On exact solutions for thin film flows of a micropolar fluid |
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| Authors: | M Sajid N Ali T Hayat |
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| Institution: | 1. Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Islamic Republic of Iran;2. Department of Mechanical and Materials Engineering, Tennessee Technological University, Cookeville, TN 38505, USA;1. Department of Mechanical Engineering, University of Mazandaran, Babolsar, Islamic Republic of Iran;2. Department of Mechanical Engineering, Babol University of Technology, P.O. Box 484, Babol, Islamic Republic of Iran;3. Esfarayen University, Engineering and Technical College, Department of Mechanical Engineering, Esfarayen, North Khorasan, Islamic Republic of Iran;1. Mathematics and its Applications in Life Sciences 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, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;4. Department of Mathematics, College of Sciences, King Khalid University, PO Box 9004, Abha 61413, Saudi Arabia |
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| Abstract: | The present paper contains the exact solutions for thin film flows of a micropolar fluid. Thin films are considered for three different geometries namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The exact solution is obtained for the velocity and micro-rotation in first two cases for both weak and strong concentrations of the microelements. However, the exact expression for the micro-rotation is obtained for the third case and a numerical solution is presented for the velocity. The micro-rotation and velocity fields are sketched and discussed for different values of the material parameters. It is observed that the rotation of the microelements at the boundary increases the velocity when compared with the case when there is no rotation at the boundary. |
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