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Invariant Solutions for the Unsteady Magnetohydrodynamics (MHD) Flow of a Fourth-Grade Fluid Induced Due to the Impulsive Motion of a Flat Porous Plate

  • General and Applied Physics
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Abstract

An analysis is carried out to study the time-dependent flow of an incompressible electrically conducting fourth-grade fluid over an infinite porous plate. The flow is caused by the motion of the porous plate in its own plane with an impulsive velocity V(t). The governing nonlinear problem is solved by invoking the Lie group theoretic approach and a numerical technique. Travelling wave solutions of the forward and backward type, together with a steady state solution, form the basis of our analytical analysis. Further, the closed-form solutions are also compared against numerical results. The essential features of the embedded parameters are described. In particular, the physical significance of the plate suction/injection and magnetic field is studied.

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Acknowledgments

Taha Aziz, A.B. Magan and F.M. Mahomed would like to thank the National Research Foundation (NRF) of South Africa for their financial support.

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Authors and Affiliations

  1. School of Computational and Applied Mathematics, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, Differential equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, 2050, South Africa

    Taha Aziz, A. B. Magan & F. M. Mahomed

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  1. Taha Aziz
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  2. A. B. Magan
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  3. F. M. Mahomed
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Correspondence to Taha Aziz.

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Aziz, T., Magan, A.B. & Mahomed, F.M. Invariant Solutions for the Unsteady Magnetohydrodynamics (MHD) Flow of a Fourth-Grade Fluid Induced Due to the Impulsive Motion of a Flat Porous Plate. Braz J Phys 45, 120–131 (2015). https://doi.org/10.1007/s13538-014-0292-9

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  • DOI: https://doi.org/10.1007/s13538-014-0292-9

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