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MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

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Institute of Computer Science and Information Technology, The University of Agriculture, Peshawar 25130, Pakistan
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Department of Mathematics, City University of Science and Information Technology, Peshawar 25130, Khyber Pakhtunkhwa, Pakistan
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
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College of Civil Engineering, National University of Sciences and Technology Islamabad, Islamabad 44000, Pakistan
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Department of Chemistry, College of Arts and Science-Wadi Al-Dawaser, Prince Sattam bin Abdulaziz University, 11991 Al-kharj, Saudi Arabia
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Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
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Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, 11991 Al-Kharj, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1295; https://doi.org/10.3390/sym11101295
Received: 4 July 2019 / Revised: 7 October 2019 / Accepted: 9 October 2019 / Published: 15 October 2019
(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)
Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model. View Full-Text
Keywords: SA–NaAlg fluid; MHD; porosity; fractional model; Atangana–Baleanu derivative SA–NaAlg fluid; MHD; porosity; fractional model; Atangana–Baleanu derivative
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MDPI and ACS Style

Khan, A.; Khan, D.; Khan, I.; Taj, M.; Ullah, I.; Aldawsari, A.M.; Thounthong, P.; Sooppy Nisar, K. MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel. Symmetry 2019, 11, 1295.

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