Fractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosity |
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| Authors: | Roberto Garra Federico Polito |
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| Affiliation: | 1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza, Universitá di Roma, Via A. Scarpa 16, 00161 Rome, Italy;2. Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123 Torino, Italy;1. Center for Space Human Robotics @PoliTo, Istituto Italiano di Tecnologia, Corso Trento 21, Torino 10129, Italy;2. Applied Science and Technology Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy;1. Department of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China;2. Department of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China |
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| Abstract: | In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the time dependent viscosity by using an integro-differential term and therefore generalizing the classical equation of a Newtonian viscous fluid. A possible useful choice, in this framework, is to use a rheology based on stress/strain relation generalized by fractional calculus modelling. This is a model that can be used in applied problems, taking into account a power law time variability of the viscosity coefficient. We find analytic solutions of initial value problems in an unbounded and bounded domain. Furthermore, we discuss the explicit solution in a meaningful particular case. |
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