Triple-Diffusive Incompressible Couple-Stress Fluid Through Porous Medium

The present study investigates the onset of triple-diffusive convection in a couple-stress fluid layer subjected to a porous medium, with heat and solute gradients imposed from below. The system is further influenced by a uniform vertical magnetic field and uniform rotation. The governing equations are formulated, incorporating the effects of couple-stress, rotation, magnetic field, and medium permeability. A linear stability analysis is performed, and the corresponding dispersion relation is derived. For the case of stationary convection, the presence of a stable solute gradient and rotation exerts a stabilizing influence on the system. In contrast, the effect of medium permeability on stability is dependent on the presence of rotation; it can be either destabilizing or stabilizing. The magnetic field and couple-stress parameter similarly exhibit dual effects, acting as either stabilizing or destabilizing agents under different conditions. However, in the absence of rotation, medium permeability destabilizes the system, while both the magnetic field and couple-stress parameter contribute to stabilization. The dispersion relation is further examined numerically to understand the system's behaviour in detail. It is observed that the presence of a stable solute gradient, rotation, and magnetic field introduces oscillatory modes into the system, which are absent when these factors are not considered. These findings highlight the complex interplay between multiple diffusive effects, couple-stress, and external forces, providing insights into the fundamental nature of convective instability in porous media.