in a square cavity a bench mark numerical solution, Int. J. Numer. Meth. Fluids, 3, 249–264 (1983).##]
Experimental investigation and proposed correlations for temperaturedependent thermal conductivity enhancement of ethylene glycol based nanofluid containing ZnO nanoparticles
2
2
Experimental study of effective thermal conductivity of ZnO/EG nanofluid is presented in thisresearch. The nanofluid was prepared by dispersing Zno nanoparticles in ethylene glycol using asonicator and adding surfactant. Ethylene glycol based nanofluid containing ZnO nanoparticlewith a nominal diameter of 18 nm at different solid volume fractions (very low to high) atvarious temperatures was examined for the investigation. The thermal conductivity of nanofluidsis experimentally measured with THW method and it is found that the thermal conductivity ofnanofluids increase with the nanoparticle volume concentration and temperature. Also, based onexperimental values of thermal conductivity of nanofluid, three experimental models areproposed to predict thermal conductivity of nanofluids. The proposed models show reasonablyexcellent agreement with our experimental results.
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Mohammad
Hemmat Esfe
Faculty of mechanical engineering, Semnan University, Semnan, Iran
Faculty of mechanical engineering, Semnan
Iran(Islamic Republic of Iran)
m.hemmatesfe@gmail.com


Seyfolah
Saedodin
Faculty of mechanical engineering, Semnan University, Semnan, Iran
Faculty of mechanical engineering, Semnan
Iran(Islamic Republic of Iran)
thermal conductivity
Heat transfer
Nanofluid
Thermophysical properties
[[1]. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, (1960). ##[2]. M. Chandrasekar, S. Suresh, A. Chandra Bose, Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid, Experimental Thermal and Fluid Science, 34, 210–216 (2010). ##[3]. C.H. Chon, K.D. Kihm, S.P. Lee, S.U.S. Choi, Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Physics Letter, 87, 1531071–1531073 (2005). ##[4]. T.P. Teng, Y.H. Hung, T.C. Teng, H.E. Moa, H.G. Hsu, The effect of alumina/water nanofluid particle size on thermal conductivity, Applied Thermal Engineering, 30, 2213–2218 (2010). ##[5]. S.M.S. Murshed, K.C. Leong, C. Yang, Investigations of thermal conductivity and viscosity of nanofluids, International Journal of Thermal Sciences, 47, 560–568 (2008). ##[6]. J.C. Maxwell, A Treatise on Electricity and Magnetism, 2nd ed. Clarendon Press, Oxford, United Kingdom, (1873). ##[7]. W. Yu, S.U.S. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model, Journal of Nanoparticle Research, 5, 167–171 (2003). ##[8]. J. Koo, C. Kleinstreuer, A new thermal conductivity model for nanofluids, Journal of Nanoparticle Research, 6, 577–588 (2004). ##[9]. H. Xie, M. Fujii, X. Zhang, Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle–fluid mixture, International Journal of Heat and Technology, 48, 2926–2932 (2005). ##[10]. D.A.G. Bruggeman, Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitäts konstanten und Leitfähigkeiten der Mischkörperaus isotropen Substanzen, Annalen der Physik, 416 (7), 636–664 (1935). ##[11]. Lee S, Choi SUS: Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121, 280289 (1999). ##[12]. C.H. Li, G.P. Peterson, Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids). Journal of Applied Physics, 99 (8), 084314 (2006). ##[13]. H.A. Mintsa, G. Roy, C.T. Nguyen, D. Doucet, New temperature dependent thermal conductivity data for waterbased nanofluids. International Journal of Thermal Sciences, 48, 363371 (2009). ##[14]. S.M.S. Murshed, K.C. Leong, C. Yang, A combined model for the effective thermal conductivity of nanofluids. Applied Thermal Engineering, 9, 24772483 (2009). ##[15]. W. Duangthongsuk, S. Wongwises, Measurement of temperature dependent thermal conductivity and viscosity of TiO2water nanofluids. Experimental Thermal and Fluid Science, 33, 706714 (2009). ##[16]. A.R. Moghadassi, S.M. Hosseini, D.E. Henneke, Effect of CuO nanoparticles in enhancing the thermal conductivities of monoethylene glycol and paraffin fluids. Industrial Engineering and Chemistry Research, 49, 19001904 (2010) ##[17]. S.K. Das, N. Putra, P. Theisen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer, 125, 567574 (2003). ##[18]. M. Abareshi, E.K. Goharshiadi, S.M. Zebarjad, H.K. Fadafan, A. Youssefi, Fabrication, characterization and measurement of thermal conductivity of Fe3O4 nanofluids. Journal of Magnetism and Magnetic Materials, 322 (24), 38953901 (2010). ##[19]. I. Tavman, A. Turgut, An investigation on thermal conductivity and viscosity of water based nanofluids. Microfluidics Based Microsystems, 0, 139162 (2010). ##[20]. C. Kleinstreuer, Y. Feng, Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Research Letters, 6, 229 (2011). ##[21]. K. Kwak, C. Kim, Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol, KoreaAust. Rheol. J., 17 (2), 35–40 (2005). ##[22]. I.M. Mahbubul, R. Saidur, M.A. Amalina, Latest developments on the viscosity of nanofluids, Int. J. Heat Mass Transfer, 55 (4), 874–885 (2012). ##[23]. C.Y. Lin, J.C. Wang, T.C. Chen, Analysis of suspension and heat transfer characteristics of Al2O3 nanofluids prepared through ultrasonic vibration, Appl. Energy, 88 (12), 4527–4533 (2011). ##[24]. K. RohiniPriya, K.S. Suganthi, K.S. Rajan, Transport properties of ultralow concentration CuO–water nanofluids containing nonspherical nanoparticles, Int. J. Heat Mass Transfer, 55 (17–18), 4734–4743 (2012). ##[25]. S.M.S. Murshed, K.C. Leong, C. Yang, Enhanced thermal conductivity of TiO2– water based nanofluids, Int. J. Therm. Sci., 44 (4), 367–373 (2005). ##[26]. R. Wahab, Y.S. Kim, H.S. Shin, Synthesis, Characterization and Effect of pH Variation on Zinc Oxide Nanostructures, Materials Transactions, 50 (8 ), 2092 – 2097 (2009). ##[27]. H. chang, C.S. Jwo, C.H. Lo, T.T.T. Tsung, M.J. Kao, H.M. Lin, Rheology of CuO nanoparticles suspension prepared by ASNSS., Rev. Adv. Mater. Sci., 1, 128132 (2005). ##[28]. K. Wongcharee, S. Eiamsaard, Enhancement of heat transfer using CuO/ water nanofluid and twisted tape with alternate axis, Int. Comm. Heat Mass Transfer, 38 (6), 742–748 (2011). ##[29]. J. Buongiorno, Convective transport in nanofluids, J. Heat Transfer, 128 (3), 240–250 (2006). ##[30]. R. Hamilton, O. Crosser, Thermal conductivity of heterogeneous two component systems, Ind. Eng. Chem. Fund., 1 (3), 187–191 (1962). ##[31]. [31] W. Yu, S.U.S. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model, J. Nanopart. Res., 5, 167–171 (2003). ##[32]. K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids. International Journal of Heat and Mass Transfer, 54, 4410–4428 (2011). ##[33]. S.M.S. Murshed, K.C. Leong, C. Yang, Investigations of thermal conductivity and viscosity of nanofluids, Int. J. Therm. Sci., 47, 560–568 (2008). ##[34]. S. Ravikanth, V. Debendra, K. Das, Experimental determination of thermal conductivity of three nanofluids and development of new correlations, Int. J. Heat Mass Transfer, 52, 4675–4682 (2009). ##[35]. R. Karthik, R. Harish Nagarajan, B. Raja , P. Damodharan, Thermal conductivity of CuO–DI water nanofluids using 3x measurement technique in a suspended microwire, Experimental Thermal and Fluid Science, 40, 1–9 (2012). ##[36]. K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids, Int. J. Heat Mass Transfer, 54, 4410–4428 (2011).##]
Boundary layer flow beneath a uniform free stream permeable continuous moving surface in a nanofluid
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2
The main purpose of this paper is to introduce a boundary layer analysis for the fluid flow andheat transfer characteristics of an incompressible nanofluid flowing over a permeable isothermalsurface moving continuously. The resulting system of nonlinear ordinary differential equations issolved numerically using the fifth–order Runge–Kutta method with shooting techniques usingMatlab and Maple softwares. Numerical results are obtained for the velocity, temperature, andconcentration distributions, as well as the friction factor, local Nusselt number, and localSherwood number for several values of the parameters, namely the velocity ratio parameter,suction/injection parameter, and nanofluid parameters. The obtained results are presentedgraphically in tabular forms and the physical aspects of the problem are discussed.
