Neural Computing and Applications

, Volume 30, Issue 3, pp 957–964 | Cite as

A revised model to study the MHD nanofluid flow and heat transfer due to rotating disk: numerical solutions

  • Junaid Ahmad Khan
  • M. MustafaEmail author
  • T. Hayat
  • A. Alsaedi
Original Article


Here our main interest is to present numerical simulations for magneto-nanofluid flow and heat transfer near a rotating disk. Buongiorno model, featuring the novel aspects of Brownian motion and thermophoresis, is accounted. Heat dissipation effect is preserved in the energy balance equation. We take into account more realistic wall condition which requires passive control of nanoparticle concentration at the disk. The traditional Von Karman relations have been invoked to attain self-similar differential system. Keller–Box method has been implemented to compute similarity solutions of the problem. Streamlines are prepared in both two and three dimensions for adequate flow visualization. The behavior of involved parameters on the flow fields is examined graphically. It is predicted that the torque required to maintain disk in steady rotation increases when magnetic field effects are enhanced. Fluid flow in the radial, azimuthal and vertical directions is opposed by the magnetic field strength. Thermophoresis effect enhances temperature and reduces heat flux from the disk. However, Brownian diffusion has a marginal influence on temperature distribution. Heat transfer coefficient is reduced due to the inclusion of heat dissipation terms. Present results are consistent with those of the available studies in a limiting situation.


Rotating disk Nanoparticle Heat transfer Keller–Box method Brownian motion Magnetic field 


