Abstract

This study conducts a numerical analysis of unsteady natural convection (UNC), heat transfer (HT), and entropy generation $(S_{\mathrm{gen}<!--FUNCTION\; APPLICATION-->})$ in a square cavity occupied with thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top wall. Simulations are performed utilizing the finite volume method (FVM) with an invariable Prandtl number (Pr) of 0.71 and an extensive range of Rayleigh numbers (Ra) varying from 10${}^1$ to 10${}^8$. The analysis includes flow visualization through streamlines and isotherm plots, temperature time series (TTS), spectral analysis, limit point and limit cycles analyses, and the largest Lyapunov exponent $({\lambda }_L)$, highlighting flow regime transitions. As Ra increases, the flow changeovers from a steady symmetric state to chaotic regime through a sequence of bifurcations: a pitchfork bifurcation $(\mathrm{Ra}<!--FUNCTION\; APPLICATION-->\approx 7\times 10^3$ to $8\times 10^3)$, a Hopf bifurcation ($\mathrm{Ra}<!--FUNCTION\; APPLICATION-->\approx 2\times 10^6$ to $3\times 10^6$), and the onset of chaos $(\mathrm{Ra}<!--FUNCTION\; APPLICATION-->\approx 10^7$ to $2\times 10^7$). Critical Ra values are identified, signifying the shift from a steady symmetric state to chaotic state. Validation against benchmark results confirms the accuracy and reliability of the simulations. The evaluation of average Nusselt number (Nu) and $S_{\mathrm{gen}<!--FUNCTION\; APPLICATION-->}$ demonstrates that heat transfer enhancement is accompanied by increased irreversibility, with a notable rise in Nu at $\mathrm{Ra}<!--FUNCTION\; APPLICATION-->=3\times 10^6$. Specifically, Nu at the top wall increases from 21.973 $(\mathrm{Ra}<!--FUNCTION\; APPLICATION-->=10^7)$ to 38.524 $(\mathrm{Ra}<!--FUNCTION\; APPLICATION-->=2\times 10^7)$, while at the bottom wall it rises from 22.029 to 38.477, corresponding to an approximate 75% increase in HT for both surfaces. These findings reveal the intricate interplay between cavity geometry, thermal stratification, and convective dynamics, offering valuable insights into the thermodynamic performance of stratified enclosures.

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