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An optimal solution for magnetohydrodynamic nanofluid flow over a stretching surface with constant heat flux and zero nanoparticles flux

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Abstract

This article examines the hydromagnetic three-dimensional flow of viscous nanoliquid. A bidirectional linear stretching surface has been used to create the flow. Novel features regarding Brownian motion and thermophoresis have been studied by employing Buongiorno model to examine the slip velocity of nanoparticle. Viscous liquid is electrically conducting subject to uniform applied magnetic field. Problem formulation in boundary-layer region is performed for low magnetic Reynolds number. Simultaneous effects of constant heat flux and zero nanoparticles flux conditions are utilized at boundary. Appropriate transformations correspond to the strongly nonlinear ordinary differential expressions. The resulting nonlinear systems have been solved through the optimal homotopy analysis method. Graphs have been sketched in order to analyze that how the temperature and concentration profiles are affected by various physical parameters. Further the coefficients of skin-friction and heat transfer rate have been numerically computed and discussed. Our findings show that the temperature distribution has a direct relationship with the magnetic parameter. Moreover, the temperature distribution and thermal boundary-layer thickness are higher for hydromagnetic flow in comparison with the hydrodynamic flow.

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Abbreviations

u, v, w :

Velocity components (m s−1)

x, y, z :

Coordinate axes (m)

σ :

Electrical conductivity (S m−1)

\(\rho_{\text{f}}\) :

Density of base fluid (kg m−3)

B 0 :

Uniform magnetic field (N m−1 A−1)

\(\alpha_{\text{m}}\) :

Thermal diffusivity (m2 s−1)

T :

Temperature (K)

C :

Concentration

D B :

Brownian diffusion coefficient (m2 s−1)

D T :

Thermophoretic diffusion coefficient (m2 s−1)

ν :

Kinematic viscosity (m2 s−1)

μ :

Dynamic viscosity (Pa s)

\((\rho c)_{\text{p}}\) :

Effective heat capacity of nanoparticles (J kg−3 K−1)

\((\rho c)_{\text{f}}\) :

Heat capacity of fluid (J kg−3 K−1)

\(T_{\infty }\) :

Ambient fluid temperature (K)

\(C_{\infty }\) :

Ambient fluid concentration

ζ :

Similarity variable

k :

Thermal conductivity (W m−1 K−1)

f, g :

Dimensionless velocities

θ :

Dimensionless temperature

ϕ :

Dimensionless concentration

M :

Magnetic parameter

Pr :

Prandtl number

\(\alpha\) :

Ratio parameter

Le :

Lewis number

\(Re_{x} ,Re_{y}\) :

Local Reynolds numbers

\(Nb\) :

Brownian motion parameter

\(Nt\) :

Thermophoresis parameter

\(C_{{{\text{f}}x}} ,C_{{{\text{f}}y}}\) :

Skin-friction coefficients

\(Nu_{x}\) :

Local Nusselt number

References

  1. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles, USA, ASME, FED 231/MD, vol 66, pp 99–105

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

    Article  Google Scholar 

  3. Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int J Therm Sci 50:1326–1332

    Article  Google Scholar 

  4. Turkyilmazoglu M (2012) Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. Chem Eng Sci 84:182–187

    Article  Google Scholar 

  5. Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Kazi SN, Jomhari N (2014) Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int J Therm Sci 75:204–220

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Sheikholeslami M, Bandpy MG, Ellahi R, Hassan M, Soleimani S (2014) Effects of MHD on Cu-water nanofluid flow and heat transfer by means of CVFEM. J Magn Magn Mater 349:188–200

    Article  Google Scholar 

  8. Sheikholeslami M, Ganji DD, Javed MY, Ellahi R (2015) Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model. J Magn Magn Mater 374:36–43

    Article  Google Scholar 

  9. Malvandi A, Safaei MR, Kaffash MH, Ganji DD (2015) MHD mixed convection in a vertical annulus filled with Al2O3-water nanofluid considering nanoparticle migration. J Magn Magn Mater 382:296–306

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Goodarzi M, Amiri A, Goodarzi MS, Safaei MR, Karimipour A, Languri EM, Dahari M (2015) Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids. Int Commun Heat Mass Transf 66:172–179

    Article  Google Scholar 

  12. Ellahi R, Hassan M, Zeeshan A (2015) Shape effects of nanosize particles in Cu-H2O nanofluid on entropy generation. Int J Heat Mass Transf 81:449–456

    Article  Google Scholar 

  13. Gireesha BJ, Gorla RSR, Mahanthesh B (2015) Effect of suspended nanoparticles on three-dimensional MHD flow, heat and mass transfer of radiating Eyring–Powell fluid over a stretching sheet. J. Nanofluids 4:474–484

    Article  Google Scholar 

  14. Hayat T, Imtiaz M, Alsaedi A (2015) MHD 3D flow of nanofluid in presence of convective conditions. J Mol Liq 212:203–208

    Article  Google Scholar 

  15. Togun H, Ahmadi G, Abdulrazzaq T, Shkarah AJ, Kazi SN, Badarudin A, Safaei MR (2015) Thermal performance of nanofluid in ducts with double forward-facing steps. J Taiwan Inst Chem Eng 47:28–42

