{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:21:30Z","timestamp":1760235690762,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T00:00:00Z","timestamp":1632268800000},"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>The flow and heat transfer fields from a nanofluid within a horizontal annulus partly saturated with a porous region are examined by the Galerkin weighted residual finite element technique scheme. The inner and the outer circular boundaries have hot and cold temperatures, respectively. Impacts of the wide ranges of the Darcy number, porosity, dimensionless length of the porous layer, and nanoparticle volume fractions on the streamlines, isotherms, and isentropic distributions are investigated. The primary outcomes revealed that the stream function value is powered by increasing the Darcy parameter and porosity and reduced by growing the porous region\u2019s area. The Bejan number and the average temperature are reduced by the increase in Da, porosity \u03b5, and nanoparticles volume fractions \u03d5. The heat transfer through the nanofluid-porous layer was determined to be the best toward high rates of Darcy number, porosity, and volume fraction of nanofluid. Further, the local velocity and local temperature in the interface surface between nanofluid-porous layers obtain high values at the smallest area from the porous region (D=0.4), and in contrast, the local heat transfer takes the lower value.<\/jats:p>","DOI":"10.3390\/e23101237","type":"journal-article","created":{"date-parts":[[2021,9,26]],"date-time":"2021-09-26T22:24:13Z","timestamp":1632695053000},"page":"1237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Energy and Entropy Production of Nanofluid within an Annulus Partly Saturated by a Porous Region"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6529-8050","authenticated-orcid":false,"given":"Zehba A. S.","family":"Raizah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2970-6600","authenticated-orcid":false,"given":"Ammar I.","family":"Alsabery","sequence":"additional","affiliation":[{"name":"Refrigeration Air-Conditioning Technical Engineering Department, College of Technical Engineering, The Islamic University, Najaf 54001, Iraq"},{"name":"School of Mathematical Sciences, Faculty of Science & Technology, University Kebangsaan Malaysia, Bangi 43600, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3369-8452","authenticated-orcid":false,"given":"Abdelraheem M.","family":"Aly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt"}],"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 & Technology, University Kebangsaan Malaysia, Bangi 43600, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,22]]},"reference":[{"key":"ref_1","first-page":"44","article-title":"Natural convection modeling of heat sinks using web-based tools","volume":"6","author":"Culham","year":"2000","journal-title":"Electron. Cool."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1115\/1.3450516","article-title":"Natural convection in enclosed spaces\u2013a review of application to solar energy collection","volume":"98","author":"Buchberg","year":"1976","journal-title":"J. Heat Transf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3034","DOI":"10.1016\/j.ijheatmasstransfer.2006.02.009","article-title":"Investigation of natural-convection heat transfer coefficient on a vertical square fin of finned-tube heat exchangers","volume":"49","author":"Chen","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2448","DOI":"10.1016\/j.applthermaleng.2006.02.007","article-title":"Modeling of transient natural convection heat transfer in electric ovens","volume":"26","author":"Mistry","year":"2006","journal-title":"Appl. Therm. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2710","DOI":"10.1016\/j.energy.2006.01.008","article-title":"Experimental and numerical performance of a multi-effect condensation\u2013evaporation solar water distillation system","volume":"31","author":"Dayem","year":"2006","journal-title":"Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1016\/j.ijthermalsci.2007.07.003","article-title":"Experimental and analytical investigation of solidification and melting characteristics of PCMs inside cylindrical encapsulation","volume":"47","author":"Kalaiselvam","year":"2008","journal-title":"Int. J. Therm. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1986","DOI":"10.1016\/j.ijheatmasstransfer.2009.12.057","article-title":"A comprehensive numerical model for melting with natural convection","volume":"53","author":"Wang","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1115\/1.3451040","article-title":"Freezing controlled by natural convection","volume":"101","author":"Sparrow","year":"1979","journal-title":"J. Heat Transf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0017-9310(81)90035-1","article-title":"Freezing on a finned tube for either conduction-controlled or natural-convection-controlled heat transfer","volume":"24","author":"Sparrow","year":"1981","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_10","unstructured":"Nield, D.A., and Bejan, A. (2006). Convection in Porous Media, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1016\/j.molliq.2017.05.015","article-title":"Two-phase mixture numerical simulation of natural convection of nanofluid flow in a cavity partially filled with porous media to enhance heat transfer","volume":"238","author":"Toosi","year":"2017","journal-title":"J. Mol. Liq."