Michele Celli , Antonio Barletta , Pedro Vayssiére Brandão , Silvia da Costa Hirata , Mohamed Najib Ouarzazi
{"title":"粘性加热对流经多孔管道的线性和非线性稳定性分析的影响","authors":"Michele Celli , Antonio Barletta , Pedro Vayssiére Brandão , Silvia da Costa Hirata , Mohamed Najib Ouarzazi","doi":"10.1016/j.icheatmasstransfer.2024.107712","DOIUrl":null,"url":null,"abstract":"<div><p>The stability of a stationary fully developed vertical flow across a porous pipe is investigated. The heating due to viscous dissipation is assumed to be non–negligible and also to be the only effect triggering the onset of thermal convection. An innovative scaling is employed to study the case of small Gebhart number. The viscous heating term present inside the energy balance equation yields a basic stationary flow characterised by dual branches of solutions: for a given vertical pressure gradient, two possible velocity profiles are obtained. The linear and nonlinear stability of the stationary dual solutions is performed. The linear stability is investigated in a usual fashion by employing the normal modes method and then solving the eigenvalue problem obtained by using the shooting method. The nonlinear stability is investigated by simulating numerically the evolution in time of the perturbed system. The linear stability analysis allows one to conclude that the critical wavenumber for the onset of instability is zero and the critical dimensionless velocity at the pipe axis is equal to <span><math><mn>3.43631</mn></math></span>. The results of the nonlinear analysis display subcritical instabilities. Indeed, the onset of instability is obtained for values of the governing parameters which are lower than the critical values obtained by the linear analysis. This feature occurs when the amplitude of the initial disturbance applied to the nonlinear problem is sufficiently high, namely when the dimensionless amplitude is larger than <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math></span>.</p></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0735193324004743/pdfft?md5=0c614aaf1fa9431ef494525b0fe98191&pid=1-s2.0-S0735193324004743-main.pdf","citationCount":"0","resultStr":"{\"title\":\"The effect of viscous heating on the linear and nonlinear stability analysis of a flow through a porous duct\",\"authors\":\"Michele Celli , Antonio Barletta , Pedro Vayssiére Brandão , Silvia da Costa Hirata , Mohamed Najib Ouarzazi\",\"doi\":\"10.1016/j.icheatmasstransfer.2024.107712\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The stability of a stationary fully developed vertical flow across a porous pipe is investigated. The heating due to viscous dissipation is assumed to be non–negligible and also to be the only effect triggering the onset of thermal convection. An innovative scaling is employed to study the case of small Gebhart number. The viscous heating term present inside the energy balance equation yields a basic stationary flow characterised by dual branches of solutions: for a given vertical pressure gradient, two possible velocity profiles are obtained. The linear and nonlinear stability of the stationary dual solutions is performed. The linear stability is investigated in a usual fashion by employing the normal modes method and then solving the eigenvalue problem obtained by using the shooting method. The nonlinear stability is investigated by simulating numerically the evolution in time of the perturbed system. The linear stability analysis allows one to conclude that the critical wavenumber for the onset of instability is zero and the critical dimensionless velocity at the pipe axis is equal to <span><math><mn>3.43631</mn></math></span>. The results of the nonlinear analysis display subcritical instabilities. Indeed, the onset of instability is obtained for values of the governing parameters which are lower than the critical values obtained by the linear analysis. This feature occurs when the amplitude of the initial disturbance applied to the nonlinear problem is sufficiently high, namely when the dimensionless amplitude is larger than <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math></span>.</p></div>\",\"PeriodicalId\":332,\"journal\":{\"name\":\"International Communications in Heat and Mass Transfer\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0735193324004743/pdfft?md5=0c614aaf1fa9431ef494525b0fe98191&pid=1-s2.0-S0735193324004743-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Communications in Heat and Mass Transfer\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0735193324004743\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Communications in Heat and Mass Transfer","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0735193324004743","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
The effect of viscous heating on the linear and nonlinear stability analysis of a flow through a porous duct
The stability of a stationary fully developed vertical flow across a porous pipe is investigated. The heating due to viscous dissipation is assumed to be non–negligible and also to be the only effect triggering the onset of thermal convection. An innovative scaling is employed to study the case of small Gebhart number. The viscous heating term present inside the energy balance equation yields a basic stationary flow characterised by dual branches of solutions: for a given vertical pressure gradient, two possible velocity profiles are obtained. The linear and nonlinear stability of the stationary dual solutions is performed. The linear stability is investigated in a usual fashion by employing the normal modes method and then solving the eigenvalue problem obtained by using the shooting method. The nonlinear stability is investigated by simulating numerically the evolution in time of the perturbed system. The linear stability analysis allows one to conclude that the critical wavenumber for the onset of instability is zero and the critical dimensionless velocity at the pipe axis is equal to . The results of the nonlinear analysis display subcritical instabilities. Indeed, the onset of instability is obtained for values of the governing parameters which are lower than the critical values obtained by the linear analysis. This feature occurs when the amplitude of the initial disturbance applied to the nonlinear problem is sufficiently high, namely when the dimensionless amplitude is larger than .
期刊介绍:
International Communications in Heat and Mass Transfer serves as a world forum for the rapid dissemination of new ideas, new measurement techniques, preliminary findings of ongoing investigations, discussions, and criticisms in the field of heat and mass transfer. Two types of manuscript will be considered for publication: communications (short reports of new work or discussions of work which has already been published) and summaries (abstracts of reports, theses or manuscripts which are too long for publication in full). Together with its companion publication, International Journal of Heat and Mass Transfer, with which it shares the same Board of Editors, this journal is read by research workers and engineers throughout the world.