Numerical Study on the Impact of the Richardson Number on Convection in an Enclosure, with Moving Sidewalls for Three Aspect Ratios: A = 1, 2 and 0.5

Abstract

Using mathematical models, this research investigation seeks to explore how varying aspect ratios and the Richardson number impact the mixing effectiveness, fluid flow velocity, and heat transfer characteristics in a rectangle-shaped space where cooling occurs along the sides and warm with a steady temperature exists throughout the 80% of the bottom section's center. Discretizing the governing equations through the finite volume approach, we solved them iteratively using the Tri-diagonal Matrix Algorithm, where pressure-velocity coupling was successfully implemented via the SIMPLER procedure. Innovative approaches for convection and diffusion terms involved employing a power-law difference scheme alongside a central differential scheme. In various simulations with specified parameters (Re = 100, Pr = 0.71), we visualized results in forms like streamlines, isothermal lines, and temperature/velocity profiles, along with local and average Nusselt numbers. We observe five unique structure formations during flow behavior by analyzing how Richardson numbers impact heat transmission within a specific geometric configuration (enclosure size A = 1). A change in aspect ratio leads to improved control over fluid movement while minimizing structural distortion. A subtle rise in heat transmission emerged as the average Nusselt number and Richardson number intersection strengthened force convection's domination while experiencing significant escalation under conditions conductive to natural convection. Decreasing the aspect ratio increased heat transfer efficiency when the Richardson number rose.