{"title":"多孔介质中热驱动的浅空腔流动:合并层结构","authors":"P. Daniels, P. Simpkins, P. Blythe","doi":"10.1098/rspa.1989.0119","DOIUrl":null,"url":null,"abstract":"An analysis is given of convective motions generated in a shallow rectangular cavity by an applied horizontal temperature gradient; the cavity is filled with a fluid-saturated porous medium. For large Rayleigh numbers R, and for large aspect ratios L, a distinguished limit arises when R = O(L2). In this limit the boundary layers on the horizontal walls merge and completely fill the cavity. The régime is characterized by a non-parallel core flow that provides the dominant structure over a surprisingly wide range of the parameter R/L 2. New results for the merged layer core are compared with the parallel flow convection-dominated boundary layer limit R/L2 → ∞, and with the parallel flow diffusion-dominated limit R/L2 → 0. Heat transfer calculations, which define the dependence of the Nusselt number on R/L2, have also been carried out.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"22 1","pages":"107 - 124"},"PeriodicalIF":0.0000,"publicationDate":"1989-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Thermally driven shallow cavity flows in porous media: the merged-layer régime\",\"authors\":\"P. Daniels, P. Simpkins, P. Blythe\",\"doi\":\"10.1098/rspa.1989.0119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An analysis is given of convective motions generated in a shallow rectangular cavity by an applied horizontal temperature gradient; the cavity is filled with a fluid-saturated porous medium. For large Rayleigh numbers R, and for large aspect ratios L, a distinguished limit arises when R = O(L2). In this limit the boundary layers on the horizontal walls merge and completely fill the cavity. The régime is characterized by a non-parallel core flow that provides the dominant structure over a surprisingly wide range of the parameter R/L 2. New results for the merged layer core are compared with the parallel flow convection-dominated boundary layer limit R/L2 → ∞, and with the parallel flow diffusion-dominated limit R/L2 → 0. Heat transfer calculations, which define the dependence of the Nusselt number on R/L2, have also been carried out.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"volume\":\"22 1\",\"pages\":\"107 - 124\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"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.1989.0119\",\"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.1989.0119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Thermally driven shallow cavity flows in porous media: the merged-layer régime
An analysis is given of convective motions generated in a shallow rectangular cavity by an applied horizontal temperature gradient; the cavity is filled with a fluid-saturated porous medium. For large Rayleigh numbers R, and for large aspect ratios L, a distinguished limit arises when R = O(L2). In this limit the boundary layers on the horizontal walls merge and completely fill the cavity. The régime is characterized by a non-parallel core flow that provides the dominant structure over a surprisingly wide range of the parameter R/L 2. New results for the merged layer core are compared with the parallel flow convection-dominated boundary layer limit R/L2 → ∞, and with the parallel flow diffusion-dominated limit R/L2 → 0. Heat transfer calculations, which define the dependence of the Nusselt number on R/L2, have also been carried out.