{"title":"使用 Levenberg-Marquardt 算法计算磁场、辐射和焦耳热对威廉姆森流体在垂直通道中自然对流的影响","authors":"Subham Jangid, Kaladhar Kolla","doi":"10.1177/09544089241264088","DOIUrl":null,"url":null,"abstract":"The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].","PeriodicalId":20552,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Magnetic field, radiation, and Joule heating effects on natural convection Williamson fluid flow through a vertical channel using Levenberg–Marquardt algorithm\",\"authors\":\"Subham Jangid, Kaladhar Kolla\",\"doi\":\"10.1177/09544089241264088\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].\",\"PeriodicalId\":20552,\"journal\":{\"name\":\"Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1177/09544089241264088\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/09544089241264088","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Magnetic field, radiation, and Joule heating effects on natural convection Williamson fluid flow through a vertical channel using Levenberg–Marquardt algorithm
The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].
期刊介绍:
The Journal of Process Mechanical Engineering publishes high-quality, peer-reviewed papers covering a broad area of mechanical engineering activities associated with the design and operation of process equipment.