{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:18:29Z","timestamp":1760170709964,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T00:00:00Z","timestamp":1636416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>Free convective heat transfer in the closed gap between concentric semi-hemispheres is quantified by means of a numerical approach based on the volume control method using the SIMPLE algorithm. The average Nusselt number is determined for several configurations obtained by varying the cavity\u2019s aspect ratio between 0.15 and 1.5, while the Rayleigh number varies within the 5.33 \u00d7 103\u20134.50 \u00d7 108 range. The results show that the correlations available in the literature dealing with concentric whole spheres cannot be used for the configuration treated here. The new correlation between the Nusselt and Rayleigh numbers proposed in this work can be applied in various engineering sectors, such as in the electronic packaging considered in this present work, buildings, and architecture.<\/jats:p>","DOI":"10.3390\/en14227479","type":"journal-article","created":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T21:39:07Z","timestamp":1636493947000},"page":"7479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Free Convective Heat Transfer in a Closed Gap between Concentric Semi-Hemispheres"],"prefix":"10.3390","volume":"14","author":[{"given":"Abderrahmane","family":"Ba\u00efri","sequence":"first","affiliation":[{"name":"Laboratoire Thermique Interfaces Environnement (LTIE), Universit\u00e9 de Paris, EA 4415, 50 Rue de S\u00e8vres, F-92410 Ville d\u2019Avray, France"}]},{"given":"Nacim","family":"Alilat","sequence":"additional","affiliation":[{"name":"Laboratoire Thermique Interfaces Environnement (LTIE), Universit\u00e9 de Paris, EA 4415, 50 Rue de S\u00e8vres, F-92410 Ville d\u2019Avray, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5352-5116","authenticated-orcid":false,"given":"Alexander","family":"Mart\u00edn-Gar\u00edn","sequence":"additional","affiliation":[{"name":"ENEDI Research Group, Department of Thermal Engineering, Faculty of Engineering of Gipuzkoa, Universidad del Pais Vasco UPV\/EHU, Plaza Europa 1, 20018 Donostia-San Sebasti\u00e1n, Spain"}]},{"given":"Kemi","family":"Adeyeye","sequence":"additional","affiliation":[{"name":"Department of Architecture and Civil Engineering, University of Bath, Bath BA2 7AY, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6547-896X","authenticated-orcid":false,"given":"Jos\u00e9-Antonio","family":"Mill\u00e1n-Garc\u00eda","sequence":"additional","affiliation":[{"name":"ENEDI Research Group, Department of Thermal Engineering, Faculty of Engineering of Gipuzkoa, Universidad del Pais Vasco UPV\/EHU, Plaza Europa 1, 20018 Donostia-San Sebasti\u00e1n, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6043-6007","authenticated-orcid":false,"given":"Luis","family":"Roseiro","sequence":"additional","affiliation":[{"name":"Polytechnic of Coimbra, ISEC, Rua Pedro Nunes\u2014Quinta da Nora, 3030-199 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1080\/10407782.2013.790265","article-title":"Analysis of convective heat flow visualization within porous right angled triangular enclosures with a concave\/convex hypotenuse","volume":"64","author":"Basak","year":"2013","journal-title":"Numer. 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Entropy, 21.","key":"ref_4","DOI":"10.3390\/e21020116"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1016\/j.apenergy.2008.02.009","article-title":"Transient thermal characteristics of airborne electronic equip-ment with discrete hot bands in a confined environment","volume":"85","year":"2008","journal-title":"Appl. Energy"},{"doi-asserted-by":"crossref","unstructured":"IMiroshnichenko, V., Sheremet, M.A., and Mohamad, A.A. (2019). The influence of surface radiation on the passive cooling of a heat-generating element. Energies, 12.","key":"ref_6","DOI":"10.3390\/en12060980"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1016\/0017-9310(94)90176-7","article-title":"Natural convection in hemispherical enclosure heated from below","volume":"37","author":"Shiina","year":"1994","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.icheatmasstransfer.2014.10.013","article-title":"A synthesis of correlations on quantification of free convective heat transfer in inclined air-filled