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Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 1, pp 533–549 | Cite as

Effects of radiation on mixed convection stagnation-point flow of MHD third-grade nanofluid over a vertical stretching sheet

  • Bijan Golafshan
  • Asghar B. RahimiEmail author
Article

Abstract

This paper considers the problem of the two-dimensional mixed convection stagnation-point flow of a magnetohydrodynamic non-Newtonian nanofluid bounded by a vertical stretching sheet. Convective surface boundary and zero surface nanoparticle mass flux conditions are employed. The effects of buoyancy, radiation, Brownian motion, thermophoresis, and viscous dissipation are taken into account. The stretching velocity is assumed to vary linearly with the distance from the stagnation point. The fluid is electrically conducted with uniform magnetic field, and the work done due to deformation is taken into consideration. The three-coupled partial differential boundary layer equations are reduced to ordinary differential equations by using proper similarity transformations. Analytical solution by homotopy analysis method is obtained. Effects of different physical parameters on the dynamics of the problem are analyzed and discussed.

Keywords

Non-Newtonian fluid Third-grade fluid Homotopy analysis method Stretching sheet Boundary layer equations 

List of symbols

\( {\mathbf{A}}_{\text{i}} \)

Kinematic tensors (–)

\( a,c \)

Positive constants (s−1)

\( {\mathbf{B}} \)

Magnetic field vector (T)

\( Bi \)

Biot number (–)

\( B_{0} \)

Magnetic field component (T)

\( b \)

Body forces (N m−3)

\( C \)

Nanoparticles concentration (kg m−3)

\( C_{\infty } \)

Ambient fluid concentration (kg m−3)

\( C_{\text{f}} \)

Skin friction coefficient (–)

\( D_{\text{B}} \)

Brownian diffusion coefficient (m2 s−1)

\( D_{\text{T}} \)

Thermophoresis diffusion coefficient (m2 s−1)

\( Ec \)

Eckert number (–)

\( f \)

Dimensionless velocity function (–)

\( g \)

Gravity acceleration (m s−2)

\( G_{\text{T}} \)

Local Grashof number (–)

\( h_{\text{f}} \)

Convection coefficient (W m−2K−1)

\( {\mathbf{j}} \)

Electric current (A)

\( K \)

Viscoelastic parameter (–)

\( k^{*} \)

Mean absorption coefficient (–)

\( L \)

Cross-viscous parameter (–)

\( M \)

Magnetic field parameter (–)

\( Nb \)

Brownian motion parameter (–)

\( Nt \)

Thermophoresis parameter (–)

\( Nu_{\text{x}} \)

Local Nusselt number (–)

\( Pr \)

Prandtl number (–)

\( Re_{\text{x}} \)

Local Reynolds number (–)

\( R_{\text{d}} \)

Radiation parameter (–)

\( {\mathbf{T}} \)

Cauchy stress tensor (–)

\( T_{\text{f}} \)

Hot fluid temperature (K)

\( T_{\infty } \)

Ambient temperature (K)

\( U_{\infty } \)

External flow velocity (m s−1)

\( (u,v) \)

Velocity components (m s−1)

\( u_{\text{w}} \)

Stretching sheet velocity (m s−1)

\( (x,y) \)

Cartesian coordinate components (m)

Greek symbols

\( \alpha \)

Thermal diffusivity (m2 s−1)

\( \alpha_{\text{i}} ,\beta_{\text{i}} \)

Material constants (–)

\( \beta \)

Third-grade fluid parameter (–)

\( \beta_{\text{c}} \)

Coefficient of mass expansion (K−1)

\( \beta_{\text{T}} \)

Coefficient of thermal expansion (K−1)

\( \phi \)

Dimensionless concentration function (–)

\( \eta \)

Similarity variable (–)

\( \mu \)

Viscosity (N s m−2)

\( \nu \)

Kinematic viscosity (m2 s−1)

\( \theta \)

Dimensionless temperature function (–)

\( \rho \)

Density (kg m−3)

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

Density of the base fluid (kg m−3)

\( \rho_{\text{p}} \)

Density of the nanoparticles (kg m−3)

\( \sigma \)

Electrical conductivity of fluid (S m−1)

\( \sigma^{*} \)

Stefan–Boltzmann constant (W m−2 K−4)

Notes

Acknowledgements

Financial support of Ferdowsi University of Mashhad under Contract No. 2/42929 is acknowledged.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringFerdowsi University of MashhadMashhadIran

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