Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions

Abstract

We investigate the linear instability of a fully developed pressure-driven flow of an electrically conducting fluid in a porous channel using the Brinkman-Darcy model and the additional effects of a uniform magnetic field and slip boundary conditions. Two Chebyshev collocation techniques are used to solve the ordinary eigenvalue system governing the onset of convection. The critical Reynolds number, Rec, wavenumber, ac, and wave speed cc are found in terms of the porous parameter M, the dimensionless slip length, N0, and the Hartmann number Ha.