Influence of magnetic field on instability of the flows in a rotating channel filled with anisotropic porous substrate.

The rotating porous media flow has relevant applications in various sectors like oil recovery, mixing-separation, coating industry, etc. Researchers have explored the instability behaviors of vertical/spanwise rotating fluid flows through porous media. The influence of magneto-hydrodynamics can effectively control the Coriolis force-based instability in porous media flows. This study aims to investigate the combined effect of spanwise rotation and applied electromagnetic field on the linear stability of fluid flow via an anisotropic porous material in a rectangular channel. The Darcy-Brinkman momentum equations, including Coriolis and Lorentz force-based terms, are considered to capture the rotational as well as magnetic effects on porous media flow instability. The stability control parameters are the rotation number, Hartmann number, and anisotropic permeability. A normal mode analysis is applied to the linearized perturbed flow system to get a fourth-order Orr-Sommerfeld-Squire-like BVP, which is numerically solved using the Chebyshev spectral collocation method. The flow can be stabilized by decreasing the permeability ratios. Besides, the Hartmann number has shown a stabilizing role. Moreover, the critical parameters that destabilize the flow are estimated, which helps to build an effective mixing-separation strategy.