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The impact of side walls on the MHD flow of a second-grade fluid through a porous medium

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Abstract

The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite plate is examined. Expressions for velocity and shear stress are determined with the help of integral transforms. In the absence of side walls, all the solutions that have been obtained are reduced to those corresponding to the motion over an infinite flat plate. The Newtonian solutions are also obtained as limiting case of the general solution. Finally, influence of magnetic and porosity parameter is graphically highlighted.

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Authors and Affiliations

  1. Department of Mathematics, Islamia College Peshawar, Peshawar, Khyber Pakhtunkhwa, 25000, Pakistan

    Sami Ul Haq &  Syed Inayat Ali Shah

  2. Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan

    Ata ur Rahman &  Farhad Ali

  3. Department of Basic Sciences, College of Engineering, Majmaah University, P.O. Box 66, Majmaah, 11952, Saudi Arabia

    Ilyas Khan

Authors
  1. Sami Ul Haq
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  2. Ata ur Rahman
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  3. Ilyas Khan
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  4. Farhad Ali
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  5. Syed Inayat Ali Shah
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Corresponding author

Correspondence to Sami Ul Haq.

Appendix

Appendix

$$\frac{2}{d}\mathop \sum \limits_{n = 1}^{\infty } \frac{{1 - ( - 1)^{n} }}{{\lambda_{n} }}\sin (\lambda_{n} z) = \frac{2}{h}\mathop \sum \limits_{n = 1}^{\infty } \frac{{( - 1)^{n + 1} \cos (\eta_{n} z)}}{{\eta_{n} }} = 1,\,\,\,\mathop \sum \limits_{n = 1}^{\infty } \frac{{( - 1)^{n + 1} }}{2n - 1} = \frac{\pi }{4}.$$
(38)

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Sami Ul Haq, Ata ur Rahman, Ilyas Khan et al. The impact of side walls on the MHD flow of a second-grade fluid through a porous medium. Neural Comput & Applic 30, 1103–1109 (2018). https://doi.org/10.1007/s00521-016-2733-6

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  • DOI: https://doi.org/10.1007/s00521-016-2733-6

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