The Onset of Instability in A Magnetohydrodynamic Channel Flow through Porous Media of Casson Fluid

Abstract

A detailed study is made on the stability of linear two-dimensional disturbances of Plane Poiseuille Flow (PPF) of Casson fluid through porous media in the presence of a vertical uniform magnetic field, B0 which is extremely useful in metals, mines, and fuels industries. Using the method of normal modes, the disturbance equations are derived. The resulting eigenvalue problem is then solved by the spectral collocation method using Chebyshev-based polynomials. The critical values of the triplets ( Rec, αc, cc ) are obtained for various values of the Casson parameter, η , Hartmann number, Ha , and porous parameter, σp. The stability of the system is discussed using the neutral stability curves for each value of the parameters present in the problem. It is found that the stability regions are enlarged for small values of η and large values of the porous parameter, σp and Hartmann number, Ha. It is also observed that the stability characteristics of plane Poiseuille flow in a porous medium are remarkably different from non-porous cases. The results obtained here contribute to the contemporary efforts to better understand the stability characteristics of PPF of Casson fluid flow through porous media in the presence of a uniform transverse magnetic field.