Effect Of Temperature Modulation On Rayleigh- Bénard Convection In Boussinesq-Stokes Suspension

Abstract

This study comprehensively investigates the influence of time-periodic boundary temperature on the onset of convection in a Boussinesq-Stokes suspension, a fluid system characterized by unique viscosity and density properties. The research focuses on how both temporal and spatial variations affect the distribution of the basic state temperature within the suspension layer, which is heated from below and cooled from above. To analyze the stability and determine the eigenvalue associated with this phenomenon, a perturbation approach is employed, accounting for the magnitude of boundary temperature perturbations. This method allows for a detailed examination of the system’s response to modulated thermal conditions. A corrected Rayleigh number is derived to assess the stability of the system, particularly to evaluate the potential for sub-critical instability, where convection may occur at lower Rayleigh numbers than predicted by classical theory. The findings are compared with exact solutions to validate the results, providing insights into controlling convection through temperature modulation. The study highlights the impact of modulation frequency and amplitude on convection onset, offering valuable implications for fluid dynamics applications involving suspensions.