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ARTICLE
MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators
Thabet Abdeljawad1,2,3, Muhammad Bilal Riaz4,5, Syed Tauseef Saeed6,*, Nazish Iftikhar6
1 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia
2 Department of Medical Research, China Medical University, Taichung, 404, Taiwan
3 Department of Computer Science and Information Engineering, Asia University, Taichung, 41354, Taiwan
4 Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan
5 Institute for Groundwater Studies (IGS), University of the Free State, Bloemfontein, 9301, South Africa
6 Department of Science & Humanities, National University of Computer and Emerging Sciences, Lahore, 54000, Pakistan
* Corresponding Author: Syed Tauseef Saeed. Email:
(This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)
Computer Modeling in Engineering & Sciences 2021, 126(2), 821-841. https://doi.org/10.32604/cmes.2021.012529
Received 03 July 2020; Accepted 19 October 2020; Issue published 21 January 2021
Abstract
The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and
ramp temperature on magnetohydrodynamic (MHD) time-dependent Maxwell fluid over an unbounded plate
embedded in a permeable medium. Non-dimensional parameters along with Laplace transformation and inversion
algorithms are used to find the solution of shear stress, energy, and velocity profile. Recently, new fractional
differential operators are used to define ramped temperature and ramped velocity. The obtained analytical solutions
are plotted for different values of emerging parameters. Fractional time derivatives are used to analyze the impact
of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed
that the fractional-order model is best to explain the memory effect as compared to classical models. Our results
suggest that the velocity profile decrease by increasing the effective Prandtl number. The existence of an effective
Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.
The incremental value of the M is observed for a decrease in the velocity field, which reflects to control resistive
force. Further, it is noted that the Atangana-Baleanu derivative in Caputo sense (ABC) is the best to highlight the
dynamics of the fluid. The influence of pertinent parameters is analyzed graphically for velocity and energy profile.
Expressions for skin friction and Nusselt number are also derived for fractional differential operators.
Keywords
Cite This Article
Abdeljawad, T., Riaz, M. B., Saeed, S. T., Iftikhar, N. (2021). MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators.
CMES-Computer Modeling in Engineering & Sciences, 126(2), 821–841.
Citations