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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)

B0 :

Uniform magnetic field (N m−1 A−1)

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

Thermal diffusivity (m2 s−1)

T :

Temperature (K)

C :

Concentration

DB :

Brownian diffusion coefficient (m2 s−1)

DT :

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

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Author information

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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  4. Taseer Muhammad

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Correspondence toTaseer 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 & Applic29, 1555–1562 (2018). https://doi.org/10.1007/s00521-016-2685-x

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