  1. 1.
    Von Kármán T (1921) Uberlaminare und turbulentereibung. Z Angew Math Mech 1:233–252CrossRefGoogle Scholar
  2. 2.
    Millsaps K, Pohlhausen K (1952) Heat transfer by laminar flow from a rotating disk. J Aeronaut Sci 19:120–126MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Batchelor GK (1951) Note on the class of solutions of the Navier–Stokes equations representing steady non-rotationally symmetric flow. Q J Mech Appl Math 4:29–41CrossRefzbMATHGoogle Scholar
  4. 4.
    Nanda RS (1960) Revolving flow of an incompressible fluid past a porous plate. J Sci Eng Res 5:59–64MathSciNetGoogle Scholar
  5. 5.
    Owens JM, Rogers RH (1989) Flow and heat transfer in rotating disk systems. Research Studies Press Ltd, Wiley, LondonGoogle Scholar
  6. 6.
    Jasmine H, Gajjar JSB (2005) Absolute instability of the von Karman, Bödewadt and Ekman flows between a rotating disc and a stationary lid. Philos Trans R Soc A 363:1131–1144CrossRefzbMATHGoogle Scholar
  7. 7.
    Attia HA (1998) Unsteady MHD flow near a rotating porous disk with uniform suction or injection. Fluid Dyn Res 23:283–290CrossRefGoogle Scholar
  8. 8.
    Attia HA (2009) Steady flow over a rotating disk in porous medium with heat transfer. Nonlinear Anal Model Control 14:21–26zbMATHGoogle Scholar
  9. 9.
    Bachok N, Ishak A, Pop I (2011) Flow and heat transfer over a rotating porous disk in a nanofluid. Phys B 406:1767–1772CrossRefGoogle Scholar
  10. 10.
    Rashidi MM, Mohimanian Pour SA, Hayat T, Obaidat S (2012) Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method. Comput Fluids 54:1–9MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Turkyilmazoglu M, Senel P (2013) Heat and mass transfer of the flow due to a rotating rough and porous disk. Int J Thermal Sci 63:146–158CrossRefGoogle Scholar
  12. 12.
    Turkyilmazoglu M (2014) Nanofluid flow and heat transfer due to a rotating disk. Comput Fluids 94:139–146MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Turkyilmazoglu M (2014) MHD fluid flow and heat transfer due to a shrinking rotating disk. Comput Fluids 90:51–56MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Shafique Z, Mustafa M, Mushtaq A (2016) Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Results Phys 6:627–633CrossRefGoogle Scholar
  15. 15.
    Mushtaq A, Mustafa M, Hayat T, Alsaedi A (2016) Numerical study for rotating flow of nanofluids caused by an exponentially stretching sheet. Adv Powder Technol 27:2223–2231CrossRefGoogle Scholar
  16. 16.
    Ahmad R, Mustafa M (2016) Model and comparative study for rotating flow of nanofluids due to convectively heated exponentially stretching sheet. J Mol Liq 220:635–641CrossRefGoogle Scholar
  17. 17.
    Mustafa M, Ahmad R, Hayat T, Alsaedi A (2016) Rotating flow of viscoelastic fluid with nonlinear thermal radiation: a numerical study. Neural Comput Appl. doi: 10.1007/s00521-016-2462-x Google Scholar
  18. 18.
    Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 231:99–105Google Scholar
  19. 19.
    Kakać S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187–3196CrossRefzbMATHGoogle Scholar
  20. 20.
    Wong KV, Leon OD (2010) Applications of nanofluids: current and future. Adv Mech Eng. Article ID 519659Google Scholar
  21. 21.
    Saidur R, Leong KY, Mohammad HA (2011) A review on applications and challenges of nanofluids. Renew Sustain Energy Rev 15:1646–1668CrossRefGoogle Scholar
  22. 22.
    Wen D, Lin G, Vafaei S, Zhang K (2011) Review of nanofluids for heat transfer applications. Particuology 7:141–150CrossRefGoogle Scholar
  23. 23.
    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 50:2002–2018CrossRefzbMATHGoogle Scholar
  24. 24.
    Kandelousi MS (2014) KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel. Phys Lett A 378:3331–3339CrossRefzbMATHGoogle Scholar
  25. 25.
    Sheikholeslami M, Rashidi MM, Hayat T, Ganji DD (2016) Free convection of magnetic nanofluid considering MFD viscosity effect. J Mol Liq 218:393–399CrossRefGoogle Scholar
  26. 26.
    Sheikholeslami M, Hayat T, Alsaedi A (2016) MHD free convection of Al2O3–water nanofluid considering thermal radiation: a numerical study. Int J Heat Mass Transf 96:513–524CrossRefGoogle Scholar
  27. 27.
    Sheikholeslami M, Chamkha AJ (2016) Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall. Numer Heat Transf Part A 69:781–793CrossRefGoogle Scholar
  28. 28.
    Sheikholeslami M, Ashorynejad HR, Rana P (2016) Lattice Boltzmann simulation of nanofluid heat transfer enhancement and entropy generation. J Mol Liq 214:86–95CrossRefGoogle Scholar
  29. 29.
    Sheikholeslami M, Vajravelu K, Rashidi MM (2016) Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int J Heat Mass Transf 92:339–348CrossRefGoogle Scholar
  30. 30.
    Sheikholeslami M, Ellahi R (2015) Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. Int J Heat Mass Transf 89:799–808CrossRefGoogle Scholar
  31. 31.
    Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250CrossRefGoogle Scholar
  32. 32.
    Nield DA, Kuznetsov AV (2009) The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 52:5792–5795CrossRefzbMATHGoogle Scholar
  33. 33.
    Turkyilmazoglu M, Pop I (2013) Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect. Int J Heat Mass Transf 59:167–171CrossRefGoogle Scholar
  34. 34.
    Nield DA, Kuznetsov AV (2014) Thermal instability in a porous medium layer saturated by a nanofluid: a revised model. Int J Heat Mass Transf 68:211–214CrossRefGoogle Scholar
  35. 35.
    Kuznetsov AV, Nield DA (2013) The Cheng–Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: a revised model. Int J Heat Mass Transf 65:682–685CrossRefGoogle Scholar
  36. 36.
    Rashidi MM, Freidoonimehr N, Hosseini A, Bég OA, Hung TK (2014) Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration. Meccan 49:469–482CrossRefzbMATHGoogle Scholar
  37. 37.
    Sheikholeslami M, Ganji DD (2014) Three dimensional heat and mass transfer in a rotating system using nanofluid. Powder Technol 253:789–796CrossRefGoogle Scholar
  38. 38.
    Khan JA, Mustafa M, Hayat T, Asif Farooq M, Alsaedi A, Liao SJ (2014) On model for three-dimensional flow of nanofluid: an application to solar energy. J Mol Liq 194:41–47CrossRefGoogle Scholar
  39. 39.
    Malvandi A, Ganji DD (2014) Magnetic field effect on nanoparticles migration and heat transfer of water/alumina nanofluid in a channel. J Magn Magn Mater 362:172–179CrossRefGoogle Scholar
  40. 40.
    Mustafa M, Khan JA, Hayat T, Alsaedi A (2015) Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet. Int J Non-Linear Mech 71:22–29CrossRefGoogle Scholar
  41. 41.
    Sheremet MA, Pop I (2015) Free convection in a triangular cavity filled with a porous medium saturated by a nanofluid: Buongiorno’s mathematical model. Int J Numer Methods Heat Fluid Flow 25:1138–1161MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Rahman MM, Grosan T, Pop I (2016) Oblique stagnation-point flow of a nanofluid past a shrinking sheet. Int J Numer Methods Heat Fluid Flow 26:189–213MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Rashidi MM, Nasiri M, Khezerloo M, Laraqi N (2016) Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. J Magn Magn Mater 401:159–168CrossRefGoogle Scholar
  44. 44.
    Ahmad R, Mustafa M, Hayat T, Alsaedi A (2016) Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet. J Magn Magn Mater 407:69–74CrossRefGoogle Scholar
  45. 45.
    Hayat T, Aziz A, Muhammad T, Ahmad B (2016) On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet. J Magn Magn Mater 408:99–106CrossRefGoogle Scholar
  46. 46.
    Kelson N, Desseaux A (2000) Note on porous rotating disk flow. ANZIAM J 42:837–855MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Junaid Ahmad Khan
    • 1
  • M. Mustafa
    • 2
    Email author
  • T. Hayat
    • 3
    • 4
  • A. Alsaedi
    • 4
  1. 1.Research Centre for Modeling and Simulation (RCMS)National University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.School of Natural Sciences (SNS)National University of Sciences and Technology (NUST)IslamabadPakistan
  3. 3.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  4. 4.Nonlinear Analysis and Applied Mathematics (NAAM) Research GroupKing Abdulaziz UniversityJeddahSaudi Arabia

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