Stability of hydromagnetic Couette flow in an anisotropic porous medium with oblique principal axes and constant wall transpiration

Understanding and controlling transitions in wall-bounded flows through porous substrates are essential for designing and improving engineering systems. This study examines the linear stability of electrically conducting plane Couette flow within a Brinkman porous layer that is mechanically anisotropic and bounded by permeable walls with uniform cross-flow (injection at the lower wall, suction at the upper wall) under an applied magnetic field. A normal-mode linearisation leads to a modified Orr-Sommerfeld eigenvalue problem, which is solved using Chebyshev spectral collocation to identify neutral curves and growth-rate patterns as variables such as the Darcy number, Hartmann number, mechanical anisotropy, perturbation wavenumber, phase angle, cross-flow Reynolds number, and the orientation of the principal permeability axis are varied. Results show that increasing the Darcy number and Hartmann number stabilizes the flow, while a higher perturbation wavenumber reduces amplification, meaning disturbances grow most at longer wavelengths. Mechanical anisotropy consistently destabilizes the flow, increasing peak growth rates, whereas changes in the orientation angle have little effect. The phase angle has a slight influence on stability at low wavenumbers but tends to stabilize the flow at higher wavenumbers. Meanwhile, the cross-flow Reynolds number causes only minor shifts in the neutral curves. These findings suggest practical methods for flow control in anisotropic porous magnetohydrodynamic systems, highlighting the stabilizing effects of magnetic damping and porous-matrix diffusion, as well as the destabilizing impact of strong anisotropy.