Adnan Ahmad, M. Nazar, M. Ahmad, Sayed M. Eldin, Zaib Un Nisa, Hassan Waqas, M. Imran
{"title":"恒定比例卡普托分式导数在具有热扩散和质量扩散的移动平面上滑移效应下的 MHD 辐射麦克斯韦流体热扩散流动中的应用","authors":"Adnan Ahmad, M. Nazar, M. Ahmad, Sayed M. Eldin, Zaib Un Nisa, Hassan Waqas, M. Imran","doi":"10.1155/2024/9306915","DOIUrl":null,"url":null,"abstract":"Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of Constant Proportional Caputo Fractional Derivative to Thermodiffusion Flow of MHD Radiative Maxwell Fluid under Slip Effect over a Moving Flat Surface with Heat and Mass Diffusion\",\"authors\":\"Adnan Ahmad, M. Nazar, M. Ahmad, Sayed M. Eldin, Zaib Un Nisa, Hassan Waqas, M. Imran\",\"doi\":\"10.1155/2024/9306915\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.\",\"PeriodicalId\":49111,\"journal\":{\"name\":\"Advances in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/9306915\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2024/9306915","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Application of Constant Proportional Caputo Fractional Derivative to Thermodiffusion Flow of MHD Radiative Maxwell Fluid under Slip Effect over a Moving Flat Surface with Heat and Mass Diffusion
Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.
期刊介绍:
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike.
As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.