Instability of magneto hydro dynamics Couette flow for electrically conducting fluid through porous media

In this article, the hydrodynamic stability of the Couette flow of an electrically conducting fluid flowing in a parallel-plate channel with a normal magnetic field is investigated through a porous medium. The transport phenomena in the porous medium have been of enduring interest from the last few decades. The linear perturbation theory of hydrodynamic stability along with the presumption of low magnetic Reynolds number is applied to the governing equations to derive the governing magnetohydrodynamic stability equation. A Chebyshev collocation method is operated to numerically elucidate the magnetohydrodynamic stability equation. A linearized velocity solution for developing flow is used in the stability calculations. The numerically determined neutral stability results for the fully developed Couette flow are in excellent agreement with those of the analytical solution. The results presented here for Hartmann flow are believed to be more accurate owing to the more exact nature of the numerical solution.