Numerical Solutions for Radiative Heat Transfer in Ferrofluid Flow due to a Rotating Disk: Tiwari and Das Model

M. Mustafa 1 , Junaid Ahmad Khan 2 , T. Hayat 3  and A. Alsaedi 4
  • 1 School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), 44000, Islamabad, Pakistan
  • 2 Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), 44000, Islamabad, Pakistan
  • 3 Department of Mathematics, Quaid-I-Azam University 45320, 44000, Islamabad, Pakistan
  • 4 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, Saudi Arabia
M. Mustafa
  • Corresponding author
  • School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan
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, Junaid Ahmad Khan
  • Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan
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, T. Hayat
  • Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan
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and A. Alsaedi
  • Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia
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Abstract

In this paper, we explore the von-Kármán infinite disk problem for the situation where ferrofluid resides in the space above the rotating disk. Furthermore, flow field is influenced by axial magnetic field. In this study, we treat water as the base fluid which consists of homogeneous suspensions of Fe3O4 ferromagnetic particles. The main motivation here is to resolve heat transfer problem in the existence of non-linear radiative heat transfer. With the aid of von-Kármán relations, the equations of fluid motion and heat transfer are changed into a set of self-similar differential equations. These equations are dealt by an implicit finite-difference method with high precision. The results reveal that wall heat transfer rate can be improved by increasing solid volume fraction of ferromagnetic particles. Drag coefficient at the disk and heat transfer rate are increased as the strength of Lorentz force is enhanced. Viscous dissipation effect has an important part in improving heart transfer process which is vital in some applications. The results demonstrate that cooling capability of magnetite–water nanofluid is much superior to the conventional coolants. An excellent correlation of present results with the previous published articles is found in the all the cases.

  • [1]

    T. Von Kármán, Uberlaminare und turbulentereibung, Z. Angew. Math. Mech. 1 (1921), 233–252.

  • [2]

    W.G. Cochran, The flow due to a rotating disk, Proc. Camb. Phil. Soc. 30 (1934), 365–375.

    • Crossref
    • Export Citation
  • [3]

    K. Millsaps and K. Pohlhausen, Heat transfer by laminar flow from a rotating disk, J Aeronaut. Sci. 19 (1952), 120–126.

    • Crossref
    • Export Citation
  • [4]

    J.T. Stuart, On the effects of uniform suction on the steady flow due to a rotating disk, Quart. J. Mech. Appl. Math. 7 (1954), 446–457.

    • Crossref
    • Export Citation
  • [5]

    M.G. Roger and G.N. Lance, The rotationally symmetric flow of a viscous fluid in presence of infinite rotating disc, J. Fluid Mech. 7 (1960), 617–631.

    • Crossref
    • Export Citation
  • [6]

    H.A. Attia, Unsteady MHD flow near a rotating porous disk with uniform suction or injection, Fluid Dynam. Res. 23 (1998), 283–290.

    • Crossref
    • Export Citation
  • [7]

    H.A. Attia and A.L. Aboul-Hassan, Effect of Hall current on the unsteady MHD flow due to a rotating disk with uniform suction or injection, Appl. Math. Model. 25 (2001), 1089–1098.

    • Crossref
    • Export Citation
  • [8]

    H.A. Attia, Steady flow over a rotating disk in porous medium with heat transfer, Nonlinear Anal. Modell. Control 14 (2009), 21–26.

    • Crossref
    • Export Citation
  • [9]

    N. Bachok, A. Ishak and I. Pop, Flow and heat transfer over a rotating porous disk in a nanofluid, Physica B 406 (2011), 1767–1772.

    • Crossref
    • Export Citation
  • [10]

    M.M. Rashidi, S.A. Mohimanian Pour, T. Hayat and S. Obaidat, Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method, Comp. Fluids 54 (2012), 1–9.

    • Crossref
    • Export Citation
  • [11]

    M. Turkyilmazoglu, MHD fluid flow and heat transfer due to a shrinking rotating disk, Comp. Fluids 90 (2014), 51–56.

    • Crossref
    • Export Citation
  • [12]

    M. Turkyilmazoglu, Nanofluid flow and heat transfer due to a rotating disk, Comp. Fluids 94 (2014), 139–146.

    • Crossref
    • Export Citation
  • [13]

    J.A. Khan, M. Mustafa, T. Hayat and A. Alsaedi, A revised model to study the MHD nanofluid flow and heat transfer due to rotating disk: Numerical solutions, Neural Comput. Appl. (2016), doi: .