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Ioan
Pop
Department of Mathematics, BabesBolyai University, 400048 ClujNapoca, Romania
Department of Mathematics, BabesBolyai University
Romania
popm.ioan@yahoo.co.uk


Sarkhosh
Seddighi
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
Department of Mathematics and Institute for
Malaysia


Norfifah
Bachok
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
Department of Mathematics and Institute for
Malaysia


Fudziah
Ismail
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
Department of Mathematics and Institute for
Malaysia
Suction/injection
Moving surface
Nanofluid
RungeKutta method
Shooting techniques
Dual solutions
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Chamkha, M, Nazari, Effects of Particle Migration on Nanofluid Forced Convection Heat Transfer in a Local Thermal NonEquilibrium Porous Channel, 3, 5159 (2014). ##[8]. S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer, 52, 31873196 (2009). ##[9]. K.V. Wong, O.D. Leon, Applications of nanofluids: current and future, Adv. Mech. Eng., Article ID 519659, 111 (2010). ##[10]. R. Saidur, K.Y. Leong, H.A. Mohammad, A review on applications and challenges of nanofluids, Renewable and Sustainable Energy Reviews, 15, 16461668 (2011). ##[11]. D. Wen, G. Lin, S. Vafai, K. Zhang, Review of nanofluids for heat transfer applications, Particuology, 7, 141150 (2011). ##[12]. O. Mahian, A. Kianifar, S.A. Kalogirou, I. Pop, S. Wongwises, A review of the applications of nanofluids in solar energy, Int. J. Heat Mass Transfer, 57, 582–594 (2013). ##[13]. T. Fang, S. Yao, J. Zhang, A. Aziz, Viscous flow over a shrinking sheet with a second order slip flow model, Commun. Nonlinear Sci. Numer. Simulat, 15, 1831–1842 (2010). ##[14]. E.M. Sparrow, J.P. Abraham, Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid, Int. J. Heat Mass Transfer, 48, 3047 3056 (2005). ##[15]. S.J. Liao, I. Pop, A new branch of solutions of boundarylayer flows over a stretching flat plate, Int. J. Heat Mass Transfer, 49, 2529–2539 (2005). ##[16]. C.Y. Wang, Exact solutions of the steady state Navier–Stokes equations, Ann. Rev. Fluid Mech., 23, 159–177 (1991). ##[17]. K. Zaimi, A. Ishak, I. Pop, Boundary layer flow and heat transfer past a permeable shrinking sheet in a nanofluid with radiation effect, Adv. Mech. Eng., Article ID 340354, 17 (2012). ##[18]. N. Bachok, A. Ishak, I. Pop, The boundary layers of an unsteady stagnationpoint flow in a nanofluid, Int. J. Heat Mass Transfer, 55, 6499–6505 (2012). ##[19]. N. Bachok, A. Ishak, I. Pop, Boundary layer stagnationpoint flow toward a stretching/shrinking sheet in a nanofluid, ASME J. Heat Transfer, 135 (Article ID 05450), 15 (2013). ##[20]. W. Ibrahim, B. Shankar, M.M. Nandeppanavar, MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, Int. J. Heat and Mass Transfer, 56, 1–9 (2013). ##[21]. A.V. Kuznetsov, D.A. Nield, Natural convective boundarylayer flow of a nanofluid past a vertical plate, Int. J. Thermal Sci., 49, 243–247 (2010). ##[22]. R.K. Tiwari, M.K. Das, Heat transfer augmentation in a twosided liddriven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer , 50, 20022018 (2007). ##[23]. K. Khanafer, K. Vafai, M. Lightstone, Buoyancydriven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46, 3639–3653 (2003). ##[24]. H.F. Oztop, E. AbuNada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29, 1326–1336 (2008). ##[25]. H.C. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phys., 20, 571581 (1952). ##[26]. P.D. Weidman, D.G. Kubitschek, A.M.J. Davis, The effect of transpiration on selfsimilar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44, 730737 (2006). ##[27]. S. Seddighi Chaharborja, S.M. Sadat Kiai, M.R. Abu Bakar, I. Ziaeian, I. Fudziah, A new impulsional potential for a Paul ion trap, Int. J. Mass Spectrom, 309, 63– 69 (2012). ##[28]. A.V. Kuznetsov, D.A. Nield, Natural convective boundarylayer flow of a nanofluid past a vertical plate, Int. J. Thermal Sci., 49, 243–247 (2010). ##[29]. R.K. Tiwari, M.K. Das, Heat transfer augmentation in a twosided liddriven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer , 50, 20022018 (2007). ##[30]. K. Khanafer, K. Vafai, M. Lightstone, Buoyancydriven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46, 3639–3653 (2003). ##[31]. H.F. Oztop, E. AbuNada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29, 1326–1336 (2008). ##[32]. H.C. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phys., 20, 571581 (1952). ##[33]. P.D. Weidman, D.G. Kubitschek, A.M.J. Davis, The effect of transpiration on selfsimilar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44, 730737 (2006). ##[34]. S. Seddighi Chaharborja, S.M. Sadat Kiai, M.R. Abu Bakar, I. Ziaeian, I. Fudziah, A new impulsional potential for a Paul ion trap, Int. J. Mass Spectrom, 309, 63– 69 (2012).##]