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Slip effects on MHD boundary layer flow of Oldroyd-B fluid past a stretching sheet: An analytic solution

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Abstract

Present analysis is made for the laminar flow of Oldroyd-B fluid induced by a deforming sheet in the existence of transverse magnetic field. Flow model is constructed in the presence of slip boundary condition. The governing problem even after utilizing boundary layer approximations comprises of non-linear differential equation with the non-linear boundary condition. Such boundary condition for the no slip case is linear. Highly accurate analytic solutions for velocity distribution are derived by powerful homotopy analysis approach. Permissible values of the convergence control parameter are obtained by the so-called h-curves. The behavior of parameters on the solutions is shown graphically. In the light of numerical results, we predict that slip effect gives opposition to the momentum transport phenomenon. Moreover, the behaviors of relaxation and retardation time are qualitatively opposite. A comparative study of slip and no-slip cases is also discussed.

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Acknowledgements

We thank the anonymous reviewers for helpful comments, which lead to definite improvement in the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, Qazvin, 34149, Iran

    S. Abbasbandy

  2. School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan

    M. Mustafa

  3. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    T. Hayat

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

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  1. S. Abbasbandy
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  2. M. Mustafa
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  4. A. Alsaedi
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Corresponding author

Correspondence to M. Mustafa.

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Technical Editor: Cezar Negrao.

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Abbasbandy, S., Mustafa, M., Hayat, T. et al. Slip effects on MHD boundary layer flow of Oldroyd-B fluid past a stretching sheet: An analytic solution. J Braz. Soc. Mech. Sci. Eng. 39, 3389–3397 (2017). https://doi.org/10.1007/s40430-017-0744-6

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  • DOI: https://doi.org/10.1007/s40430-017-0744-6

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