Numerical simulations of unsteady flows in a rotating channel using a novel eigenfunction expansion method

Starting flows of a viscous incompressible fluid, modeled by the time-fractional derivatives, within a rotating channel due to an impulsive pressure gradient are studied. Using the eigenfunction expansion, the analytic solutions in series form are obtained. The flow of the ordinary fluid is studied...

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Bibliographic Details
Published inAIP advances Vol. 10; no. 6; pp. 065035 - 065035-11
Main Authors Rubbab, Q., Mahsud, Y., Irshad, S., Imran, M. A., Ahmadian, A., Salahshour, S., Ferrara, M.
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.06.2020
AIP Publishing LLC
Subjects
Algorithms
Computational fluid dynamics
Computer simulation
Eigenvectors
Exact solutions
Flow velocity
Fluid flow
Fluids
Incompressible flow
Incompressible fluids
Mathematical models
Rotation
Unsteady flow
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Summary:Starting flows of a viscous incompressible fluid, modeled by the time-fractional derivatives, within a rotating channel due to an impulsive pressure gradient are studied. Using the eigenfunction expansion, the analytic solutions in series form are obtained. The flow of the ordinary fluid is studied as a special case of the time-fractional problem. The convergence of series solutions is proved. In addition, using the classical analytical method, coupled with the Laplace transform and Stehfest’s algorithm, an approximate solution is found. The flow rates in x- and y-directions are determined. In the case of the ordinary fluid, the steady-state and transient components of velocities are obtained. The numerical calculations are carried out by using the Mathcad software. It is found that, for fractional fluids, the reversal flow is much attenuated if the values of the fractional parameter are less than 1.
ISSN:2158-3226
2158-3226
DOI:10.1063/5.0012874