Magnetohydrodynamic stability of pressure-driven flow in an anisotropic porous channel: Accurate solution

Abstract

The stability of fully developed pressure-driven flow of an electrically conducting fluid through a channel filled with a saturated anisotropic porous medium is studied under the influence of a uniform transverse magnetic field using a modified Brinkman equation. An analogue of Squire's transformation is used to show that two-dimensional motions are more unstable than three-dimensional ones. The modified Orr–Sommerfeld equation for the problem is solved numerically and a more accurate solution is obtained using the Chebyshev collocation method combined with Newton's and golden section search methods. The critical Reynolds number Rc and the corresponding critical wave number αc are computed for a wide range of porous parameter σp, the ratio of effective viscosity to the fluid viscosityΛ, the mechanical anisotropy parameter K1, the porosity ε and the Hartman number M. It is found that the system remains unconditionally stable to small-amplitude disturbances for the Darcy case and the energy stability analysis is also performed to corroborate this fact.