{"title":"Horizontal free convection","authors":"N. Amin, N. Riley","doi":"10.1098/rspa.1990.0018","DOIUrl":null,"url":null,"abstract":"The boundary-layer flow over a heated horizontal plane boundary is analysed. Temperature variations along the boundary induce a pressure gradient that drives the flow. From consideration of an exact solution it is shown that no steady boundary-layer solution exists at a point where the temperature is a maximum. This is confirmed from the unsteady flow development that, at such a point, reveals a singular behaviour at a finite time. Steady, spatially periodic flows are considered for which it is shown that the boundary-layer solution terminates in a collision at points where the temperature is a maximum.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"58 1","pages":"371 - 384"},"PeriodicalIF":0.0000,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 16
Abstract
The boundary-layer flow over a heated horizontal plane boundary is analysed. Temperature variations along the boundary induce a pressure gradient that drives the flow. From consideration of an exact solution it is shown that no steady boundary-layer solution exists at a point where the temperature is a maximum. This is confirmed from the unsteady flow development that, at such a point, reveals a singular behaviour at a finite time. Steady, spatially periodic flows are considered for which it is shown that the boundary-layer solution terminates in a collision at points where the temperature is a maximum.