Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
Natural convection flow of unsteady Prabhakar-like fractional Brinkman type fluids over an infinite vertical heated wall with uniform heat flux is studied. Exact dimensionless solutions of momentum and energy equations, under Boussinesq approximation, are obtained using Laplace transforms. They sati...
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| Published in: | Case studies in thermal engineering Vol. 26; p. 101126 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
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01-08-2021
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| Abstract | Natural convection flow of unsteady Prabhakar-like fractional Brinkman type fluids over an infinite vertical heated wall with uniform heat flux is studied. Exact dimensionless solutions of momentum and energy equations, under Boussinesq approximation, are obtained using Laplace transforms. They satisfy all imposed conditions and reduce to known solutions from the literature as special cases. The velocity and heat transfer of Prabhakar-like fractional Brinkman type fluids with generalized thermal transport are compared with ordinary Brinkman type fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Finally, the influence of different parameters like fractional parameters, Prandtl number, Grashof number, time and Brinkman parameter on temperature and velocity is shown by graphs. |
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| AbstractList | Natural convection flow of unsteady Prabhakar-like fractional Brinkman type fluids over an infinite vertical heated wall with uniform heat flux is studied. Exact dimensionless solutions of momentum and energy equations, under Boussinesq approximation, are obtained using Laplace transforms. They satisfy all imposed conditions and reduce to known solutions from the literature as special cases. The velocity and heat transfer of Prabhakar-like fractional Brinkman type fluids with generalized thermal transport are compared with ordinary Brinkman type fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Finally, the influence of different parameters like fractional parameters, Prandtl number, Grashof number, time and Brinkman parameter on temperature and velocity is shown by graphs. |
| ArticleNumber | 101126 |
| Author | Mahrous, Y.M. Khan, Zar Ali Ahmad, Bakhtiar Sun, Yu-Liang Khan, M. Niaz Shah, Nehad Ali Chung, Jae Dong |
| Author_xml | – sequence: 1 givenname: Yu-Liang surname: Sun fullname: Sun, Yu-Liang organization: School of Science, Huzhou University, Huzhou, 313000, PR China – sequence: 2 givenname: Nehad Ali surname: Shah fullname: Shah, Nehad Ali organization: Department of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea – sequence: 3 givenname: Zar Ali surname: Khan fullname: Khan, Zar Ali organization: Department of Mathematics, Government Superior Science College Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan – sequence: 4 givenname: Y.M. surname: Mahrous fullname: Mahrous, Y.M. organization: Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia – sequence: 5 givenname: Bakhtiar surname: Ahmad fullname: Ahmad, Bakhtiar organization: Department of Mathematics, Government College Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan – sequence: 6 givenname: Jae Dong surname: Chung fullname: Chung, Jae Dong email: jdchung@sejong.ac.kr organization: Department of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea – sequence: 7 givenname: M. Niaz surname: Khan fullname: Khan, M. Niaz organization: Department of Mathematics, Lahore Leads University, Lahore, Pakistan |
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| Cites_doi | 10.1007/BF01094898 10.1007/s00231-009-0552-3 10.1115/1.3450729 10.1016/j.cjph.2019.05.006 10.1016/j.cnsns.2017.08.018 10.1016/0735-1933(83)90016-7 10.3390/math7020150 10.1007/BF02120318 10.1023/A:1006593330865 10.1016/0017-9310(85)90190-5 10.7153/fdc-06-05 10.1016/j.cnsns.2017.08.002 10.1007/BF00651403 10.1016/j.chaos.2019.109489 10.1016/j.cjph.2018.02.007 10.1007/s11012-009-9257-4 10.1016/j.molliq.2019.110964 10.1142/S0218202507001899 10.1063/1.5032165 10.1016/j.rinp.2018.04.034 10.1007/BF02120313 |
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| Keywords | Prabhakar-like fractional derivative Mittag-Leffler functions Brinkman type fluids Laplace transform Exact solutions |
| Language | English |
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| Snippet | Natural convection flow of unsteady Prabhakar-like fractional Brinkman type fluids over an infinite vertical heated wall with uniform heat flux is studied.... |
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| SubjectTerms | Brinkman type fluids Exact solutions Laplace transform Mittag-Leffler functions Prabhakar-like fractional derivative |
| Title | Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport |
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