{"id":"https://openalex.org/W2728906270","doi":"https://doi.org/10.3390/e19070337","title":"Natural Convection and Entropy Generation in a Square Cavity with Variable Temperature Side Walls Filled with a Nanofluid: Buongiorno\u2019s Mathematical Model","display_name":"Natural Convection and Entropy Generation in a Square Cavity with Variable Temperature Side Walls Filled with a Nanofluid: Buongiorno\u2019s Mathematical Model","publication_year":2017,"publication_date":"2017-07-05","ids":{"openalex":"https://openalex.org/W2728906270","doi":"https://doi.org/10.3390/e19070337","mag":"2728906270"},"language":"en","primary_location":{"id":"doi:10.3390/e19070337","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070337","pdf_url":"https://www.mdpi.com/1099-4300/19/7/337/pdf?version=1499339098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/7/337/pdf?version=1499339098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087096547","display_name":"Mikhail \u0410. Sheremet","orcid":"https://orcid.org/0000-0002-4750-0227"},"institutions":[{"id":"https://openalex.org/I196355604","display_name":"National Research Tomsk State University","ror":"https://ror.org/02he2nc27","country_code":"RU","type":"education","lineage":["https://openalex.org/I196355604"]},{"id":"https://openalex.org/I30849647","display_name":"Tomsk Polytechnic University","ror":"https://ror.org/00a45v709","country_code":"RU","type":"education","lineage":["https://openalex.org/I30849647"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Mikhail Sheremet","raw_affiliation_strings":["Department of Nuclear and Thermal Power Plants, Tomsk Polytechnic University, Tomsk 634050, Russia","Department of Theoretical Mechanics, Tomsk State University, Tomsk 634050, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Nuclear and Thermal Power Plants, Tomsk Polytechnic University, Tomsk 634050, Russia","institution_ids":["https://openalex.org/I196355604","https://openalex.org/I30849647"]},{"raw_affiliation_string":"Department of Theoretical Mechanics, Tomsk State University, Tomsk 634050, Russia","institution_ids":["https://openalex.org/I196355604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054108301","display_name":"Teodor Gro\u0219an","orcid":null},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Teodor Grosan","raw_affiliation_strings":["Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca 400084, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca 400084, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046453069","display_name":"Ioan Pop","orcid":"https://orcid.org/0000-0002-0660-6543"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Ioan Pop","raw_affiliation_strings":["Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca 400084, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca 400084, Romania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046453069"],"corresponding_institution_ids":["https://openalex.org/I3125347698"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.2796,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.92265974,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"19","issue":"7","first_page":"337","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11945","display_name":"Heat Transfer Mechanisms","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bejan-number","display_name":"Bejan number","score":0.9401036500930786},{"id":"https://openalex.org/keywords/nanofluid","display_name":"Nanofluid","score":0.8525956869125366},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.721362292766571},{"id":"https://openalex.org/keywords/streamlines-streaklines-and-pathlines","display_name":"Streamlines, streaklines, and pathlines","score":0.7076501846313477},{"id":"https://openalex.org/keywords/thermophoresis","display_name":"Thermophoresis","score":0.702424168586731},{"id":"https://openalex.org/keywords/nusselt-number","display_name":"Nusselt number","score":0.7022481560707092},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5408182144165039},{"id":"https://openalex.org/keywords/rayleigh-number","display_name":"Rayleigh number","score":0.5279539823532104},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4836079180240631},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.45917490124702454},{"id":"https://openalex.org/keywords/dimensionless-quantity","display_name":"Dimensionless quantity","score":0.4463290274143219},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4452736973762512},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.4343096911907196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34248048067092896},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.21782216429710388},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.07733514904975891}],"concepts":[{"id":"https://openalex.org/C181587685","wikidata":"https://www.wikidata.org/wiki/Q3110607","display_name":"Bejan number","level":5,"score":0.9401036500930786},{"id":"https://openalex.org/C21946209","wikidata":"https://www.wikidata.org/wiki/Q1989679","display_name":"Nanofluid","level":3,"score":0.8525956869125366},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.721362292766571},{"id":"https://openalex.org/C60439489","wikidata":"https://www.wikidata.org/wiki/Q634407","display_name":"Streamlines, streaklines, and