hemispherical enclosures","volume":"59","year":"2014","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1080\/10407782.2010.516681","article-title":"Modeling of various heat transfer problems using dissipative particle dynamics","volume":"58","year":"2010","journal-title":"Numer. Heat Transf. Part A Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.icheatmasstransfer.2017.06.011","article-title":"Free convec-tion in ZnO nanofluid-filled and tilted hemispherical enclosures containing a cubic electronic device","volume":"87","author":"Haddad","year":"2017","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1080\/10407782.2017.1337985","article-title":"Nu-Ra-Pr correlations for nanofluidic natural convection in tilted hemispherical enclosures with active disk","volume":"71","author":"Haddad","year":"2017","journal-title":"Numer. Heat Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1108\/HFF-10-2016-0392","article-title":"Natural convective heat transfer in the air-filled interstice be-tween inclined concentric hemispheres: Application to thermoregulation in electronics","volume":"27","author":"Alilat","year":"2017","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1140\/epjp\/s13360-020-00205-1","article-title":"Numerical study of natural convection of ZnO-water nanofluid enclosed between two inclined and concentric hemispheres","volume":"135","author":"Alilat","year":"2020","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1080\/08916152.2018.1526230","article-title":"Experimental quantification of natural convective heat transfer within annulus space filled with a H2O-Cu nanofluid saturated porous medium. Application to electronics cooling","volume":"32","author":"Laraqi","year":"2019","journal-title":"Exp. Heat Transf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1615\/ComputThermalScien.2011002942","article-title":"Mathematical simulation of unsteady natural convection inside a sphere","volume":"3","author":"Sheremet","year":"2011","journal-title":"Comput. Therm. Sci. Int. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0065-2717(08)70076-5","article-title":"A general method of obtaining approximate solutions to laminar and turbulent free convection problems","volume":"11","author":"Raithby","year":"1975","journal-title":"Adv. Heat Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0035-3159(97)80685-X","article-title":"Etude num\u00e9rique du mod\u00e8le de Boussinesq de convection naturelle laminaire axisym\u00e9trique permanente dans un espace annulaire compris entre deux sph\u00e8res","volume":"36","author":"Daoudi","year":"1997","journal-title":"Rev. G\u00e9n\u00e9rale Therm."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1016\/0017-9310(70)90089-X","article-title":"Natural convection heat transfer between concentric spheres","volume":"13","author":"Scanlan","year":"1970","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1115\/1.2188476","article-title":"Natural convection meas-urements for a concentric spherical enclosure","volume":"128","author":"Teertstra","year":"2006","journal-title":"J. Heat Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1016\/0017-9310(92)90196-Y","article-title":"Natural convection between concentric spheres","volume":"35","author":"Garg","year":"1992","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"102443","DOI":"10.1016\/j.jobe.2021.102443","article-title":"Quantification of free convection in a quarter-spherical innovative Trombe wall design","volume":"42","author":"Alilat","year":"2021","journal-title":"J. Build. Eng."},{"doi-asserted-by":"crossref","unstructured":"Pastori, S., Mereu, R., Mazzucchelli, E.S., Passoni, S., and Dotelli, G. (2021). Energy performance evaluation of a ventilated fa\u00e7ade system through CFD modeling and comparison with international standards. Energies, 14.","key":"ref_22","DOI":"10.3390\/en14010193"},{"doi-asserted-by":"crossref","unstructured":"Ba\u00efri, A., Mart\u00edn-Gar\u00edn, A., Ilinca, A., Alilat, N., and Mill\u00e1n-Garc\u00eda, J.A. (2021). Thermal state of a concentric quarter spherical enclosure subjected to air free convection. J. Therm. Anal. Calorim.","key":"ref_23","DOI":"10.1007\/s10973-021-10739-w"},{"doi-asserted-by":"crossref","unstructured":"Bejan, A. (2013). Convection Heat Transfer, John Wiley & Sons, Inc.. 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