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Two-layer flows of generalized immiscible second grade fluids in a rectangular channel |
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| Authors: | Liang Luo Nehad Ali Shah Ibrahim M Alarifi Dumitru Vieru |
| Institution: | 1. Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan, China
School of Transportation, Wuhan University of Technology, Wuhan, China;2. Department of Mathematics, Lahore Leads University, Lahore, Pakistan;3. Department of Mechanical and Industrial Engineering College of Engineering, Majmaah University, Al-Majmaah, Saudi Arabia;4. Department of Theoretical Mechanics, Technical University “Gheorghe Asachi” of Iasi, Iasi, Romania |
| Abstract: | Unsteady one-dimensional flows of two incompressible and immiscible generalized second grade fluids in a rectangular channel are studied. A constant pressure gradient acts in the flow direction, while the channel walls have oscillating translational motions in their planes. The generalization considered in this paper consists into a mathematical model based on constitutive equations of second grade fluid with Caputo time-fractional derivative in which the history of the shear stress influences the velocity gradient. The velocity and shear stress fields in the Laplace transform domain are obtained. Numerical solutions for the real velocity and shear stress have been found by employing the Stehfest numerical algorithm for the inverse Laplace transform. The influence of the fractional parameters on the velocity and shear stress has been studied by numerical simulations and graphical illustrations. It is found that the memory effects are significant only for small values of the time t. |
| Keywords: | fractional calculus immiscible fluids memory effects two-layer flow |