Stokes' first problem for viscoelastic fluids |
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| Affiliation: | 1. Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47906;2. School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906;3. Ray W. Herrick Laboratories, Purdue University, West Lafayette, Indiana 47907;2. University of Rochester School of Medicine & Dentistry, Rochester, New York,;3. Valley Hospital, Ridgewood, New Jersey;1. Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada;2. Mechanical Engineering Department, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada;1. Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (Perak), 32610 Seri Iskandar, Perak, Malaysia;2. School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia;3. Research Institute, Center for Modeling & Computer Simulation, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia;4. Mechanical Engineering Department, Prince Mohammad Bin Fahd University (PMU), Al-Khobar 31952, Saudi Arabia;1. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan 250100, China;2. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China;3. Institute for Advanced Study, Tsinghua University, Beijing 10084, China;1. Northern Technical University, Engineering Technical College of Mosul, Cultural Group Street, Mosul, Iraq;2. Instituto Superior Técnico, Department of Mechanical Engineering, Avenue Rovisco Pais, 1049-001 Lisbon, Portugal;3. TU Bergakademie Freiberg, Institute of Thermal Engineering, Chair of Gas and Heat Technology, Gustav-Zeuner-Straße 7, D-09596 Freiberg, Sachsen, Germany;4. Karlsruhe Institute of Technology, Engler-Bunte-Institute, Combustion Technology, Engler-Bunte-Ring 1, D-76131 Karlsruhe, Germany |
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| Abstract: | The theory given in this paper is based on a generalization of Boltzmann's equation of linear viscoelasticity in which the presence of a Newtonian viscosity is acknowledged. The solution of Stokes' first problem for this kind of fluid, with a viscosity and a relaxation kernel, are derived here for the first time. The formulas given in this paper form a basis for the numerical interpretation of the idea of an effective viscosity and relaxation modulus. |
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