Unsteady Natural Convection and Entropy Generation in Thermally Stratified Trapezoidal Cavities: A Comparative Study

This study numerically investigates unsteady natural convection (NC) heat transfer (HT) and entropy generation (E_gen) in trapezoidal cavities filled with two thermally stratified fluids. Both air-filled and water-filled configurations are analyzed to evaluate and compare their thermal performance under varying conditions. The cavities are characterized by a heated base, thermally stratified sloped walls, and a cooled top wall. The governing equations are numerically solved using the finite volume (FV) approach. The study considers a Prandtl number (Pr) of 0.71 for air and 7.01 for water, Rayleigh numbers (Ra) ranging from 10³ to 5 × 10⁷, and an aspect ratio (AR) of 0.5. Flow behavior is examined through various parameters, including temperature time series (TTS), average Nusselt number (Nu), average entropy generation (E_avg), average Bejan number (Be_avg), and ecological coefficient of performance (ECOP). Three bifurcations are identified during the transition from steady to chaotic flow for both fluids. The first is a pitchfork bifurcation, occurring between Ra = 10⁵ and 2 × 10⁵ for air, and between Ra = 9 × 10⁴ and 10⁵ for water. The second, a Hopf bifurcation, is observed between Ra = 4.7 × 10⁵ and 4.8 × 10⁵ for air, and between Ra = 10⁵ and 2 × 10⁵ for water. The third bifurcation marks the onset of chaotic flow, occurring between Ra = 3 × 10⁷ and 4 × 10⁷ for air, and between Ra = 4 × 10⁵ and 5 × 10⁵ for water. At Ra = 10⁶, the average HT in the air-filled cavity is 85.35% higher than in the water-filled cavity, while E_avg is 94.54% greater in the air-filled cavity compared to water-filled cavity. At Ra = 10⁶, the thermal performance of the cavity filled with water is 4.96% better than that of the air-filled cavity. These findings provide valuable insights for optimizing thermal systems using trapezoidal cavities and varying working fluids.