    • Crossref
    • Export Citation
  • [14]

    A.J. Hunt, Small particle heat exchangers, Lawrence Berkeley Lab Report Number LBL-7841.

  • [15]

    J. Buongiorno and L.W. Hu, Nanofluid heat transfer enhancement for nuclear reactor application, Proceedings of the ASME 2009 2nd Micro/Nanoscale Heat & Mass Transfer International Conference, MNHMT, 2009. DOI: .

    • Crossref
    • Export Citation
  • [16]

    G. Huminic and A. Huminic, Application of nanofluids in heat exchangers: A review, Renew. Sust. Ener. Rev. 16 (2012), 5625–5638.

    • Crossref
    • Export Citation
  • [17]

    J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006), 240–250.

    • Crossref
    • Export Citation
  • [18]

    R.K. Tiwari and M.K. Das, Heat transfer augmentation in a two-sided lid driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass. Transf. 50 (2007), 2002–2018.

    • Crossref
    • Export Citation
  • [19]

    A.V. Kuznetsov and D.A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci. 49 (2010), 243–247.

    • Crossref
    • Export Citation
  • [20]

    D.A. Nield and A.V. Kuznetsov, The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, Int. J. Heat Mass Transf. 52 (2009), 5792–5795.

    • Crossref
    • Export Citation
  • [21]

    W.A. Khan and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat Mass Transf. 53 (2010), 2477–2483.

    • Crossref
    • Export Citation
  • [22]

    M. Mustafa, T. Hayat, I. Pop, S. Asghar and S. Obaidat, Stagnation-point flow of a nanofluid towards a stretching sheet, Int. J. Heat Mass Transf. 54 (2011), 5588–5594.

    • Crossref
    • Export Citation
  • [23]

    M. Mustafa, M.A. Farooq, T. Hayat and A. Alsaedi, Numerical and series solutions for stagnation-point flow of nanofluid over an exponentially stretching sheet, PLoS ONE 8 (2013), doi: .

    • Crossref
    • PubMed
    • Export Citation
  • [24]

    M. Mustafa, T. Hayat and A. Alsaedi, Unsteady boundary layer flow of nanofluid past an impulsively stretching sheet, J. Mech. 29 (2013), 423–432.

    • Crossref
    • Export Citation
  • [25]

    O.D. Makinde, W.A. Khan and Z.H. Khan, Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet, Int. J. Heat Mass Transf. 62 (2013), 526–533.

    • Crossref
    • Export Citation
  • [26]

    A.V. Kuznetsov and D.A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate: A revised model, Int. J. Therm. Sci. 77 (2014), 126–129.

    • Crossref
    • Export Citation
  • [27]

    A. Mushtaq, M. Mustafa, T. Hayat and A. Alsaedi, Nonlinear radiative heat transfer in the flow of nanofluid due to solar energy: A numerical study, J. Taiwan Inst. Chem. Eng. 45 (2014), 1176–1183.

    • Crossref
    • Export Citation
  • [28]

    M.M. Rashidi, N. Freidoonimehr, A. Hosseini, O.A. Bég and T.K. Hung, Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration, Meccan 49 (2014), 469–482.

    • Crossref
    • Export Citation
  • [29]

    M.M. Rashidi, S. Abelman and N. Freidoonimehr, Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid, Int. J. Heat Mass Transf. 62 (2013), 515–525.

    • Crossref
    • Export Citation
  • [30]

    M. Mustafa, T. Hayat and A. Alsaedi, Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions, Int. J. Num. Meth. Heat Fluid Flow 23 (2013), 945–959.

    • Crossref
    • Export Citation
  • [31]

    M. Turkyilmazoglu and I. Pop, 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 (2013), 167–171.

    • Crossref
    • Export Citation
  • [32]

    M. Sheikholeslami and M. Gorji-Bandpy, Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field, Powder Technol. 256 (2014), 490–498.

