MODELING OF LAMINAR UNSTEADY FLOW OF VISCOELASTIC FLUID IN A FLAT CHANNEL
Keywords:
Laminar unsteady flow, Deborah number, viscoelastic fluid, Maxwellian fluid, Oldroyd-B fluid, Laplace-Carson transformation, mass fraction, hydrodynamic characteristics, generalized two-fluid Maxwell modelAbstract
The problems of unsteady flow of a viscoelastic fluid in a flat channel under the influence of a constant pressure gradient are solved based on the generalized Maxwell model. By solving the problem, formulas for velocity distribution, fluid flow and other hydrodynamic quantities were determined. Based on the formulas found, transient processes during unsteady flow of a viscoelastic fluid in a flat channel are analyzed. Based on the results of the analysis, it was shown that the processes of transition of the characteristics of a viscoelastic fluid from an unsteady state to a stationary state at small values of the Deborah number practically do not differ from the transition processes of a Newtonian fluid. Exceeding the Deborah number relatively unity, it has been established that the process of transition of a viscoelastic fluid from an unsteady state to a stationary state is of a wave nature, in contrast to the transition process of a Newtonian fluid, and the transition time is several times longer than that of a Newtonian fluid. It was also discovered that perturbed processes can arise during the transition. These disturbances occurring in unsteady flows of a viscoelastic fluid can be stabilized by stirring the Newtonian fluid. The implementation of this property is important in technical and technological processes, in preventing technical failures or malfunctions.
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