Run-up and spin-up in a viscoelastic fluid. I.

Kazakia, J. Y.; Rivlin, R. S.

doi:10.1007/bf01513054

Cited by 41 publications

(13 citation statements)

References 2 publications

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“…Then, we write m = mx + m2, with ml and m2 as above and m2 small enough so that the procedure outlined above yields estimates for derivatives of m2 through order N. For each e > 0, we set m2(t) = m2(t + e), 0, (a. 17) and denote by f2 the solution of ft/2 J0 2/S/2 (t) + 2 ('/2f2 (t -t)/2 (t) dr = -m2{t).…”

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confidence: 99%

On wave propagation in linear viscoelasticity

Hrusa¹,

Renardy²

1985

Quart. Appl. Math.

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Abstract. We discuss the initial value problem in one-dimensional linear visco-elasticity with a step-jump in the initial data. If the memory kernel is sufficiently smooth on [0 , oo), the solution exhibits discontinuities propagating along characteristics and a (higher order) stationary discontinuity at the position of the original step-jump. For a singular memory kernel, the propagating waves are smoothed in a manner depending on the nature of the singularity in the kernel, but the stationary discontinuity remains. We also discuss the effects of these phenomena on the regularity of solutions with arbitrary initial data.

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confidence: 99%

On wave propagation in linear viscoelasticity

Hrusa¹,

Renardy²

1985

Quart. Appl. Math.

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“…10.007 given the same constant velocity. Kazakia and Rivlin [8] and later Rivlin [9,10] have studied this interesting unidirectional unsteady flow with reference to a viscoelastic fluid. The flow generated by the above mechanism is termed as a run up flow.…”

Section: Introductionmentioning

confidence: 99%

Run up flow of an incompressible micropolar fluid between parallel plates – A state space approach

Devakar

Iyengar

2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we study the run up flow of an incompressible micropolar fluid between two horizontal infinitely long parallel plates. Initially a flow of the fluid is induced by a constant pressure gradient until steady state is reached. After the steady state is reached, the pressure gradient is suddenly withdrawn while the two plates are impulsively started with different velocities in their own plane. Using the Laplace transform technique and adopting the state space approach, we obtain the velocity and microrotation components in Laplace transform domain. A standard numerical inversion procedure is used to find the velocity and microrotation in space-time domain for various values of time, distance, material parameters and pressure gradient. The variation of velocity and microrotation components is studied and the results are illustrated through graphs. It is observed that the micropolarity parameter has a decreasing effect on velocity component. It is also found that as the gyration parameter increases there is a decrease in microrotation component and an increase in velocity component.

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“…Smooth convolution kernels with one derivative bounded at 0 yield hyperbolic behavior in the sense that singularities are propagated much as in the purely elastic case, although they are exponentially damped (e.g., see [1,6,7,9,10,12,17,23,25]). However, recent literature indicates that many materials may be better described by equations involving singular kernels, such as fractional derivative models [2,3,26].…”

Section: Introductionmentioning

confidence: 99%