Natural convection in a square Cavity: Effects of Rayleigh and Prandtl numbers on heat transfer and flow patterns
Saleh A. Bawazeer, Mohammad S. Alsoufi
Abstract
Natural convection within enclosures plays a crucial role in heat transfer across various thermal systems. This study presents a validated numerical benchmark for buoyancy-driven flow in a square cavity with differential heating, focusing solely on the effects of Rayleigh ( Ra ) and Prandtl ( Pr ) numbers. The equations are solved using the finite element method (FEM) in COMSOL Multiphysics®, with mesh convergence tests ensuring second-order accuracy and grid independence. Simulations examine a wide range of Ra (10 to 10 6 ) and Pr (0.1–10), illustrating the transition from conduction-dominated to fully convective flow. Results demonstrate a significant increase in the average Nusselt number, from 1.0 at Ra ≤ 10 2 to 9.2 at Ra = 10 6 and Pr = 10, driven by the formation of thin thermal boundary layers and complex vortex structures. Higher Prandtl numbers lead to sharper velocity gradients and more localized thermal transport, while lower Prandtl numbers promote overall circulation. Stream function analysis tracks the strength and symmetry shifts of vortices across the parameter space. When compared with existing high-fidelity datasets, deviations are below 0.2 %, confirming the model as a reliable reference for CFD validation and experimental studies of natural convection in simple enclosures.