{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:26Z","timestamp":1760145266733,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T00:00:00Z","timestamp":1720915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The phenomenon of natural convection is the subject of significant research interest due to its widespread occurrence in both natural and industrial contexts. This study focuses on investigating natural convection phenomena within triangular enclosures, specifically emphasizing a valley-shaped configuration. Our research comprehensively analyses unsteady, non-dimensional time-varying convection resulting from natural fluid flow within a valley-shaped cavity, where the inclined walls serve as hot surfaces and the top wall functions as a cold surface. We explore unsteady natural convection flows in this cavity, utilizing air as the operating fluid, considering a range of Rayleigh numbers from Ra = 100 to 108. Additionally, various non-dimensional times \u03c4, spanning from 0 to 5000, are examined, with a fixed Prandtl number (Pr = 0.71) and aspect ratio (A = 0.5). Employing a two-dimensional framework for numerical analysis, our study focuses on identifying unstable flow mechanisms characterized by different non-dimensional times, including symmetric, asymmetric, and unsteady flow patterns. The numerical results reveal that natural convection flows remain steady in the symmetric state for Rayleigh values ranging from 100 to 7 \u00d7 103. Asymmetric flow occurs when the Ra surpasses 7 \u00d7 103. Under the asymmetric condition, flow arrives in an unsteady stage before stabilizing at the fully formed stage for 7 \u00d7 103 &lt; Ra &lt; 107. This study demonstrates that periodic unsteady flows shift into chaotic situations during the transitional stage before transferring to periodic behavior in the developed stage, but the chaotic flow remains predominant in the unsteady regime with larger Rayleigh numbers. Furthermore, we present an analysis of heat transfer within the cavity, discussing and quantifying its dependence on the Rayleigh number.<\/jats:p>","DOI":"10.3390\/computation12070146","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T08:35:17Z","timestamp":1721032517000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Natural Convection Fluid Flow and Heat Transfer in a Valley-Shaped Cavity"],"prefix":"10.3390","volume":"12","author":[{"given":"Sidhartha","family":"Bhowmick","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh"}]},{"given":"Laxmi Rani","family":"Roy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh"}]},{"given":"Feng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9962-8919","authenticated-orcid":false,"given":"Suvash C.","family":"Saha","sequence":"additional","affiliation":[{"name":"School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Sydney, NSW 2007, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1017\/S0022112066001368","article-title":"The boundary-layer regime for convection in a rectangular cavity","volume":"26","author":"Gill","year":"1966","journal-title":"J. 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