A mathematical study of natural convection flow through a channel with non-singular kernels: An application to transport phenomena
In this manuscript, we have obtained closed form solution using Laplace transform, inversion algorithm and convolution theorem. The study of mass transfer flow of an incompressible fluid is carried out near vertical channel. Recently, new classes of differential operators have been introduced and re...
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| Published in: | Alexandria engineering journal Vol. 59; no. 4; pp. 2269 - 2281 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.08.2020
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| ISSN: | 1110-0168 |
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| Abstract | In this manuscript, we have obtained closed form solution using Laplace transform, inversion algorithm and convolution theorem. The study of mass transfer flow of an incompressible fluid is carried out near vertical channel. Recently, new classes of differential operators have been introduced and recognized to be efficient in capturing processes following the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly differential operators say Atangana-Baleanu (ABC) and Caputo-Fabrizio (CF) to model such flow. This model for temperature, concentration and velocity gradient is presented in dimensionless form. The obtained solutions have been plotted for various values physical parameters like α,Df,Gm,Gr,Sc and Pr on temperature and velocity profile. Our results suggest that for the variation of time the velocity behavior for CF and ABC are reversible. Finally, an incremental value of prandtl number is observed for decrease in the velocity field which reflects the control of thickness of momentum and enlargement of thermal conductivity. Further, dynamical analysis of fluid with memory effect are efficient for ABC as compared to CF. |
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| AbstractList | In this manuscript, we have obtained closed form solution using Laplace transform, inversion algorithm and convolution theorem. The study of mass transfer flow of an incompressible fluid is carried out near vertical channel. Recently, new classes of differential operators have been introduced and recognized to be efficient in capturing processes following the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly differential operators say Atangana-Baleanu (ABC) and Caputo-Fabrizio (CF) to model such flow. This model for temperature, concentration and velocity gradient is presented in dimensionless form. The obtained solutions have been plotted for various values physical parameters like α,Df,Gm,Gr,Sc and Pr on temperature and velocity profile. Our results suggest that for the variation of time the velocity behavior for CF and ABC are reversible. Finally, an incremental value of prandtl number is observed for decrease in the velocity field which reflects the control of thickness of momentum and enlargement of thermal conductivity. Further, dynamical analysis of fluid with memory effect are efficient for ABC as compared to CF. |
| Author | Baleanu, Dumitru Saeed, Syed Tauseef Riaz, Muhammad Bilal Abro, Kashif Ali |
| Author_xml | – sequence: 1 givenname: Syed Tauseef surname: Saeed fullname: Saeed, Syed Tauseef email: tauseefsaeed301@gmail.com organization: Department of Sciences & Humanities, National University of Computer & Emerging Sciences, 54000 Lahore, Pakistan – sequence: 2 givenname: Muhammad Bilal surname: Riaz fullname: Riaz, Muhammad Bilal organization: Department of Mathematics, University of Management and Technology Lahore, Pakistan – sequence: 3 givenname: Dumitru surname: Baleanu fullname: Baleanu, Dumitru organization: Department of Mathematics, Cankaya University, Turkey – sequence: 4 givenname: Kashif Ali surname: Abro fullname: Abro, Kashif Ali organization: Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan |
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| Issue | 4 |
| Keywords | Convection flow Dufour effect Convolution Inversion algorithm Mass transfer Modern fractional operator |
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| Title | A mathematical study of natural convection flow through a channel with non-singular kernels: An application to transport phenomena |
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