Effect of Magnetic Interaction Parameter and the Electrical Conductivity of the Fluid on the Stability of Hydromagnetic Channel Flow

Abstract

The influence of magnetic interaction parameter and conductivity of the fluid on the stability against small perturbations on the streamlined base flow between two infinitely long parallel fixed plates is studied numerically. By normal mode analysis, the disturbance equations are reduced to Orr-Sommerfeld-type. Using the energy method, sufficient conditions for stability are derived by using the nature of the growth rate and sufficiently small values of the Reynold numbers. The disturbance equations are then solved using the Galerkin method corresponding to the base functions as Legendre-polynomials. Critical values for the Reynolds number, wave number, and speed of the wave are computed for various ranges of the magnetic interaction parameter and the magnetic Reynolds number. The curves of neutral stability are presented for different values of the nondimensional parameters that appeared in this study. The stability analysis is also discussed with the help of the plots of the rate of growth of disturbances for several values of the electrical conductivity and the magnetic interaction parameter. It is observed that both the fluid conductivity and the magnetic interaction parameter have direct control over fluctuations in the system. The results of this study are accurate and are comparable with the existing literature in the absence of a parallel magnetic field.