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

摘要

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 R-c and the corresponding critical wave number alpha(c) are computed for a wide range of porous parameter sigma(p), the ratio of effective viscosity to the fluid viscosity Lambda, the mechanical anisotropy parameter K-1, the porosity epsilon 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. (C) 2017 Elsevier Inc. All rights reserved.