{"doi":"10.1017/s0022112000001464","title":"Prandtl number dependence of Nusselt number in direct numerical simulations","abstract":"<jats:p>The dependence of the Nusselt number <jats:italic>Nu</jats:italic> on the Rayleigh <jats:italic>Ra</jats:italic> and Prandtl <jats:italic>Pr</jats:italic> number \nis determined for 10<jats:sup>4</jats:sup> &lt; <jats:italic>Ra</jats:italic> &lt; 10<jats:sup>7</jats:sup> and 0.07 &lt; <jats:italic>Pr</jats:italic> &lt; 7 using DNS with no-slip upper \nand lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, \nvelocity scales and boundary layer thicknesses are calculated. For <jats:italic>Nu</jats:italic> there are good \ncomparisons with experimental data and scaling laws for all the cases, including <jats:italic>Ra</jats:italic><jats:sup>2/7</jats:sup> \nlaws at <jats:italic>Pr</jats:italic> = 0.7 and <jats:italic>Pr</jats:italic> = 7 and at low <jats:italic>Pr</jats:italic>, a <jats:italic>Ra</jats:italic><jats:sup>1/4</jats:sup> regime. \nCalculations at <jats:italic>Pr</jats:italic> = 0.3 predict a new <jats:italic>Nu</jats:italic> ∼ <jats:italic>Ra</jats:italic><jats:sup>2/7</jats:sup> \nregime at slightly higher <jats:italic>Ra</jats:italic> than the <jats:italic>Pr</jats:italic> = 0.07 calculations \nreported here and the mercury <jats:italic>Pr</jats:italic> = 0.025 experiments.</jats:p>","journal":"Journal of Fluid Mechanics","year":2000,"id":27947,"datarank":7.20876089651245,"base_score":4.624972813284271,"endowment":4.624972813284271,"self_citation_contribution":0.6937459219926407,"citation_network_contribution":6.515014974519809,"self_endowment_contribution":0.6937459219926407,"citer_contribution":6.515014974519809,"corpus_percentile":null,"corpus_rank":null,"citation_count":101,"citer_count":99,"citers_with_citation_signal":88,"citers_with_endowment":88,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":157852,"name":"JACKSON R. HERRING","orcid":null,"position":1,"is_corresponding":false},{"id":157850,"name":"ROBERT M. KERR","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":4.624972813284271,"endowment":4.624972813284271,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W2138076026","authors":[],"funders":[],"total_grants":0,"fwci":4.9888,"citation_percentile":0.95325306,"influential_citations":6,"citation_trend":[{"year":2012,"count":2},{"year":2013,"count":6},{"year":2014,"count":2},{"year":2015,"count":5},{"year":2016,"count":2},{"year":2017,"count":2},{"year":2019,"count":2},{"year":2020,"count":3},{"year":2021,"count":4},{"year":2022,"count":2},{"year":2023,"count":5},{"year":2024,"count":4},{"year":2025,"count":6},{"year":2026,"count":1}],"oa_status":"closed","license":"https://www.cambridge.org/core/terms","oa_locations":[{"url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112000001464","host_type":"publisher"},{"url":"https://doi.org/10.1017/s0022112000001464","host_type":"journal"}],"fields_of_study":["Fluid Dynamics and Turbulent Flows","Computational Fluid Dynamics and Aerodynamics","Gas Dynamics and Kinetic Theory","Physics","Engineering"],"mesh_terms":[],"keywords":["Nusselt number","Prandtl number","Physics","Thermodynamics","Boundary layer","Slip (aerodynamics)","Mechanics","Materials science","Heat transfer","Reynolds number","Turbulence"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-08T20:01:22.164239Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}