FRACTIONAL MAGNETOHYDRODYNAMIC FLOW OF A SECOND GRADE FLUID IN A POROUS MEDIUM WITH VARIABLE WALL VELOCITY AND NEWTONIAN HEATING

Talha Anwar, Poom Kumam, Ilyas Khan and Phatiphat Thounthong
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Talha Anwar: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand‡Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Poom Kumam: ��KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand‡Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand§Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Ilyas Khan: �Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Phatiphat Thounthong: ��Renewable Energy Research Center, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-15

Abstract: In this study, two different fractional models are developed for a second grade fluid coupled with the energy equation. These two fractional models are based on the definitions of Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The fluid transport is considered over an infinite upright plate, that is nested in a permeable medium under the influence of an imposed magnetic field. The variable wall velocity and Newtonian heating boundary conditions are simultaneously applied for the very first time. Based on two different fractional derivatives, double fractional analysis is accomplished to evaluate the resulting two models. The momentum and energy solutions are separately established for each model by employing Laplace transform and Durbin’s numerical Laplace inversion. The verification analysis of these obtained solutions is performed with the aid of Zakian’s and Stehfest’s algorithms. The rise and fall in momentum and energy profiles due to variation of incipient parametric values are elucidated graphically and physical arguments behind these behaviors are interpreted. The velocity and temperature gradients are evaluated at the boundary to estimate the wall shear stress and heat transfer rate in terms of the skin friction coefficient and Nusselt number. The noteworthy physical impacts of incipient parameters on shear stress and heat transfer rate are analyzed through tabular study. In comparison, it is found that the energy profile for the ABC model is higher than CF model and ordinary model, respectively. Similarly, for velocity distribution, the ABC model exhibits the highest profile as compared to CF and ordinary models in the case of ramped velocity. However, an exactly opposite pattern of velocity profiles is observed for an isothermal velocity case. On the basis of this comparative analysis, it can be stated that the ABC model is the best choice to appropriately explain the memory effect of energy and momentum distributions.

Keywords: Variable Wall Velocity; Newtonian Heating; Second Grade Fluid; CF; ABC Fractional Models; Laplace Transform; Magnetohydrodynamic (MHD) (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500602

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