Carbon nanotubes effects in magneto nanofluid flow over a curved stretching surface with variable viscosity

  • S. Nadeem
  • Z. Ahmed
  • S. Saleem
Technical Paper


The present study investigates the influence of temperature dependent viscosity on dynamics of pressure driven nanofluid flow over a curved surface. A uniform applied magnetic field perpendicular to the surface is taken into consideration. Governing nonlinear partial differential equations are modeled with the help of boundary layer approximation. Suitable similarity transformations are used to convert governing equations into nonlinear ordinary differential equations. These highly nonlinear ordinary differential equations are then solved with the help of a second order implicit finite difference scheme. Graphical and numerical results depict the impact of temperature sensitive viscosity and other physical parameters on flow of nanofluid. Viscosity parameter evidently resist the flow velocity and rise the temperature distribution in the nanofluid. It also increases the Skin friction near the boundary of the fluid.

LIst of symbols

\( u, v \)

Velocities along s and r axis, respectively

\( {\rho_{nf}}, {\mu_{nf}} \)

Effective density and dynamic viscosity of nanofluid

\( p \)

Fluid pressure

\( B\left( t \right), \sigma \)

Magnetic field and electric charge density, respectively

\( {\sigma_e} \)

Stefan Boltzmann constant

\( \kappa \)

Curvature parameter

\( T \)

Fluid temperature

\( {T_w}, {T_\infty } \)

Temperature at the boundary and at far away, respectively

\( f, \theta \)

Dimensionless velocity and temperature, respectively

\( {\theta_r} \)

Dimensionless Variable viscosity parameter

\( {K_{nf}}, {\alpha_{nf}} \)

Thermal conductivity and diffusivity of nanofluid

\( \phi \)

Volume fraction of CNT

\( {\beta_R} \)

Mean absorption constant

\( M, Pr \)

Magnetic parameter and Prandtl number, respectively



The authors would like to express their gratitude to King Khalid University, Abha 61413, Saudi Arabia for providing administrative and technical support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam University, 45320IslamabadPakistan
  2. 2.Department of Mathematics, College of SciencesKing Khalid UniversityAbhaSaudi Arabia

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