Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary
The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fra...
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doaj-0a3c0e1c903c4354af64ff0e21012bab2020-11-25T01:43:52ZengElsevierResults in Physics2211-37972018-03-01810611067Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundaryM.A. Imran0M.B. Riaz1N.A. Shah2A.A. Zafar3Department of Mathematics, University of Management and Technology Lahore, Pakistan; Corresponding author.Department of Mathematics, University of Management and Technology Lahore, PakistanAbdus Salam School of Mathematical Sciences, GC University Lahore, PakistanDepartment of Mathematics, GC University Lahore, PakistanThe aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest’s and Tzou’s algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids. Keywords: Free convection, Slip, Maxwell fluid, Newtonian heating, Exponentially accelerated plate, Caputo-Fabrizio fractional derivatives, Stehfest’s and Tzou’s algorithmshttp://www.sciencedirect.com/science/article/pii/S2211379717323409 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
M.A. Imran M.B. Riaz N.A. Shah A.A. Zafar |
spellingShingle |
M.A. Imran M.B. Riaz N.A. Shah A.A. Zafar Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary Results in Physics |
author_facet |
M.A. Imran M.B. Riaz N.A. Shah A.A. Zafar |
author_sort |
M.A. Imran |
title |
Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary |
title_short |
Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary |
title_full |
Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary |
title_fullStr |
Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary |
title_full_unstemmed |
Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary |
title_sort |
boundary layer flow of mhd generalized maxwell fluid over an exponentially accelerated infinite vertical surface with slip and newtonian heating at the boundary |
publisher |
Elsevier |
series |
Results in Physics |
issn |
2211-3797 |
publishDate |
2018-03-01 |
description |
The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest’s and Tzou’s algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids. Keywords: Free convection, Slip, Maxwell fluid, Newtonian heating, Exponentially accelerated plate, Caputo-Fabrizio fractional derivatives, Stehfest’s and Tzou’s algorithms |
url |
http://www.sciencedirect.com/science/article/pii/S2211379717323409 |
work_keys_str_mv |
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