MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative |
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| Institution: | 1. Department of Mathematics, Islamia College Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan;2. Department of Mathematics, Kohat University of Science & Technology, Kohat, Khyber Pakhtunkhwa, Pakistan;3. Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan;4. Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;5. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;1. Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan;2. Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;4. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia;1. Academy of Romanian Scientists, 050094 Bucharest, Romania;2. Department of Mathematics, GC University, Lahore, Pakistan;3. Department of Theoratical Mechanics, Technical University of Iasi, Romania;4. Department of Automation, Biomechanics, Lodz University of Technology, and Mechatronics, 1/15 Stefanowski St. 90-924 Lodz Poland;1. Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan;4. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia;5. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia;1. Department of Mathematics, University of Management and Technology, Lahore, 54770 Pakistan;2. Department of Mathematics, Comsats University Islamabad, Lahore Campus, 54000 Pakistan;3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915 Vietnam |
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| Abstract: | This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducting and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number “Re”, fractional parameter “α”, effective permeability “Keff” and the time “t”, on the fluid's motion are observed. |
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