{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T05:36:05Z","timestamp":1768714565986,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T00:00:00Z","timestamp":1535932800000},"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":["DIP-2017-010"],"award-info":[{"award-number":["DIP-2017-010"]}],"id":[{"id":"10.13039\/501100004515","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Malaysian Ministry of Higher Education","award":["GSP\/1\/2015\/SG04\/UKM\/01\/1."],"award-info":[{"award-number":["GSP\/1\/2015\/SG04\/UKM\/01\/1."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This numerical study considers the mixed convection and the inherent entropy generated in Al     2    O     3    \u2013water nanofluid filling a cavity containing a rotating conductive cylinder. The vertical walls of the cavity are wavy and are cooled isothermally. The horizontal walls are thermally insulated, except for a heat source segment located at the bottom wall. The dimensionless governing equations subject to the selected boundary conditions are solved numerically using the Galerkin finite-element method. The study is accomplished by inspecting different ranges of the physical and geometrical parameters, namely, the Rayleigh number (     10 3  \u2264 R a \u2264  10 6     ), angular rotational velocity (    0 \u2264 \u03a9 \u2264 750    ), number of undulations (    0 \u2264 N \u2264 4    ), volume fraction of Al     2    O     3     nanoparticles (    0 \u2264 \u03d5 \u2264 0.04    ), and the length of the heat source     ( 0.2 \u2264 H \u2264 0.8 )    . The results show that the rotation of the cylinder boosts the rate of heat exchange when the Rayleigh number is less than     5 \u00d7  10 5     . The number of undulations affects the average Nusselt number for a still cylinder. The rate of heat exchange increases with the volume fraction of the Al     2    O     3     nanoparticles and the length of the heater segment.<\/jats:p>","DOI":"10.3390\/e20090664","type":"journal-article","created":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T10:50:51Z","timestamp":1535971851000},"page":"664","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":68,"title":["Numerical Investigation of Mixed Convection and Entropy Generation in a Wavy-Walled Cavity Filled with Nanofluid and Involving a Rotating Cylinder"],"prefix":"10.3390","volume":"20","author":[{"given":"Ammar","family":"Alsabery","sequence":"first","affiliation":[{"name":"Department of Refrigeration &amp; Air-conditioning Technical Engineering, College of Technical Engineering, The Islamic University, Najaf 54001, Iraq"},{"name":"School of Mathematical Sciences, Faculty of Science &amp; Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muneer","family":"Ismael","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Engineering College, University of Basrah, Basrah 61004, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8335-3121","authenticated-orcid":false,"given":"Ali","family":"Chamkha","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Prince Sultan Endowment for Energy and the Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia"},{"name":"RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box 10021, Ras Al Khaimah 86416, UAE"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4237-7140","authenticated-orcid":false,"given":"Ishak","family":"Hashim","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Faculty of Science &amp; Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"645","DOI":"10.2118\/185173-PA","article-title":"The effects of perforation erosion on practical hydraulic-fracturing applications","volume":"22","author":"Long","year":"2017","journal-title":"SPE J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6811","DOI":"10.1166\/jnn.2017.14502","article-title":"Research on relative permeability of nanofibers with capillary pressure effect by means of Fractal-Monte Carlo technique","volume":"17","author":"Xiao","year":"2017","journal-title":"J. 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