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.ijmecsci.2018.03.017","article-title":"Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media","volume":"140","author":"Raizah","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104442","DOI":"10.1016\/j.icheatmasstransfer.2019.104442","article-title":"Effect of nonhomogeneous nanofluid model on transient natural convection in a non-Darcy porous cavity containing an inner solid body","volume":"110","author":"Alsabery","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.ijheatmasstransfer.2018.04.108","article-title":"Natural convection of alumina-water nanofluid in an open cavity having multiple porous layers","volume":"125","author":"Miroshnichenko","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"104925","DOI":"10.1016\/j.icheatmasstransfer.2020.104925","article-title":"Effects of porous medium and wavy surface on heat transfer and entropy generation of Cu-water nanofluid natural convection in square cavity containing partially-heated surface","volume":"119","author":"Cho","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"104551","DOI":"10.1016\/j.icheatmasstransfer.2020.104551","article-title":"Magnetohydrodynamics forced convection of nanofluid in multi-layered U-shaped vented cavity with a porous region considering wall corrugation effects","volume":"113","author":"Selimefendigil","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.powtec.2020.04.005","article-title":"Numerical study on natural convection of Ag\u2013MgO hybrid\/water nanofluid inside a porous enclosure: A local thermal non-equilibrium model","volume":"367","author":"Mehryan","year":"2020","journal-title":"Powder Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106161","DOI":"10.1016\/j.ijmecsci.2020.106161","article-title":"Unsteady flow and entropy analysis of nanofluids inside cubic porous container holding inserted body and wavy bottom wall","volume":"193","author":"Alsabery","year":"2021","journal-title":"Int. J. Mech. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.1016\/j.asej.2020.09.026","article-title":"Natural convection flow of a nanofluid-filled V-shaped cavity saturated with a heterogeneous porous medium: Incompressible smoothed particle hydrodynamics analysis","volume":"12","author":"Raizah","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"122623","DOI":"10.1016\/j.physa.2019.122623","article-title":"Incompressible smoothed particle hydrodynamics simulation of natural convection in a nanofluid-filled complex wavy porous cavity with inner solid particles","volume":"537","author":"Aly","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.powtec.2021.01.033","article-title":"Numerical study of heat transfer enhancement of non-Newtonian nanofluid in porous blocks in a channel partially","volume":"383","author":"Javaherdeh","year":"2021","journal-title":"Powder Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105007","DOI":"10.1016\/j.icheatmasstransfer.2020.105007","article-title":"Natural convection in a wavy porous cavity subjected to a partial heat source","volume":"120","author":"Rao","year":"2021","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"106570","DOI":"10.1016\/j.ijthermalsci.2020.106570","article-title":"Effects of temperature-dependent viscosity on natural convection in a porous cavity with a circular cylinder under local thermal non-equilibrium condition","volume":"159","author":"Wang","year":"2021","journal-title":"Int. J. Therm. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2480","DOI":"10.1016\/j.apt.2020.04.012","article-title":"A 3D numerical study on natural convection flow of nanofluid inside a cubical cavity equipped with porous fins using two-phase mixture model","volume":"31","author":"Esfe","year":"2020","journal-title":"Adv. Powder Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3955","DOI":"10.1016\/S0017-9310(97)00008-2","article-title":"Natural convective heat transfer in a fluid saturated variable porosity medium","volume":"40","author":"Nithiarasu","year":"1997","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1016\/j.enconman.2010.06.072","article-title":"Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids","volume":"52","author":"Corcione","year":"2011","journal-title":"Energy Convers. Manag."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","unstructured":"Alsabery, A., Ismael, M., Chamkha, A., 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"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Alsabery, A.I., Hashim, I., Hajjar, A., Ghalambaz, M., Nadeem, S., and Saffari Pour, M. (2020). Entropy generation and natural convection flow of hybrid nanofluids in a partially divided wavy cavity including solid blocks. Energies, 13.","DOI":"10.3390\/en13112942"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2717(08)70172-2","article-title":"Second-law analysis in heat transfer and thermal design","volume":"15","author":"Bejan","year":"1982","journal-title":"Adv. Heat Transf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1017\/S0022112076002012","article-title":"An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders","volume":"74","author":"Kuehn","year":"1976","journal-title":"J. Fluid Mech."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1017\/S0022112088000138","article-title":"Natural convection in vertical enclosures containing simultaneously fluid and porous layers","volume":"186","author":"Beckermann","year":"1988","journal-title":"J. Fluid Mech."},{"key":"ref_33","unstructured":"Bergman, T.L., and Incropera, F.P. (2011). Introduction to Heat Transfer, Wiley. [6th ed.]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1237\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:03:08Z","timestamp":1760166188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,22]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["e23101237"],"URL":"https:\/\/doi.org\/10.3390\/e23101237","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,9,22]]}}}