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

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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  • 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.

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

    Citation:

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

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

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

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

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

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

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