Triple diffusive convection in Boussinesq–Stokes suspensions with thermal and compositional buoyancy under rotation modulation

This study investigates the linear and weakly nonlinear stability of triple diffusive convection driven by thermal and compositional buoyancy in a Boussinesq-Stokes suspension fluid-saturated porous layer under rotational modulation. A linear stability analysis is performed to analytically solve a complex generalized eigenvalue problem. The onset of stationary convection is examined to determine the critical thermal Rayleigh number based on the physical governing parameters. Key findings emphasize the significant impact of the couple stress parameter, the Soret parameter, and the Taylor number in stabilizing the flow and enhancing stability. Perturbation analysis is performed to explore the weakly nonlinear regime, focusing on the small supercritical Rayleigh number. The heat and mass transport, represented by the Nusselt and Sherwood numbers, are governed by a non-autonomous Ginzburg–Landau equation, with the assumption that the rotation modulation amplitude is small. The effects of varying Taylor number, couple stress parameter, frequency of modulation, amplitude modulation, separation parameter, and Soret parameter on heat and mass transfer are thoroughly explored. The results show that the Sherwood number tend to stabilize more promptly than the Nusselt number. Furthermore, increasing the separation parameter leads to a decrease in both heat and mass transfer, thereby enhancing system stability.