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Open AccessArticle

Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
2
Department of Mathematics, Islamia College University, Peshawar 25000, Pakistan
3
Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Majmaah 11952, Saudi Arabia
4
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
5
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 449; https://doi.org/10.3390/sym11040449
Received: 3 January 2019 / Revised: 15 March 2019 / Accepted: 17 March 2019 / Published: 1 April 2019
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed. View Full-Text
Keywords: viscous fluid; Caputo–Fabrizio time-fractional derivative; Laplace and Fourier transformations; side walls; oscillating shear stress viscous fluid; Caputo–Fabrizio time-fractional derivative; Laplace and Fourier transformations; side walls; oscillating shear stress
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MDPI and ACS Style

Asif, M.; Ul Haq, S.; Islam, S.; Abdullah Alkanhal, T.; Khan, Z.A.; Khan, I.; Nisar, K.S. Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative. Symmetry 2019, 11, 449. https://doi.org/10.3390/sym11040449

AMA Style

Asif M, Ul Haq S, Islam S, Abdullah Alkanhal T, Khan ZA, Khan I, Nisar KS. Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative. Symmetry. 2019; 11(4):449. https://doi.org/10.3390/sym11040449

Chicago/Turabian Style

Asif, Muhammad; Ul Haq, Sami; Islam, Saeed; Abdullah Alkanhal, Tawfeeq; Khan, Zar A.; Khan, Ilyas; Nisar, Kottakkaran S. 2019. "Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative" Symmetry 11, no. 4: 449. https://doi.org/10.3390/sym11040449

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