Abstract
The one-dimensional viscoelastic fluid flow between two infinite parallel plates with oscillatory inlet condition is examined using the Johnson–Segalman model. The symmetric and antisymmetric Chandrasekhar functions in space are utilized to represent the velocity and stress fields. The non-dimensional form of the conservation laws in addition to the constitutive equations are solved numerically based on the Galerkin projection method. Two critical Weissenberg numbers (We) for various Reynolds numbers (Re) and viscosity ratios (ε) are obtained to determine the stable range of nonlinear system behavior. Moreover, for the unsteady case, the effects of Re, viscosity ratio of solvent to solution as well as We are investigated. According to the obtained results, increasing of oscillations frequency in subcritical zone, the same as low frequency case, has almost no effect on the velocity and its gradient. Nevertheless, the normal stress amplitude of oscillations is reduced. The Re number determines the number of oscillations and the needed time prior to the steady condition. For lower Re, due to higher effect of viscosity, the initial fluctuations are intensely occurred in a short time period in contrary to the high Re case.
Highlights
Over the past few decades, the focus on viscoelastic fluids behavior especially in oscillatory conditions has been increased substantially due to their wide use in many industries
Despite the fact that up to now, several investigations focus on the non-Newtonian fluid flow between parallel plates, the lack of a comprehensive examination regarding the flow stability analysis and parameter study is still existed
The present study investigates the one-dimensional flow of a viscoelastic fluid between two infinite parallel plates
Summary
Over the past few decades, the focus on viscoelastic fluids behavior especially in oscillatory conditions has been increased substantially due to their wide use in many industries. Fluid parameters including solution to solvent viscosity ratio and relaxation time was investigated using the Weissenberg number According to their results, the flow was stable prior to reaching the maximum We. One of the most familiar examples of oscillating non-Newtonian flood is blood. The dependence of shear stress on the affecting parameters such as relaxation and retardation time, for hydro-magnetic, viscoelastic fluid passing over an oscillating surface is investigated using Oldroyd model for free convection flow [12]. Despite the fact that up to now, several investigations focus on the non-Newtonian fluid flow between parallel plates, the lack of a comprehensive examination regarding the flow stability analysis and parameter study is still existed. The effect of Reynolds number and polymer solute to solution viscosity ratio on velocity, normal and shear stresses are the other examined parameters
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