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Series solution of magneto-hydrodynamic boundary layer flow over bi-directional exponentially stretching surfaces

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Abstract

This study investigated theoretically the problem of three-dimensional, magnetohydrodynamic, boundary layer flow of a Jeffrey fluid with heat transfer in the presence of thermal radiation over an exponentially stretching surface. Highly nonlinear coupled partial differential equations are obtained using boundary layer approach. These equations are reduced to a set of ordinary differential equations using appropriate similarity transformations. The solution of the problem is found with the help of homotopy analysis method along with optimal homotopy analysis method to find optimal/best value for the convergence control parameter appearing in a series solution. The solution behaviors, for different emerging parameters, of velocity profiles (along \(x\) and \(y\) direction) as well as temperature profile are investigated and the effect of these parameters are explained through graphs. Moreover, for the present study, effective Prandtl number is used in the description of temperature profile. The skin friction coefficients along \(x\)-axis and \(y\)-axis are also discussed through graphs. The tabulated values of dimensionless heat transfer coefficient, Nusselt number, is presented.

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Acknowledgments

This research was supported by a National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIP) (20090093134, 2014R1A2A2A01006544).

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Authors and Affiliations

  1. Department of Computational Science and Engineering, Yonsei University, Seoul, Korea

    Sajjad ur-Rehman & Changhoon Lee

  2. Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan

    Sohail Nadeem

  3. Department of Mechanical Engineering, Yonsei University, Seoul, Korea

    Changhoon Lee

Authors
  1. Sajjad ur-Rehman
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  2. Sohail Nadeem
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  3. Changhoon Lee
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Correspondence to Changhoon Lee.

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Technical Editor: Francisco Ricardo Cunha.

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ur-Rehman, S., Nadeem, S. & Lee, C. Series solution of magneto-hydrodynamic boundary layer flow over bi-directional exponentially stretching surfaces. J Braz. Soc. Mech. Sci. Eng. 38, 443–453 (2016). https://doi.org/10.1007/s40430-015-0344-2

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  • DOI: https://doi.org/10.1007/s40430-015-0344-2

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