Abstract
In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al2O3) and titanium oxide (TiO2) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.
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Abbreviations
- A 1, A 2, A 3 :
-
Constants
- a :
-
Radius of cylinder
- c :
-
Positive constant
- C f :
-
Skin friction coefficient
- f :
-
Dimensionless stream function
- k :
-
Thermal conductivity
- M :
-
Magnetic parameter
- Nu :
-
Nusselt number
- Pr :
-
Prandtl number
- q w :
-
Heat transfer from the cylinder surface
- Re :
-
Reynolds number
- T :
-
Temperature of the nanofluid
- T w :
-
Temperature of the cylinder surface
- \( T_{\infty } \) :
-
Ambient temperature
- u, v :
-
Velocity components along the x and y directions, respectively
- x, y :
-
Cartesian coordinates along x and y axes, respectively
- α :
-
Thermal diffusivity
- η :
-
Similarity variable
- θ :
-
Similarity function for temperature
- ρ :
-
Density
- \( \phi \) :
-
Nanoparticle volume fraction
- \( \mu \) :
-
Dynamic viscosity
- v :
-
Kinematic viscosity
- \( \tau_{w} \) :
-
Wall shear stress
- \( \psi \) :
-
Stream function
- \( \sigma \) :
-
Electrical conductivity
- w :
-
Condition at the surface
- \( \infty \) :
-
Far field
- nf :
-
Nanofluid
- f :
-
Base fluid
- s :
-
Nano-solid-particles
References
Liron N, Wilhelm HE (1974) Integration of the magneto-hydrodynamic boundary layer equations by Meksyn’s method. J Appl Math Mech (ZAMM) 54:27–37
Pavlov KB (1974) Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a planesurface. Magnitnaya Gidrodinamika 4:146–147
Ishak A, Jafar K, Nazar N, Pop I (2009) MHD stagnation point flow towards a stretching sheet. Phys A 388:3377–3383
Hamad MAA, Pop I, Md Ismail AI (2011) Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate. Nonlinear Anal Real World Appl 12:1338–1346
Anjali Devi SP, Thiyagarajan M (2006) Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature. Heat Mass Transf 42:671–677
Kumaran V, Kumar AV, Pop I (2010) Transition of MHD boundary layer flow past a stretching sheet. Commun Nonlinear Sci Numer Simul 15:300–311
Prasad KV, Pal D, Umesh V, Rao NSP (2010) The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet. Commun Nonlinear Sci Numer Simul 15:331–344
Magyari E, Keller B (1999) Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J Phys D Appl Phys 32:577–585
Wang CY (1988) Fluid flow due to a stretching cylinder. Phys Fluids 31:466–468
Ishak A, Nazar R, Pop I (2008) Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy Convers Manag 49:3265–3269
Choi S (1995) Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonian flows. In: Siginer DA, Wang HP (eds) Development and applications of non-Newtonian flows. ASME MD, vol 231 and FED, vol 66, pp 99–105
Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7:227–233
Soheil S, Sheikholeslami M, Ganji DD, Gorji-Bandpay M (2012) Natural convection heat transfer in a nanofluid filled semi-annulus enclosure. Int Commun Heat Mass Transf 39:565–574
Domairry D, Sheikholeslami M, Ashorynejad Hamid R, Gorla RSR, Khani M (2012) Natural convection flow of a non-Newtonian nanofluid between two vertical flat plates. Proc IMechE Part N J Nanoeng Nanosyst 225(3):115–122 ©IMechE. doi:10.1177/17403499114334681
Sheikholeslami M, Ganji DD, Ashorynejad HR, Rokni HB (2012) Analytical investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method. Appl Math Mech Engl Ed 33(1):25–36
Sheikholeslami M, Ashorynejad HR, Domairry G, Hashim I (2012) Flow and heat transfer of Cu–water nanofluid between a stretching sheet and a porous surface in a rotating system. J Appl Math, article ID 421320, 19 p. doi:10.1155/2012/421320
Nemati H, Farhadi M, Sedighi K, Ashorynejad HR, Fattahi E (2012) Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the lattice Boltzmann model. Sci Iran B 19(2):303–310
Sheikholeslami M, Gorji-Bandpay M, Ganji DD (2012) Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid. Int Commun Heat Mass Transf. doi:10.1016/j.icheatmasstransfer.2012.05.020
Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018
Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336
Aldos TK, Ali YD (1997) MHD free forced convection from a horizontal cylinder with suction and blowing. Int Commun Heat Mass Transf 24:683–693
Ganesan P, Loganathan P (2003) Magnetic field effect on a moving vertical cylinder with constant heat flux. Heat Mass Transf 39:381–386
Aminossadati SM, Ghasemi B (2009) Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B Fluids 28:630–640
Enright WH, Jackson KR, Norsett SP, Thomsen PG (1986) Interpolants for Runge–Kutta formulas. ACM Trans Math Softw 12:193–218
Fehlberg E (1970) Klassische Runge–Kutta–Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Waermeleitungsprobleme. Computing 6:61–71
Forsythe GE, Malcolm MA, Moler CB (1977) Computer methods for mathematical computations. Prentice Hall, NJ
Shampine LF, Corles RM (2000) Initial value problems for ODEs in problem solving environments. J Comput Appl Math 125(1–2):31–40
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1992) “Runge–Kutta method” and “adaptive step size control for Runge–Kutta.” §16.1 and 16.2 in numerical recipes in FORTRAN: the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, pp 704–716
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The authors wish to express their thanks to the reviewers for the valuable comments and suggestions.
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Ashorynejad, H.R., Sheikholeslami, M., Pop, I. et al. Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field. Heat Mass Transfer 49, 427–436 (2013). https://doi.org/10.1007/s00231-012-1087-6
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DOI: https://doi.org/10.1007/s00231-012-1087-6