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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/095/0027

    • Keywords

       

      Instability; magnetohydrodynamics; Chebyshev collocation method; electrically conductive fluid.

    • Abstract

       

      Magnetohydrodynamics (MHD) is a very challenging problem which affects the stability of Poiseuille flow. Therefore, in this work we investigate the instability of an electrically conductive fluid between two parallel plates under the influence of a transverse magnetic field. We apply the Chebyshev collocation method to solve the generalised Orr–Summerfield equations to determine wave number, growth rates and spatial modes of the eigenmodes. To get the neutral curves of MHD instability, the QZ method is used. It is observed that the magnetic field has a stabilising effect on the flow and the stability increases as we increase the Hartmann number and for various wave numbers, magnetic field put down the growth of perturbation. It is concluded that effect of perturbations is little in span-wise direction for different Hartmann numbers that increase the critical values of Reynolds numbers.

    • Author Affiliations

       

      ZAKIR HUSSAIN1 2 RAJA ZEESAHAN1 MUHAMMAD SHAHZAD3 MEHBOOB ALI3 4 FAISAL SULTAN3 4 AHMED M ANTER2 5 HUISHENG ZHANG2 NAZAR KHAN6

      1. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Mansehra 22060, Pakistan
      2. Department of Biomedical Engineering, School of Medicine, Shenzhen University, Shenzhen 518060, People’s Republic of China
      3. Department of Pure and Applied Mathematics, University of Haripur, Haripur 22620, Pakistan
      4. Department of Mathematics & Statistics, Hazara University, Mansehra 21300, Pakistan
      5. Faculty of Computers and Information, Beni-Suef University, Benisuef, Egypt
      6. Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan

    • Dates

       
      Published
      6 February 2021
      Manuscript received
      16 July 2019
      Manuscript revised
      14 September 2020
      Accepted
      23 September 2020
      Final version published online
      6 February 2021

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