, Volume 50, Issue 8, pp 2023–2035 | Cite as

MHD convective stagnation-point flow of nanofluids over a non-isothermal stretching sheet with induced magnetic field

  • Dulal Pal
  • Gopinath Mandal


This paper is concern with the investigation of buoyancy-driven hydromagnetic mixed convection stagnation-point flow of nanofluids over a stretching sheet in the presence of induced magnetic field. Three types of nanofluids namely, Cu–water, \(\hbox {Al}_2\hbox {O}_3\)–water, \(\hbox {TiO}_2\)–water are considered. The resulting system is solved numerically by a fifth-order Runge–Kutta–Fehlberg scheme with shooting technique. Numerical results are validated by comparing the present results with previously published results. Investigations predict that the effects of magnetic field is to increase induced magnetic field, whereas reverse effects is seen by increasing the volume fraction of the nanoparticles.


Nanofluids Stagnation-point flow Induced magnetic field Mixed convection Nanoparticles Stretching sheet 

List of symbols


Skin friction coefficient


Grashof number


Magnetic induction vector


Uniform magnetic field at infinity upstream


Magnetic component at x-direction


Magnetic component at y-direction


Current density


Characteristic length


Magnetic parameter


Local Nusselt number


Fluid pressure


Magnetohydrodynamic pressure


Thermal Prandtl number


Magnetic Prandtl number


Reynolds number


Suction/injection parameter


Temperature of the fluid

\(T_{\infty }\)

Free stream temperature


Temperature at the wall


Velocity component in x-direction


Stretching/shrinking sheet velocity


Free stream velocity of the nanofluid


Fluid velocity


Velocity component in y-direction


Direction along and perpendicular to the sheet, respectively

Greek symbols

\({\alpha _{nf}}\)

Effective thermal diffusivity of the nanofluid

\({\alpha _f}\)

Fluid thermal diffusivity

\(\alpha _1\)

Magnetic diffusivity

\({\beta }\)

Coefficient of thermal expansion

\({{\beta }_{nf}}\)

Thermal expansion of nanofluid

\({\beta _f}\)

Thermal expansion coefficient of the fluid

\({\beta _s}\)

Thermal expansion coefficient of the nanoparticles

\({\phi } \)

Solid volume fraction of the nanoparticles

\({\eta }\)

Similarity variable

\({\varLambda }\)

Buoyancy parameter

\(\mu _0\)

Magnetic permeability

\({\mu _{nf}}\)

Effective dynamic viscosity of the nanofluid

\({\mu _f}\)

Dynamic viscosity of the fluid

\({\nu _f}\)

Kinematic viscosity of the fluid

\({\rho _{nf}}\)

Effective density of the nanofluid

\(\theta \)

Dimensionless temperature of the fluid

\({\psi }\)

Stream function

\(\sigma \)

Electric conductivity

\(\kappa _{nf}\)

Effective thermal conductivity of the nanofluid

\(\kappa _f\)

Thermal conductivity of the fluid



Differentiation with respect to y










We are very thankful to the Editor and the referees for their valuable comments and suggestions, which have definitely improved the quality of the paper considerably.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Siksha BhavanaVisva-Bharati UniversitySantiniketanIndia
  2. 2.Siksha SatraVisva-Bharati UniversitySriniketanIndia

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