{"title":"水平自由对流","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":"{\"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}","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}
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.