Peristaltic flow of a Bingham fluid in a channel |
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| Affiliation: | 1. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan;2. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mechanical and Manufacturing Engineering, Bilecik Şeyh Edebali University, Bilecik 11230, Turkey;2. School of Mechanical and Systems Engineering, Newcastle University, Newcastle-Upon-Tyne NE1 7RU, UK;1. Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK;2. School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia;1. Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India;2. Department of Chemical Engineering, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli 229316, India;1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, CIIT, Islamabad, Pakistan |
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| Abstract: | We study the peristaltic transport of a Bingham fluid in a channel with small aspect ratio whose walls behave as a periodic traveling wave. The governing equations in the unyielded phase are obtained writing the integral formulation for the momentum balance. As shown in Fusi et al. (2015), this approach allows to overcome the so-called “lubrication paradox” which may arise in the thin film approximation. We consider the case in which the inlet flux is prescribed and the one in which the flow is driven by a given pressure drop. In both cases the solution of the problem is determined solving a nonlinear integral equation for the yield surface. We perform some numerical simulations to illustrate the behavior of the yield surface, assuming that the traveling wave describing the peristaltic motion has a sinusoidal shape. |
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| Keywords: | Bingham fluids Peristaltic flow Lubrication approximation Numerical simulations |
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