Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport

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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Main Authors: Yu-Liang Sun, Nehad Ali Shah, Zar Ali Khan, Y.M. Mahrous, Bakhtiar Ahmad, Jae Dong Chung, M. Niaz Khan
Format: Article
Language:English
Published: Elsevier 2021-08-01
Series:Case Studies in Thermal Engineering
Subjects:
Brinkman type fluids
Prabhakar-like fractional derivative
Laplace transform
Mittag-Leffler functions
Exact solutions
Online Access:http://www.sciencedirect.com/science/article/pii/S2214157X21002896
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spelling doaj-0ee5c127f3634be0af415a9f491599a12021-07-09T04:43:54ZengElsevierCase Studies in Thermal Engineering2214-157X2021-08-0126101126Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transportYu-Liang Sun0Nehad Ali Shah1Zar Ali Khan2Y.M. Mahrous3Bakhtiar Ahmad4Jae Dong Chung5M. Niaz Khan6School of Science, Huzhou University, Huzhou, 313000, PR ChinaDepartment of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea; Department of Mathematics, Lahore Leads University, Lahore, PakistanDepartment of Mathematics, Government Superior Science College Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, PakistanDepartment of Studies and Basic Sciences, Faculty of Community, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi ArabiaDepartment of Mathematics, Government College Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, PakistanDepartment of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea; Corresponding author.Department of Mathematics, Lahore Leads University, Lahore, PakistanNatural 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.http://www.sciencedirect.com/science/article/pii/S2214157X21002896Brinkman type fluidsPrabhakar-like fractional derivativeLaplace transformMittag-Leffler functionsExact solutions
collection DOAJ
language English
format Article
sources DOAJ
author Yu-Liang Sun
Nehad Ali Shah
Zar Ali Khan
Y.M. Mahrous
Bakhtiar Ahmad
Jae Dong Chung
M. Niaz Khan
spellingShingle Yu-Liang Sun
Nehad Ali Shah
Zar Ali Khan
Y.M. Mahrous
Bakhtiar Ahmad
Jae Dong Chung
M. Niaz Khan
Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
Case Studies in Thermal Engineering
Brinkman type fluids
Prabhakar-like fractional derivative
Laplace transform
Mittag-Leffler functions
Exact solutions
author_facet Yu-Liang Sun
Nehad Ali Shah
Zar Ali Khan
Y.M. Mahrous
Bakhtiar Ahmad
Jae Dong Chung
M. Niaz Khan
author_sort Yu-Liang Sun
title Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
title_short Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
title_full Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
title_fullStr Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
title_full_unstemmed Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport
title_sort exact solutions for natural convection flows of generalized brinkman type fluids: a prabhakar-like fractional model with generalized thermal transport
publisher Elsevier
series Case Studies in Thermal Engineering
issn 2214-157X
publishDate 2021-08-01
description 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.
topic Brinkman type fluids
Prabhakar-like fractional derivative
Laplace transform
Mittag-Leffler functions
Exact solutions
url http://www.sciencedirect.com/science/article/pii/S2214157X21002896
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