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Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction

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Abstract

In this article, an investigation has been performed to explore the two-dimensional boundary layer flow problem and heat transfer characteristic of ferromagnetic viscoelastic fluid flow over a stretching surface with a linear velocity under the impact of magnetic dipole and suction. The governing PDEs are converted into a system of nonlinear ODEs by applying appropriate similarity approach. The modelled equations are then solved numerically by utilizing efficient Runge–Kutta–Fehlberg procedure based on shooting algorithm. Influence of pertinent flow parameter involved, such as ferromagnetic interaction parameter, suction parameter, viscoelastic parameter, Prandtl number on dimensionless velocity, temperature, skin friction, and Nusselt inside the boundary layer, are portrayed graphically and discussed. The results show that pressure profile and skin friction coefficient increase with the variation of ferromagnetic interaction parameter and opposite behaviour is noted for local Nusselt number.

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Abbreviations

a :

Distance

\(c_{\text{p}}\) :

Specific heat transfer (J kg−1 K−1)

\(C_{{f_{x} }}\) :

Skin friction coefficient

\(k\) :

Thermal conductivity (W m−1 K−1)

H :

Magnetic field (A m−1)

\(Nu_{x}\) :

Local Nusselt number

\(K^{*}\) :

Pyromagnetic coefficient

\(l\) :

Characteristic length

M :

Magnetization (A m−1)

\(\text{Re}_{x}\) :

Reynolds number

\((u,v)\) :

Velocity components (m s−1)

\((x,y)\) :

Cartesian component (m)

\(Pr\) :

Prandtl number

S :

Suction/injection parameter

\(\mu_{\text{o}}\) :

Magnetic permeability

μ :

Viscosity

T :

Fluid temperature

T c :

Curie temperature (K)

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

Wall mass flux

\(\rho\) :

Density (kg m−3)

\(\rho c_{\text{p}}\) :

Heat capacity

\(\varPhi\) :

Magnetic potential

\(\psi\) :

Stream function (m2 s−1)

\(\delta\) :

Velocity slip parameter

\(\phi\) :

Volume fraction of nanoparticle

\(\varepsilon\) :

Dimensionless Curie temperature

\(\tau\) :

Shear stress

\(\lambda\) :

Viscous dissipation parameter

\(\lambda^{ * }\) :

Viscoelastic parameter

\(\alpha\) :

Thermal diffusivity

\(\alpha_{1}\) :

Dimensionless distance

\(\beta\) :

Ferromagnetic interaction parameter

\(\gamma\) :

Magnetic field strength (A m−1)

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Acknowledgements

R. Ellahi is grateful to Prof. Sultan Z Alamri, Dean Faculty of Science and Prof. Yousef Alharbi, Chairman Mathematics Department, Taibah University, Madinah Munawwarah, Saudi Arabia, for their kind cooperation. R. Ellahi is also thankful to PCST to honour him with 7th top most Productive Scientist Award in category A.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, FBAS, IIUI, Islamabad, 44000, Pakistan

    Aaqib Majeed, Ahmad Zeeshan & Rahmat Ellahi

  2. Department of Mathematics, Faculty of Science, Taibah University, Madinah Al Munawwarah, Saudi Arabia

    Sultan Z. Alamri

  3. Department of Mechanical Engineering, University of California Riverside, Riverside, CA, USA

    Rahmat Ellahi

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  1. Aaqib Majeed
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Correspondence to Rahmat Ellahi.

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Majeed, A., Zeeshan, A., Alamri, S.Z. et al. Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction. Neural Comput & Applic 30, 1947–1955 (2018). https://doi.org/10.1007/s00521-016-2830-6

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  • DOI: https://doi.org/10.1007/s00521-016-2830-6

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