pathlines","level":2,"score":0.7076501846313477},{"id":"https://openalex.org/C15401063","wikidata":"https://www.wikidata.org/wiki/Q610090","display_name":"Thermophoresis","level":4,"score":0.702424168586731},{"id":"https://openalex.org/C130230704","wikidata":"https://www.wikidata.org/wiki/Q898280","display_name":"Nusselt number","level":4,"score":0.7022481560707092},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5408182144165039},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.5279539823532104},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4836079180240631},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.45917490124702454},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.4463290274143219},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4452736973762512},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.4343096911907196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34248048067092896},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.21782216429710388},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.07733514904975891}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e19070337","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070337","pdf_url":"https://www.mdpi.com/1099-4300/19/7/337/pdf?version=1499339098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3ce1ce80a9f946ca8b88b3cd59f6cb9d","is_oa":true,"landing_page_url":"https://doaj.org/article/3ce1ce80a9f946ca8b88b3cd59f6cb9d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 19, Iss 7, p 337 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/7/337/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19070337","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 19; Issue 7; Pages: 337","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19070337","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070337","pdf_url":"https://www.mdpi.com/1099-4300/19/7/337/pdf?version=1499339098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2728906270.pdf","grobid_xml":"https://content.openalex.org/works/W2728906270.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W566210338","https://openalex.org/W1603751942","https://openalex.org/W1986143726","https://openalex.org/W1987095832","https://openalex.org/W2002901338","https://openalex.org/W2003520431","https://openalex.org/W2005693225","https://openalex.org/W2015921940","https://openalex.org/W2022413122","https://openalex.org/W2024804136","https://openalex.org/W2030320308","https://openalex.org/W2035685097","https://openalex.org/W2038133462","https://openalex.org/W2039354501","https://openalex.org/W2053099124","https://openalex.org/W2060334639","https://openalex.org/W2066850605","https://openalex.org/W2073033625","https://openalex.org/W2074879172","https://openalex.org/W2076384945","https://openalex.org/W2080027181","https://openalex.org/W2083330389","https://openalex.org/W2085169464","https://openalex.org/W2093717036","https://openalex.org/W2094629064","https://openalex.org/W2094883149","https://openalex.org/W2095339087","https://openalex.org/W2099447166","https://openalex.org/W2111352333","https://openalex.org/W2136419670","https://openalex.org/W2161188997","https://openalex.org/W2169323782","https://openalex.org/W2218056472","https://openalex.org/W2402560855","https://openalex.org/W2498734863","https://openalex.org/W2547480482","https://openalex.org/W2549943247","https://openalex.org/W2559952221","https://openalex.org/W2600131551","https://openalex.org/W2979562792","https://openalex.org/W4213136431","https://openalex.org/W4243692799","https://openalex.org/W4251920113"],"related_works":["https://openalex.org/W4220937649","https://openalex.org/W2587466926","https://openalex.org/W2960920183","https://openalex.org/W2031248579","https://openalex.org/W2076660666","https://openalex.org/W4317933863","https://openalex.org/W2735358284","https://openalex.org/W4323362660","https://openalex.org/W4213122764","https://openalex.org/W2921084473"],"abstract_inverted_index":{"Natural":[0],"convection":[1],"heat":[2],"transfer":[3],"combined":[4],"with":[5,13,38],"entropy":[6,63,111],"generation":[7,64],"in":[8,34,108,116,126],"a":[9,14,84,124],"square":[10],"cavity":[11],"filled":[12],"nanofluid":[15],"under":[16],"the":[17,45,87,90,94,101,109],"effect":[18],"of":[19,59,76,86,89,100],"variable":[20],"temperature":[21,91],"distribution":[22,92],"along":[23,93],"left":[24,95],"vertical":[25],"wall":[26,96],"has":[27,70,80],"been":[28,52,71,81],"studied":[29],"numerically.":[30],"Governing":[31],"equations":[32],"formulated":[33],"dimensionless":[35],"non-primitive":[36],"variables":[37],"corresponding":[39],"boundary":[40],"conditions":[41],"taking":[42],"into":[43],"account":[44],"Brownian":[46],"diffusion":[47],"and":[48,97],"thermophoresis":[49],"effects":[50],"have":[51],"solved":[53],"by":[54],"finite":[55],"difference":[56],"method.":[57],"Distribution":[58],"streamlines,":[60],"isotherms,":[61],"local":[62],"as":[65,67],"well":[66],"Nusselt":[68],"number":[69,103,122],"obtained":[72],"for":[73,119],"different":[74],"values":[75],"key":[77],"parameters.":[78],"It":[79],"found":[82],"that":[83],"growth":[85],"amplitude":[88],"an":[98,106,114],"increase":[99,107,115],"wave":[102],"lead":[104],"to":[105],"average":[110,127],"generation.":[112],"While":[113],"abovementioned":[117],"parameters":[118],"low":[120],"Rayleigh":[121],"illustrates":[123],"decrease":[125],"Bejan":[128],"number.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":8}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}
