Thermal Performance and Entropy Generation of Unsteady Natural Convection in a Trapezoid-Shaped Cavity

Abstract

In this study, a numerical investigation of unsteady natural convection heat transfer (HT) and entropy generation (EG) is performed within a trapezoid-shaped cavity containing thermally stratified water. The cavity’s bottom wall is heated, the sloped walls are thermally stratified, and the top wall is cooled. The finite volume (FV) method is employed to solve the governing equations. This study uses a Prandtl number (Pr) of 7.01 for water, an aspect ratio (AR) of 0.5, and Rayleigh numbers (Ra) varying between 10 and 106. To examine the flow behavior within the cavity, various relevant parameters are determined for different Ra values. These parameters include streamline and isotherm contours, temperature time series, limit point and limit cycle analysis, average Nusselt number (Nu) at the heated walls, average entropy generation (Eavg), and average Bejan number (Beavg). It is found that the flow transitions from a steady symmetrical state to a chaotic state as the Ra value increases. During this transition, three bifurcations occur. The first is a pitchfork bifurcation between Rayleigh numbers of 9 × 104 and 105, followed by a Hopf bifurcation between Rayleigh numbers of 105 and 2 × 105. Finally, another bifurcation occurs, shifting the flow from periodic to chaotic between Rayleigh numbers of 4 × 105 and 5 × 105. The present study shows an increase in Eavg of 94.97% between Rayleigh numbers of 103 and 106, while the rate of increase in Nu is 81.13%. The findings from this study will enhance understanding of the fluid flow phenomena in a trapezoid-shaped cavity filled with stratified water. The current numerical results are compared and validated against previously published numerical and experimental data.

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