Flows of a generalized second grade fluid in a cylinder due to a velocity shock |
| |
| Institution: | 1. Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan;2. Department of Mathematics, University of Management and Technology, Lahore, Pakistan;1. Universidade Tecnológica Federal do Paraná, 84016-210 Ponta Grossa-PR, Brazil;2. Universidade Federal de Santa Catarina, C. P. 101, 89520-000 Curitibanos-SC, Brazil;1. Department of Mathematics, Faculty of Basic Sciences University of Wah, Wah Cantt, Pakistan;2. Department of Mathematics, Faculty of Natural Sciences, HITEC University, Taxila Cantt, Pakistan;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, 266590, China;1. Department of Computer Science and Engineering, Air University Multan Campus, Multan, 60000, Pakistan;2. Abdus Salam School of Mathematical Sciences, The Government College University, Lahore, 54600, Pakistan;3. Department of Mathematics, University of Management & Technology, Lahore, 54770, Pakistan;1. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia;2. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia;3. Department of Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania |
| |
| Abstract: | Unsteady axial flows of second grade fluids with generalized fractional constitutive equation in a circular cylinder are studied. Flows are generated by a time-dependent pressure gradient in the axial direction, an external magnetic field perpendicular on the flow direction and by the cylinder motion. Two different problems are analyzed; one in which the cylinder velocity supports a shock at the instant t = 0 and another in which the cylinder motion is a translation with time-dependent velocity along the axis of cylinder. The generalized fractional constitutive equation of second grade fluid is described by the Caputo time-fractional derivative. Analytical solutions for the velocity field are obtained by using the Laplace transform with respect to time variable and the finite Hankel transform of order zero with respect to the radial coordinate. The influence of the fractional parameter of Caputo derivative on the fluid velocity has been studied by numerical simulations and graphical illustrations. It is found that the fractional fluid flows are faster than the ordinary second grade fluid. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
