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Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating

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Abstract

In this present study, a numerical investigation has been carried out to discuss the steady, two dimensional flow and heat transfer on micropolar nanofluid over a stretching/shrinking sheet with variable suction or injection in the presence of magnetic field and Newtonian heating. Copper (\( {\text{Cu}} \)), alumina (\( {\text{Al}}_{ 2} {\text{O}}_{ 3} \)) and titanium (\( {\text{TiO}}_{ 2} \)) in water-based micropolar nanofluid has been considered for the present investigation. The solutions of the transformed nonlinear equations have been obtained using Runge–Kutta–Gill procedure together with the shooting method. The results are presented graphically and discussed for various resulting parameters. Dual solutions are found to exist in a certain range of the governing parameters. The thickness of thermal boundary layer for Cu nanofluid is more than that of other nanofluids in the cases of shrinking and stretching sheets. Newtonian heating effect significantly increases the thermal boundary layer thickness for both sheets under investigation.

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Abbreviations

\( B_{0} \) :

Magnetic induction (T)

\( c \) :

Constant defined by Eq. (2.8)

\( C_{f} \) :

Skin friction coefficient

\( C_{{n}} \) :

Wall couple stress

\( c_{\text{p}} \) :

Specific heat at constant pressure (J/kg K)

\( f \) :

Dimensionless stream function

\( f_{w} \) :

Suction/injection parameter

\( g \) :

Dimensionless micro rotation

\( h \) :

Convective heat transfer coefficient

\( j \) :

Microinertia density

\( K \) :

Micropolar or material parameter

\( k \) :

Thermal conductivity (W/mK)

\( M \) :

Magnetic parameter

\( n \) :

Constant defined by Eq. (2.5)

N :

Microrotation component

\( Nu_{x} \) :

Local Nusselt number

\( Pr \) :

Prandtl number

\( q_{w} \) :

Surface heat flux (W/m2)

\( Re_{x} \) :

Local Reynolds number

\( T \) :

Temperature of the fluid (°C)

\( u_{w} \) :

Stretching velocity

\( u,v \) :

Velocity components (m/s)

\( v_{w} \) :

Mass transfer velocity

\( x,y \) :

Dimensionless coordinates

\( \alpha \) :

Thermal diffusivity (m2/s)

\( \gamma \) :

Conjugate parameter for Newtonian heating

\( \delta \) :

Spin-gradient viscosity

\( \eta \) :

Similarity variable

\( \theta \) :

Dimensionless temperature

\( \kappa \) :

Vortex viscosity

\( \lambda \) :

Stretching/shrinking parameter

\( \mu \) :

Thermal viscosity (kg s/m)

\( \upsilon \) :

Kinematic viscosity (m2/s)

\( \rho \) :

Density (kg/m3)

\( \sigma \) :

Electrical conductivity (s/m)

\( \tau_{w} \) :

Wall shear stress

\( \phi \) :

Nanoparticle volume fraction

\( \psi \) :

Stream function (m2/s)

\( f \) :

Base fluid

nf:

Nanofluid

s:

Solid

w:

Condition at the surface

\( \infty \) :

Condition at infinity

′:

Differentiation with respect to \( \eta \)

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Acknowledgements

The authors gratefully acknowledge the reviewers for their constructive comments and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh, 523001, India

    K. Gangadhar

  2. Department of Mathematics, K. S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, 637215, India

    T. Kannan

  3. Department of Mathematics, Vemu Institute of Technology, P. Kothakota, Chittoor, Andhra Pradesh, 517512, India

    P. Jayalakshmi

Authors
  1. K. Gangadhar
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  2. T. Kannan
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Correspondence to T. Kannan.

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Technical Editor: Jader Barbosa Jr.

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Gangadhar, K., Kannan, T. & Jayalakshmi, P. Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating. J Braz. Soc. Mech. Sci. Eng. 39, 4379–4391 (2017). https://doi.org/10.1007/s40430-017-0765-1

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  • DOI: https://doi.org/10.1007/s40430-017-0765-1

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