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

Rahaman, MM; Bhowmick, S; Saha, SC

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

Rahaman, MM Bhowmick, S Saha, SC

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Publisher:: MDPI
Publication Type:: Journal Article
Citation:: Processes, 2025, 13, (3)
Issue Date:: 2025-03-01

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Field	Value	Language
dc.contributor.author	Rahaman, MM
dc.contributor.author	Bhowmick, S
dc.contributor.author	Saha, SC
dc.date.accessioned	2025-09-22T01:51:57Z
dc.date.available	2025-09-22T01:51:57Z
dc.date.issued	2025-03-01
dc.identifier.citation	Processes, 2025, 13, (3)
dc.identifier.issn	2227-9717
dc.identifier.issn	2227-9717
dc.identifier.uri	http://hdl.handle.net/10453/189996
dc.description.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 10<sup>6</sup>. 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 (E<inf>avg</inf>), and average Bejan number (Be<inf>avg</inf>). 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 × 10<sup>4</sup> and 10<sup>5</sup>, followed by a Hopf bifurcation between Rayleigh numbers of 10<sup>5</sup> and 2 × 10<sup>5</sup>. Finally, another bifurcation occurs, shifting the flow from periodic to chaotic between Rayleigh numbers of 4 × 10<sup>5</sup> and 5 × 10<sup>5</sup>. The present study shows an increase in E<inf>avg</inf> of 94.97% between Rayleigh numbers of 10<sup>3</sup> and 10<sup>6</sup>, 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.
dc.language	English
dc.publisher	MDPI
dc.relation.ispartof	Processes
dc.relation.isbasedon	10.3390/pr13030921
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0904 Chemical Engineering
dc.subject.classification	4004 Chemical engineering
dc.title	Thermal Performance and Entropy Generation of Unsteady Natural Convection in a Trapezoid-Shaped Cavity
dc.type	Journal Article
utslib.citation.volume	13
utslib.for	0904 Chemical Engineering
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	open_access	*
dc.rights.license	This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
dc.date.updated	2025-09-22T01:51:55Z
pubs.issue	3
pubs.publication-status	Published
pubs.volume	13
utslib.citation.issue	3

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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