{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T21:51:18Z","timestamp":1767909078029,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2015,8,26]],"date-time":"2015-08-26T00:00:00Z","timestamp":1440547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This current work studies the heat transfer performance and entropy generation of natural convection in a nanofluid-filled U-shaped cavity. The flow behavior and heat transfer performance in the cavity are governed using the continuity equation, momentum equations, energy equation and Boussinesq approximation, and are solved numerically using the finite-volume method and SIMPLE C algorithm. The simulations examine the effects of the nanoparticle volume fraction, Rayleigh number and the geometry parameters of the U-shaped cavity on the mean Nusselt number and total entropy generation. It shows that the mean Nusselt number increases and the total entropy generation reduces as the volume fraction of nanoparticles increases. In addition, the results show that the mean Nusselt number and the total entropy generation are both increased as the Rayleigh number increases. Finally, it also shows that mean Nusselt number can be increased and the total entropy generation can be reduced by extending the length of the low temperature walls or widening the width of the low temperature walls.<\/jats:p>","DOI":"10.3390\/e17095980","type":"journal-article","created":{"date-parts":[[2015,8,26]],"date-time":"2015-08-26T10:23:31Z","timestamp":1440584611000},"page":"5980-5994","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Numerical Investigation into Natural Convection and Entropy Generation in a Nanofluid-Filled U-Shaped Cavity"],"prefix":"10.3390","volume":"17","author":[{"given":"Ching-Chang","family":"Cho","sequence":"first","affiliation":[{"name":"Department of Vehicle Engineering, National Formosa University, No.64, Wunhua Rd., Huwei Township, Yunlin County 632, Taiwan R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Her-Terng","family":"Yau","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Chin-Yi University of Technology, 35, 215 Lane, Sec. 1, Chung Shan Road, Taiping, Taichung City, Taiwan R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ching-Huang","family":"Chiu","sequence":"additional","affiliation":[{"name":"Department of Vehicle Engineering, National Formosa University, No.64, Wunhua Rd., Huwei Township, Yunlin County 632, Taiwan R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kuo-Ching","family":"Chiu","sequence":"additional","affiliation":[{"name":"Department of Vehicle Engineering, National Formosa University, No.64, Wunhua Rd., Huwei Township, Yunlin County 632, Taiwan R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,8,26]]},"reference":[{"key":"ref_1","first-page":"1728","article-title":"Entropy generation through heat and fluid flow","volume":"26","author":"Bejan","year":"1982","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bejan, A. (1996). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, CRC Press.","DOI":"10.1063\/1.362674"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1115\/1.3250619","article-title":"Natural convection in enclosures","volume":"110","author":"Ostrach","year":"1988","journal-title":"ASME J. Heat Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"496","DOI":"10.3390\/e5050496","article-title":"An analysis of the entropy generation in a square enclosure","volume":"5","author":"Erbay","year":"2003","journal-title":"Entropy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1007\/s00231-003-0497-x","article-title":"Entropy generation in a square enclosure with partial heating from a vertical lateral wall","volume":"40","author":"Erbay","year":"2004","journal-title":"Heat Mass Transf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3441","DOI":"10.1016\/S0017-9310(03)00133-9","article-title":"Entropy generation at the onset of natural convection","volume":"46","author":"Magherbi","year":"2003","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.3390\/e13051020","article-title":"Entropy generation at natural convection in an inclined rectangular cavity","volume":"13","author":"Bouabid","year":"2011","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1016\/j.icheatmasstransfer.2008.02.002","article-title":"Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls","volume":"35","author":"Ilis","year":"2008","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/j.icheatmasstransfer.2010.05.007","article-title":"Analysis of entropy generation due to natural convection in square enclosures with multiple discrete heat sources","volume":"37","author":"Mukhopadhyay","year":"2010","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.icheatmasstransfer.2007.01.003","article-title":"Entropy generation for natural convection in \u0393-shaped enclosures","volume":"34","author":"Dagtekin","year":"2007","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_11","first-page":"99","article-title":"Enhancing thermal conductivity of fluids with nanoparticles. International mechanical engineering congress and exhibition","volume":"231","author":"Choi","year":"1995","journal-title":"ASME-Publications-Fed"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1016\/j.icheatmasstransfer.2011.04.008","article-title":"Entropy generation due to natural convection cooling of a nanofluid","volume":"38","author":"Shahi","year":"2011","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.powtec.2014.12.042","article-title":"FDLBM simulation of entropy generation due to natural convection in an enclosure filled with non-Newtonian nanofluid","volume":"273","author":"Kefayati","year":"2015","journal-title":"Powder Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.icheatmasstransfer.2014.02.031","article-title":"An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid","volume":"54","author":"Parvin","year":"2014","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.ijheatmasstransfer.2013.02.044","article-title":"Natural convection heat transfer and entropy generation in wavy-wall enclosure containing water-based nanofluid","volume":"61","author":"Cho","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1016\/j.ijheatmasstransfer.2014.05.063","article-title":"Heat transfer and entropy generation of natural convection in nanofluid-filled square cavity with partially-heated wavy surface","volume":"77","author":"Cho","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1080\/10407782.2013.742728","article-title":"Magnetohydrodynamic natural convection of nanofluids in U-shaped enclosures","volume":"63","author":"Ghasemi","year":"2013","journal-title":"Numer. Heat Transf. Part A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.ijthermalsci.2012.05.001","article-title":"Natural convection heat transfer performance in complex-wavy wall enclosed cavity filled with nanofluid","volume":"60","author":"Cho","year":"2012","journal-title":"Int. J. Therm. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1016\/j.icheatmasstransfer.2011.03.005","article-title":"Lattice Boltzmann simulation of natural convection in tall enclosures using water\/SiO2 nanofluid","volume":"38","author":"Kefayati","year":"2011","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ijthermalsci.2011.09.005","article-title":"Lattice Boltzmann simulation of natural convection an open enclosure subjugated to water\/copper nanofluid","volume":"52","author":"Kefayati","year":"2012","journal-title":"Int. J. Therm. Sci."},{"key":"ref_21","unstructured":"Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow, McGraw-Hill."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1002\/fld.1650030305","article-title":"Natural convection of air in a square cavity a bench mark numerical solution","volume":"3","author":"Davis","year":"1983","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_23","first-page":"199","article-title":"A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution","volume":"40","author":"Wan","year":"2004","journal-title":"Numer. Heat Transf. Part B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/9\/5980\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:47:27Z","timestamp":1760215647000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/9\/5980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,26]]},"references-count":23,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["e17095980"],"URL":"https:\/\/doi.org\/10.3390\/e17095980","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,26]]}}}