    Article  Google Scholar 

  16. Hayat T, Muhammad T, Shehzad SA, Chen GQ, Abbas IA (2015) Interaction of magnetic field in flow of Maxwell nanofluid with convective effect. J Magn Magn Mater 389:48–55

    Article  Google Scholar 

  17. Sheikholeslami M, Ellahi R (2015) Electrohydrodynamic nanofluid hydrothermal treatment in an enclosure with sinusoidal upper wall. Appl Sci 5:294–306

    Article  Google Scholar 

  18. Khan U, Ahmed N, Mohyud-Din ST, Bin-Mohsin B (2016) Nonlinear radiation effects on MHD flow of nanofluid over a nonlinearly stretching/shrinking wedge. Neural Comput Appl. doi:10.1007/s00521-016-2187-x

    Google Scholar 

  19. Prabhakar B, Bandari S, Haq RU (2016) Impact of inclined Lorentz forces on tangent hyperbolic nanofluid flow with zero normal flux of nanoparticles at the stretching sheet. Neural Comput Appl. doi:10.1007/s00521-016-2601-4

    Google Scholar 

  20. Hayat T, Ullah I, Muhammad T, Alsaedi A, Shehzad SA (2016) Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions. Chin Phys B 25:074701

    Article  Google Scholar 

  21. Rahman SU, Ellahi R, Nadeem S, Zia QMZ (2016) Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis. J Mol Liq 218:484–493

    Article  Google Scholar 

  22. Akbarzadeh M, Rashidi S, Bovand M, Ellahi R (2016) A sensitivity analysis on thermal and pumping power for the flow of nanofluid inside a wavy channel. J Mol Liq 220:1–13

    Article  Google Scholar 

  23. Bashirnezhad K, Bazri S, Safaei MR, Goodarzi M, Dahari M, Mahian O, Dalkılıça AS, Wongwises S (2016) Viscosity of nanofluids: a review of recent experimental studies. Int Commun Heat Mass Transf 73:114–123

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Hayat T, Waqas M, Khan MI, Alsaedi A (2016) Analysis of thixotropic nanomaterial in a doubly stratified medium considering magnetic field effects. Int J Heat Mass Transf 102:1123–1129

    Article  Google Scholar 

  26. Sakiadis BC (1961) Boundary-layer behaviour on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J 7:221–225

    Article  Google Scholar 

  27. Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645–647

    Article  Google Scholar 

  28. Wang CY (1984) The three-dimensional flow due to a stretching flat surface. Phys Fluids 27:1915–1917

    Article  MathSciNet  MATH  Google Scholar 

  29. Ariel PD (2007) The three-dimensional flow past a stretching sheet and the homotopy perturbation method. Comput Math Appl 54:920–925

    Article  MathSciNet  MATH  Google Scholar 

  30. Xu H, Liao SJ, Pop I (2007) Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Eur J Mech B Fluids 26:15–27

    Article  MathSciNet  MATH  Google Scholar 

  31. Hayat T, Qasim M, Abbas Z (2010) Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space. Commun Nonlinear Sci Numer Simul 15:2375–2387

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu IC, Wang HH, Peng YF (2013) Flow and heat transfer for three-dimensional flow over an exponentially stretching surface. Chem Eng Commun 200:253–268

    Article  Google Scholar 

  33. Hayat T, Muhammad T, Shehzad SA, Alsaedi A (2015) Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink. Int J Numer Methods Heat Fluid Flow 25:762–781

    Article  MathSciNet  MATH  Google Scholar 

  34. Liao SJ (2010) An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simul 15:2003–2016

    Article  MathSciNet  MATH  Google Scholar 

  35. Dehghan M, Manafian J, Saadatmandi A (2010) Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer Methods Partial Differ Equ 26:448–479

    MathSciNet  MATH  Google Scholar 

  36. Turkyilmazoglu M (2012) Solution of the Thomas–Fermi equation with a convergent approach. Commun Nonlinear Sci Numer Simul 17:4097–4103

    Article  MathSciNet  MATH  Google Scholar 

  37. Abbasbandy S, Hayat T, Alsaedi A, Rashidi MM (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Oldroyd-B fluid. Int J. Numer Methods Heat Fluid Flow 24:390–401

    Article  MathSciNet  MATH  Google Scholar 

  38. Zeeshan A, Majeed A, Ellahi R (2016) Effect of magnetic dipole on viscous ferro-fluid past a stretching surface with thermal radiation. J Mol Liq 215:549–554

    Article  Google Scholar 

  39. Hayat T, Hussain Z, Muhammad T, Alsaedi A (2016) Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness. J Mol Liq 221:1121–1127

    Article  Google Scholar 

  40. Hayat T, Muhammad T, Shehzad SA, Alsaedi A (2016) On three-dimensional boundary layer flow of Sisko nanofluid with magnetic field effects. Adv Powder Technol 27:504–512

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    Tasawar Hayat, Zakir Hussain & Taseer Muhammad

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

Authors
  1. Tasawar Hayat
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  2. Zakir Hussain
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  3. Ahmed Alsaedi
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Correspondence to Taseer Muhammad.

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Hayat, T., Hussain, Z., Alsaedi, A. et al. An optimal solution for magnetohydrodynamic nanofluid flow over a stretching surface with constant heat flux and zero nanoparticles flux. Neural Comput & Applic 29, 1555–1562 (2018). https://doi.org/10.1007/s00521-016-2685-x

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