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On MHD radiative Jeffery nanofluid flow with convective heat and mass boundary conditions

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Abstract

The prime objective of present exploration is to study effects of magnetohydrodynamic, Joule heating and thermal radiation on an incompressible Jeffrey nanofluid flow over a linearly stretched surface. Simultaneous effects of convective heat and mass boundary conditions are also considered. Obtained system of boundary layer equations is converted into ordinary differential equations with high linearity using appropriate transformations. Analytical solutions via homotopy analysis method are obtained and deliberated accordingly. Discussion of graphs pertaining different prominent parameters is also added. Numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are also given and well deliberated. It is noted that higher values of thermophoretic parameter boost temperature and concentration distributions. Moreover, temperature field is an increasing function of radiation parameter.

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Abbreviations

\(a\) :

Dimensional constants

\(B_{0}\) :

Magnetic field strength (kg s−2A−1)

b, c :

Constants

C :

Concentration of fluid (kg m−3)

\(c_{p}\) :

Specific heat (J kg−1 K−1)

\(C_{\text{w}}\) :

Concentration on wall (kg m−3)

\(C_{\infty }\) :

Ambient concentration (kg m−3)

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

Brownian diffusion coeff. (kg m−1 s−1)

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

Thermophoretic diff. coeff. (kg m−1 s−1 K−1)

\(Ec\) :

Eckert number

\(f^{{\prime }}\) :

Dimensionless velocity

\(g\) :

Gravitational acceleration (m2 s−1)

\(Gr_{x}\) :

Grashoff number

\(h_{{f_{\text{t}} }}\) :

Heat transfer coefficient

\(h_{{f_{\text{c}} }}\) :

Mass transfer coefficient

\(k\) :

Thermal conductivity (W mK−1)

\(k^{ * }\) :

Mean absorption coefficient

\(Le\) :

Lewis number

M :

Magnetic parameter

N :

Concentration buoyancy parameter

\({\text{Nb}}\) :

Brownian motion parameter

\({\text{Nt}}\) :

Thermophoresis parameter

Nu x :

Nusselt number

Pr :

Prandtl number

\({\text{Rd}}\) :

Thermal radiation parameter

\(Re_{x}\) :

Reynolds number

\(Sh_{x}\) :

Sherwood number

\(T\) :

Temperature of fluid (K)

\(T_{\text{w}}\) :

Wall temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\((u,\,v)\) :

Velocity components

\(u_{w} (x)\) :

Stretching velocity along x-axis (m s−1)

\((x,\,y)\) :

Rectangular coordinate axis (m)

\(\beta\) :

Deborah number

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

Solutal expansion coefficient (m3 kg−1)

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

Thermal expansion coefficient (K−1)

\(\gamma_{1}\) :

Thermal Biot number

\(\gamma_{2}\) :

Concentration Biot number

\(\lambda_{1}\) :

Fluid relaxation time

\(\lambda_{2}\) :

Fluid retardation time

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\theta\) :

Dimensionless temperature

\(\sigma^{ * }\) :

Steffan–Boltzman constant

\(\sigma\) :

Electrical conductivity (m−3 kg−1 s3 A2)

\(Cf_{x}\) :

Skin friction coefficient

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\eta\) :

Similarity variable

\(\rho\) :

Density of fluid

\(\phi\) :

Dimensionless concentration

\(\delta\) :

Local buoyancy parameter

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Acknowledgments

This research is supported by Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy of Korea (No. 20132010101780).

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Authors and Affiliations

  1. Department of Computer Science, Bahria University, Islamabad Campus, Islamabad, 44000, Pakistan

    M. Ramzan

  2. Department of Mathematics, Faculty of Computing, Capital University of Science and Technology, Islamabad, Pakistan

    M. Bilal

  3. Department of Mechanical Engineering, Sejong University, Seoul, 143-747, Korea

    Jae Dong Chung

  4. Department of Mathematical Sciences, Federal Urdu University of Arts, Science and Technology, Near Zero Point, G-7/1, Islamabad, 44000, Pakistan

    A. B. Mann

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Correspondence to M. Ramzan.

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Ramzan, M., Bilal, M., Chung, J.D. et al. On MHD radiative Jeffery nanofluid flow with convective heat and mass boundary conditions. Neural Comput & Applic 30, 2739–2748 (2018). https://doi.org/10.1007/s00521-017-2852-8

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