{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T00:17:40Z","timestamp":1774484260554,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T00:00:00Z","timestamp":1590710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004515","name":"Universiti Kebangsaan Malaysia","doi-asserted-by":"publisher","award":["FRGS\/1\/2019\/STG06\/UKM\/01\/2"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UKM\/01\/2"]}],"id":[{"id":"10.13039\/501100004515","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at     T h    . The temperature of the right vertical surface, however, is maintained at lower temperature     T c    . The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number     R a =  10 3      and     10 5    , number of oscillations:     1 \u2264 N \u2264 4    , angular rotational velocity:     \u2212 1000 \u2264 \u03a9 \u2264 1000    , and heat source length:     0 . 2 \u2264 H \u2264 0 . 8    . A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.<\/jats:p>","DOI":"10.3390\/e22060606","type":"journal-article","created":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T11:49:21Z","timestamp":1591012161000},"page":"606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Entropy Generation and Mixed Convection Flow Inside a Wavy-Walled Enclosure Containing a Rotating Solid Cylinder and a Heat Source"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2970-6600","authenticated-orcid":false,"given":"Ammar I.","family":"Alsabery","sequence":"first","affiliation":[{"name":"Refrigeration &amp; Air-conditioning Technical Engineering Department, College of Technical Engineering, The Islamic University, 54001 Najaf, Iraq"},{"name":"Department of Mathematical Sciences, Faculty of Science &amp; Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5524-385X","authenticated-orcid":false,"given":"Tahar","family":"Tayebi","sequence":"additional","affiliation":[{"name":"Faculty of Sciences &amp; Technology, Mohamed El Bachir El Ibrahimi University, Bordj Bou Arreridj, El-Anasser, Algeria"},{"name":"Energy Physics Laboratory, Department of Physics, Faculty of Science, Mentouri Brothers Constantine 1 University, Constantine, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1526-4183","authenticated-orcid":false,"given":"Rozaini","family":"Roslan","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, Faculty of Applied Sciences &amp; Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar 84600, Johor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali J.","family":"Chamkha","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi 100000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4237-7140","authenticated-orcid":false,"given":"Ishak","family":"Hashim","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Science &amp; Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.ijmecsci.2018.10.069","article-title":"Impact of nonhomogeneous nanofluid model on transient mixed convection in a double lid-driven wavy cavity involving solid circular cylinder","volume":"150","author":"Alsabery","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1080\/104077800274181","article-title":"A study of free convection induced by a vertical wavy surface with heat flux in a porous enclosure","volume":"37","author":"Kumar","year":"2000","journal-title":"Numer. Heat Tranf. A-Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1016\/S0017-9310(01)00304-0","article-title":"Laminar natural convection in an inclined cavity with a wavy wall","volume":"45","author":"Adjlout","year":"2002","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/S1290-0729(02)00040-6","article-title":"Numerical investigation of natural convection inside a wavy enclosure","volume":"42","author":"Das","year":"2003","journal-title":"Int. J. Therm. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1016\/j.ijheatmasstransfer.2006.10.008","article-title":"Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity","volume":"50","author":"Khanafer","year":"2007","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_6","first-page":"717","article-title":"Natural convection in a cavity with a wavy wall heated from below and uniformly cooled from the top and both sides","volume":"128","author":"Dalal","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1007\/s00231-007-0349-1","article-title":"Unsteady natural convection in an enclosure with vertical wavy walls","volume":"44","author":"Rostami","year":"2008","journal-title":"Heat Mass Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.icheatmasstransfer.2014.07.013","article-title":"Mixed convection flow of a nanofluid in a lid-driven cavity with a wavy wall","volume":"57","author":"Chamkha","year":"2014","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1080\/10407782.2015.1125709","article-title":"Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field","volume":"69","author":"Sheikholeslami","year":"2016","journal-title":"Numer. Heat Tranf. A-Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1115\/1.2911322","article-title":"Numerical calculation of convective heat transfer between rotating coaxial cylinders with periodically embedded cavities","volume":"114","author":"Hayase","year":"1992","journal-title":"J. Heat Transfer"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1016\/0017-9310(94)90329-8","article-title":"Enhancement of natural convection heat transfer of an enclosure by a rotating circular cylinder","volume":"37","author":"Fu","year":"1994","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2514\/3.788","article-title":"Natural convection over rotating cylindrical heat source in an enclosure","volume":"10","author":"Ghaddar","year":"1996","journal-title":"J. Thermophys. Heat Transf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1002\/htj.10099","article-title":"Heat transfer regulation in a rectangular enclosure using a rotating plate","volume":"32","author":"Kimura","year":"2003","journal-title":"Heat Transf. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1016\/j.ijheatfluidflow.2009.04.009","article-title":"Fluid flow due to combined convection in lid-driven enclosure having a circular body","volume":"30","author":"Oztop","year":"2009","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1016\/j.ijheatmasstransfer.2008.12.031","article-title":"Numerical investigation of heat and fluid flow across a rotating circular cylinder maintained at constant temperature in 2-D laminar flow regime","volume":"52","author":"Paramane","year":"2009","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.ijheatmasstransfer.2013.12.081","article-title":"Mixed convection of a heated rotating cylinder in a square enclosure","volume":"72","author":"Liao","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.icheatmasstransfer.2010.12.006","article-title":"Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations","volume":"38","author":"Hussain","year":"2011","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.icheatmasstransfer.2014.06.002","article-title":"Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center","volume":"56","author":"Chatterjee","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1016\/j.ijheatmasstransfer.2009.10.007","article-title":"Steady mixed convection in a differentially heated square enclosure with an active rotating circular cylinder","volume":"53","author":"Costa","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.icheatmasstransfer.2017.05.025","article-title":"Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder","volume":"86","author":"Khanafer","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/S1290-0729(03)00076-0","article-title":"Laminar free convection and entropy generation inside an inclined wavy enclosure","volume":"42","author":"Mahmud","year":"2003","journal-title":"Int. J. Therm. Sci."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ijthermalsci.2007.02.008","article-title":"On the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure","volume":"47","author":"Zahmatkesh","year":"2008","journal-title":"Int. J. Therm. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.icheatmasstransfer.2008.01.010","article-title":"Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses","volume":"35","author":"Varol","year":"2008","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_25","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_26","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_27","doi-asserted-by":"crossref","unstructured":"Chamkha, A., Ismael, M., Kasaeipoor, A., and Armaghani, T. (2016). Entropy generation and natural convection of CuO-water nanofluid in C-shaped cavity under magnetic field. Entropy, 18.","DOI":"10.3390\/e18020050"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sheremet, M.A., Oztop, H.F., Pop, I., and Abu-Hamdeh, N. (2016). Analysis of entropy generation in natural convection of nanofluid inside a square cavity having hot solid block: Tiwari and Das\u2019 model. Entropy, 18.","DOI":"10.3390\/e18010009"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1108\/HFF-10-2015-0408","article-title":"Entropy generation optimization for MHD natural convection of a nanofluid in porous media-filled enclosure with active parts and viscous dissipation","volume":"27","author":"Mansour","year":"2017","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"052001","DOI":"10.1063\/1.4981911","article-title":"Effects of heat sink and source and entropy generation on MHD mixed convection of a Cu-water nanofluid in a lid-driven square porous enclosure with partial slip","volume":"29","author":"Chamkha","year":"2017","journal-title":"Phys. Fluids"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.molliq.2018.04.119","article-title":"Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field","volume":"263","author":"Mehryan","year":"2018","journal-title":"J. Mol. Liq."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"7247","DOI":"10.1016\/j.ijheatmasstransfer.2012.07.051","article-title":"Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids","volume":"55","author":"Roslan","year":"2012","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.011","article-title":"Natural convection in an enclosure containing a sinusoidally heated cylindrical source","volume":"70","author":"Roslan","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.rser.2014.08.040","article-title":"Review of convection heat transfer and fluid flow in porous media with nanofluid","volume":"41","author":"Mahdi","year":"2015","journal-title":"Renew. Enew. Sust. Energ. Rev."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jtice.2015.04.016","article-title":"Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium","volume":"55","author":"Pourmehran","year":"2015","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jcis.2017.09.067","article-title":"Enhanced oil displacement by nanofluid\u2019s structural disjoining pressure in model fractured porous media","volume":"511","author":"Zhang","year":"2018","journal-title":"J. Colloid Interface Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Alsabery, A.I., Ishak, M.S., Chamkha, A.J., and Hashim, I. (2018). Entropy generation analysis and natural convection in a nanofluid-filled square cavity with a concentric solid insert and different temperature distributions. Entropy, 20.","DOI":"10.3390\/e20050336"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Alsabery, A.I., Ismael, M.A., Chamkha, A.J., and Hashim, I. (2018). Numerical investigation of mixed convection and entropy generation in a wavy-walled cavity filled with nanofluid and involving a rotating cylinder. Entropy, 20.","DOI":"10.3390\/e20090664"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/606\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:33:55Z","timestamp":1760175235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,29]]},"references-count":38,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["e22060606"],"URL":"https:\/\/doi.org\/10.3390\/e22060606","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,29]]}}}