Comparative Analysis of Unsteady Natural Convection and Thermal Performance in Rectangular and Square Cavities Filled with Stratified Air

A comprehensive numerical analysis has been conducted to investigate unsteady natural convection (UNC), bifurcation behavior, and heat transfer (HT) in a rectangular enclosure containing thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top wall. To assess thermal performance, square and rectangular cavities with identical boundary conditions and working fluid are considered. The finite volume method (FVM) is used to solve the governing equations over a wide range of Rayleigh numbers (Ra = 101 to 109) for air with a Prandtl number (Pr) of 0.71. Flow dynamics and thermal performance are analyzed using temperature time series (TTS), limit point–limit cycle behavior, average Nusselt number (Nuavg), average entropy generation (Savg), average Bejan number (Beavg), and the ecological coefficient of performance (ECOP). In the rectangular cavity, the transition from steady to chaotic flow exhibits three bifurcations: a pitchfork bifurcation at Ra = 3 × 104–4 × 104, a Hopf bifurcation at Ra = 3 × 106–4 × 106, and the onset of chaotic flow at Ra = 9 × 107–2 × 108. The comparative analysis indicates that Nuavg remains nearly identical for both cavities within Ra = 105 to 107. However, at Ra = 108, the HT rate in the rectangular cavity is 29.84% higher than that of the square cavity, while Savg and Beavg differ by 39.32% and 37.50%, respectively. Despite higher HT and Savg in the rectangular enclosure, the square cavity demonstrates superior overall thermal performance by 13.52% at Ra = 108. These results offer significant insights for optimizing cavity geometries in thermal system design based on energy efficiency and entropy considerations.