MHD flow of fractional Newtonian fluid embedded in a porous medium via Atangana-Baleanu fractional derivatives

Kashif Ali Abro; Ilyas Khan

doi:10.3934/dcdss.2020021

Article Contents

2020, Volume 13, Issue 3: 377-387. Doi: 10.3934/dcdss.2020021

This issue Previous Article Fractional operators with boundary points dependent kernels and integration by parts Next Article Implementation of the vehicular occupancy-emission relation using a cubic B-splines collocation method

MHD flow of fractional Newtonian fluid embedded in a porous medium via Atangana-Baleanu fractional derivatives

Kashif Ali Abro^1, and
Ilyas Khan^2, ,

1.
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
2.
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^* Corresponding author: Ilyas Khan (ilyaskhan@tdt.edu.vn)
^* Corresponding author: Ilyas Khan (ilyaskhan@tdt.edu.vn)

Received: April 30, 2018

Revised: August 31, 2018

Published: December 2019

The author Kashif Ali Abro is highly thankful and grateful to Mehran University of Engineering and Technology, Jamshoro, Pakistan, for generous support and facilities of this research work.

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Abstract

The novelty of this research is to utilize the modern approach of Atangana-Baleanu fractional derivative to electrically conducting viscous fluid embedded in porous medium. The mathematical modeling of the governing partial differential equations is characterized via non-singular and non-local kernel. The set of governing fractional partial differential equations is solved by employing Laplace transform technique. The analytic solutions are investigated for the velocity field corresponding with shear stress and expressed in term of special function namely Fox-H function, moreover a comparative study with an ordinary and Atangana-Baleanu fractional models is analyzed for viscous flow in presence and absence of magnetic field and porous medium. The Atangana-Baleanu fractional derivative is observed more reliable and appropriate for handling mathematical calculations of obtained solutions. Finally, graphical illustration is depicted via embedded rheological parameters and comparison of models plotted for smaller and larger time on the fluid flow.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Profile of velocity field via Atangana-Baleanu fractional differential operator for fractional parameter

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Figure 2. Profile of velocity field via Atangana-Baleanu fractional differential operator for porous medium

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Figure 3. Profile of velocity field via Atangana-Baleanu fractional differential operator for magnetic field

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Figure 4. Comparative analysis of velocity field via Atangana-Baleanu fractional differential operator verses ordinary differential operator for short time

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Figure 5. Comparative analysis of velocity field via Atangana-Baleanu fractional differential operator verses ordinary differential operator for unit time

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Figure 6. Comparative analysis of velocity field via Atangana-Baleanu fractional differential operator verses ordinary differential operator for larger time

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