Muhammad Imran Asjad, Maryam Aleem, W. Ali, Muhammad Abubakar, F. Jarad
{"title":"用变阶广义Caputo分数阶导数和修正拉普拉斯变换方法增强物理模型的传热传质","authors":"Muhammad Imran Asjad, Maryam Aleem, W. Ali, Muhammad Abubakar, F. Jarad","doi":"10.48185/jmam.v2i3.380","DOIUrl":null,"url":null,"abstract":"In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.","PeriodicalId":393347,"journal":{"name":"Journal of Mathematical Analysis and Modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method\",\"authors\":\"Muhammad Imran Asjad, Maryam Aleem, W. Ali, Muhammad Abubakar, F. Jarad\",\"doi\":\"10.48185/jmam.v2i3.380\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.\",\"PeriodicalId\":393347,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Modeling\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48185/jmam.v2i3.380\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48185/jmam.v2i3.380","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method
In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.