Energetische Betrachtungen zum Rayleigh‐Stokes Problem

Bühler, Karl; Zierep, Jürgen

doi:10.1002/pamm.200510246

Cited by 11 publications

(8 citation statements)

References 5 publications

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“…In recent years, the interest for flows of non-Newtonian fluids has considerably increased, while the energetic aspects regarding these motions are scarcely met in the literature. To the best of our knowledge, the first results of this kind seem to be those of Bühler and Zierep [1] concerning the Rayleigh-Stokes problem for Newtonian fluids. These results have been recently extended to second grade and Maxwell fluids by Zierep and Fetecau [2,3].…”

Section: Introductionmentioning

confidence: 79%

Energetic Balance for the Flow Induced by a Constantly Accelerating Plate in a Second Grade Fluid

Fetecău¹

2010

Engineering

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Dissipation, power due to the shear stress at the wall and the boundary layer thickness corresponding to the unsteady flow of a second grade fluid, due to a constantly accelerating plate, are established in exact and approximate forms. The changing of the kinetic energy with time is also determined from the energetic balance. Exact expressions of the same entities for Newtonian fluids are recovered as limiting cases of general results

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Section: Introductionmentioning

confidence: 79%

Energetic Balance for the Flow Induced by a Constantly Accelerating Plate in a Second Grade Fluid

Fetecău¹

2010

Engineering

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“…Exact or approximate solutions are well-known in the literature (see for instance [1][2][3][4][5][6][7][8][9][10][11][12][13] for the flow over an infinitely extended plate), while energetic aspects as regards these motions are scarcely met. The first notable results of this kind seem to be those of Bühler and Zierep [14] concerning the Rayleigh-Stokes problem for Newtonian fluids. These results have been recently extended to second-grade and Maxwell fluids [15,16].…”

Section: Introductionmentioning

confidence: 89%

On the energetic balance for the flow of an Oldroyd-B fluid due to a flat plate subject to a time-dependent shear stress

Zierep¹,

Bohning²,

Fetecău³

2010

Computers & Mathematics with Applications

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a b s t r a c tExact and approximate expressions for the power due to the shear stress at the wall L, the dissipation Φ and the boundary layer thickness δ are established for the unsteady flow of an Oldroyd-B fluid driven by the transverse motion of an infinite plate subject to a timedependent shear stress. The change of the kinetic energy with time is also obtained from the energetic balance. Similar expressions for Newtonian, Maxwell and second-grade fluids are obtained as limiting cases of general results. Series solutions for the velocity and shear stress are also obtained for small values of the dimensionless relaxations and retardation times. Graphical illustrations corresponding to the exact expressions for L, Φ and δ agree with the associated asymptotic approximations. Usually for many industrial applications the velocity of the wall is given and what is required is the energy that is necessary to keep the wall running with the prescribed value. The problem discussed by us now is that where, on the contrary, the wall shear stress is given but the velocity and the energy of the medium are required.

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“…It is easy to calculate the wall shear stress, the dissipation, and the kinetic energy for the energy balance [2]. For Newtonian medium this had been extensively done in [6]. These considerations may be of interest for many applications.…”

Section: Discussion Of the Different Solutionsmentioning

confidence: 99%

“…The last cannot be neglected in the neighbourhood of the wall as before. For α = 0 and sufficient large N with Nπ L 2 α 1 (6) we get after some calculations…”

Section: Appendix IImentioning

confidence: 99%