Stability of Plane Poiseuille Channel Flow of a Classical Newtonian Fluid in the Presence of Uniform Transverse Magnetic Field: Modal and Non-modal Approach

Abstract

The effect of a uniform transverse magnetic field on the stability of plane Poiseuille channel flow of a classical Newtonian fluid has been investigated. The Navier-Stokes equation has been linearized, reducing it to a generalized fourth-order Orr-Sommerfeld-type equation. The Chebyshev spectral collocation method has been employed to solve the obtained stability equations. Neutral stability curves (R,\(\alpha\)) and the transient energy growth curves G(t) were plotted. A comprehensive study of the short-term behavior through non-modal analysis and the long-term behavior through modal analysis revealed that a uniform transverse magnetic field acts as a stabilizing agent, delaying the onset of instability in the fluid system. The accuracy of the obtained results has been verified and found to be comparable with existing studies.