Analytical Solutions of Fractional Walter’s B Fluid with Applications
Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/8131329 |
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| author | Qasem Al-Mdallal Kashif Ali Abro Ilyas Khan |
| author_facet | Qasem Al-Mdallal Kashif Ali Abro Ilyas Khan |
| author_sort | Qasem Al-Mdallal |
| collection | DOAJ |
| description | Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function MΩ2,Ω3Ω1χ and Fox-H function Hp,q+11,p satisfying imposed conditions on the problem. These solutions have combined effects of heat and mass transfer; this is due to free convections differences between mass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters. |
| format | Article |
| id | doaj-art-16ad90c345844457a6d0faeddb295bb2 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-16ad90c345844457a6d0faeddb295bb22025-02-03T01:28:52ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/81313298131329Analytical Solutions of Fractional Walter’s B Fluid with ApplicationsQasem Al-Mdallal0Kashif Ali Abro1Ilyas Khan2Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al Ain, UAEDepartment of Basic Sciences and Related Studies, Mehran University of Engineering Technology, Jamshoro, PakistanBasic Engineering Sciences Department, College of Engineering, Majmaah University, Al Majmaah, Saudi ArabiaFractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function MΩ2,Ω3Ω1χ and Fox-H function Hp,q+11,p satisfying imposed conditions on the problem. These solutions have combined effects of heat and mass transfer; this is due to free convections differences between mass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters.http://dx.doi.org/10.1155/2018/8131329 |
| spellingShingle | Qasem Al-Mdallal Kashif Ali Abro Ilyas Khan Analytical Solutions of Fractional Walter’s B Fluid with Applications Complexity |
| title | Analytical Solutions of Fractional Walter’s B Fluid with Applications |
| title_full | Analytical Solutions of Fractional Walter’s B Fluid with Applications |
| title_fullStr | Analytical Solutions of Fractional Walter’s B Fluid with Applications |
| title_full_unstemmed | Analytical Solutions of Fractional Walter’s B Fluid with Applications |
| title_short | Analytical Solutions of Fractional Walter’s B Fluid with Applications |
| title_sort | analytical solutions of fractional walter s b fluid with applications |
| url | http://dx.doi.org/10.1155/2018/8131329 |
| work_keys_str_mv | AT qasemalmdallal analyticalsolutionsoffractionalwaltersbfluidwithapplications AT kashifaliabro analyticalsolutionsoffractionalwaltersbfluidwithapplications AT ilyaskhan analyticalsolutionsoffractionalwaltersbfluidwithapplications |