    • Crossref
    • Export Citation
  • [33]

    M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji and S. Soleimani, Thermal management for free convection of nanofluid using two phase model, J. Mol. Liq. 194 (2014), 179–187.

    • Crossref
    • Export Citation
  • [34]

    M.A. Sheremet and I. Pop, Free convection in a triangular cavity filled with a porous medium saturated by a nanofluid: Buongiorno’s mathematical model, Int. J. Num. Meth. Heat Fluid Flow 25 (2015), 1138–1161.

    • Crossref
    • Export Citation
  • [35]

    S. Dinarvand, R. Hosseini and I. Pop, Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model, Int. J. Num. Meth. Heat Fluid Flow 25 (2015), 1176–1197.

    • Crossref
    • Export Citation
  • [36]

    M. Mustafa and A. Mushtaq, Model for natural convective flow of viscoelastic nanofluid past an isothermal vertical plate, Eur. Phys. J. Plus 130 (2015), doi: .

    • Crossref
    • Export Citation
  • [37]

    T. Hayat, T. Muhammad, S.A. Shehzad and A. Alsaedi, On magnetohydrodynamic flow of nanofluid due to a rotating disk with slip effect: A numerical study, Comput. Meth. Appl. Mech. Eng. 315 (2017), 467–477.

    • Crossref
    • Export Citation
  • [38]

    T. Hayat, T. Muhammad, S.A. Shehzad and A. Alsaedi, An analytical solution for magnetohydrodynamic Oldroyd-B nanofluid flow induced by a stretching sheet with heat generation/absorption, Int. J. Therm. Sci. 111 (2017), 274–288.

    • Crossref
    • Export Citation
  • [39]

    T. Hayat, F. Haider, T. Muhammad and A. Alsaedi, On Darcy-Forchheimer flow of viscoelastic nanofluids: A comparative study, J. Mol. Liq. 233 (2017), 278–287.

    • Crossref
    • Export Citation
  • [40]

    T. Hayat, A. Aziz, T. Muhammad and A. Alsaedi, On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface, Int. J. Heat Mass Transf. 100 (2016), 566–572.

    • Crossref
    • Export Citation
  • [41]

    T. Hayat, T. Muhammad, A. Alsaedi and M.S. Alhuthali, Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation, J. Magn. Magn. Mater. 385 (2015), 222–229.

    • Crossref
    • Export Citation
  • [42]

    N.S. Bondareva, M.A. Sheremet and I. Pop, Magnetic field effect on the unsteady natural convection in a right-angle trapezoidal cavity filled with a nanofluid: Buongiorno’s mathematical model, Int. J. Numer. Meth. Heat Fluid Flow 25 (2015), 1924–1946.

    • Crossref
    • Export Citation
  • [43]

    M.A. Sheremet, I. Pop and N.C. Roşca, Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno’s mathematical model, J. Taiwan Inst. Chem. Eng. 61 (2016), 211–222.

    • Crossref
    • Export Citation
  • [44]

    M.A. Sheremet, H.F. Oztop and I. Pop, MHD natural convection in an inclined wavy cavity with corner heater filled with a nanofluid, J. Magn. Magn. Mater. 416 (2016), 37–47.

    • Crossref
    • Export Citation
  • [45]

    T. Cebeci and P. Bradshaw, Physical and computational aspects of convective heat transfer, Springer-Verlag, New York, 1988. (Chapter 13).

  • [46]

    H.C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys. 20 (1952), 571–581.

    • Crossref
    • Export Citation
  • [47]

    K. Khanafer, K. Vafai and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass. Transf. 46 (2003), 3639–3653.

    • Crossref
    • Export Citation
  • [48]

    J.C. Maxwell, A treatise on electricity and magnetism, 3rd Edition, Oxford, Clarendon Press, 1904.

  • [49]

    N. Kelson and A. Desseaux, Note on porous rotating disk flow, Anziam J. 42 (2000), 837–855.

    • Crossref
    • Export Citation
  • [50]

    M. Turkyilmazoglu, Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian decomposition method, Mediterranean J. Math. 13 (2016), 4019–4037.

    • Crossref
    • Export Citation
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