Evaluating chemical reactions in fluid convection with rigid salt finger boundaries

Numerous disciplines, including fluid dynamics, heat transfer, geophysics, materials science, and environmental engineering, use Rayleigh numbers, both thermal and solute, extensively. They are crucial resources for foreseeing and comprehending fluid convective processes and their effects on many physical systems. In this analysis, we first derive the governing equations that describe the evolution of density perturbations in a stratified fluid system with a salinity gradient. Linear stability analysis is then applied to these equations to identify the conditions under which salt finger instability can occur. For the Rayleigh-Bénard convection of a chemically reactive pair stress fluid with rotation acting in the vertical direction, the non-autonomous Ginzburg-Landau equations are derived. For determining the amplitude for Ginzburg-Landau equations, the Lorenz model is introduced. Many physical parameters are taken into consideration when drawing the stationary and oscillatory curves. Heat transport is measured using the Nusselt number and Sherwood number, which are determined as a function of the lengthy time scale. The study provokes in understanding and predicting Rayleigh-Bénard convection contribute not only to our knowledge of ocean dynamics but also to our ability to address climate-related challenges and sustain marine ecosystems.