Thermosolutal convection of a bi-viscous Bingham fluid in a saturated porous medium with transverse magnetic field

Application of a magnetic field to a convective fluid flow generates a Lorentz force, which typically acts to increase the hydrodynamic stability of the system. Stability in day-to-day applications is of immense importance. Hence, the primary objective of this study is to explore how a transverse magnetic field influences the thermosolutal convection of a bi-viscous Bingham fluid in a saturated porous layer. Additionally, the effects of vertical throughflow are considered. To thoroughly investigate the system's stability, both linear and nonlinear stability analyses are carried out. The normal mode technique is utilized to analyze linear stability, while the nonlinear stability is investigated through the well-established energy method. The eigenvalue problems arising from both stability analyses are numerically solved using the bvp4c (boundary value problem, 4th-order, collocation) routine in MATLAB (matrix laboratory). By minimizing the neutral stability curves for selected governing flow parameters, the critical Rayleigh numbers for both linear and nonlinear theories are obtained. The results obtained are presented graphically. The findings indicate that a transverse magnetic field postpones the onset of convection in the bi-viscous Bingham fluid, independent of vertical throughflow conditions.