Flows induced by power-law stretching surface motion modulated by transverse or orthogonal surface shear

Patrick Weidman

doi:10.1016/j.crme.2016.10.016

Flows induced by power-law stretching surface motion modulated by transverse or orthogonal surface shear

Patrick Weidman ¹

¹ Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA

Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 169-176.

Abstract

Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.

Received: 2016-07-29
Accepted: 2016-10-21
Published online: 2016-11-16

DOI: 10.1016/j.crme.2016.10.016

Mots-clés : Boundary-layer flow, Power-law stretching, Transverse shearing motion, Orthogonal shearing motion, General solutions

Author's affiliations:

Patrick Weidman ¹

¹ Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA

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     title = {Flows induced by power-law stretching surface motion modulated by transverse or orthogonal surface shear},
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Patrick Weidman. Flows induced by power-law stretching surface motion modulated by transverse or orthogonal surface shear. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 169-176. doi : 10.1016/j.crme.2016.10.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.10.016/

References
Cited by

[1] W.H.H. Banks Similarity solutions of the boundary-layer equations for a stretching wall, J. Méc. Théor. Appl., Volume 2 (1983), pp. 375-392

[2] L.J. Crane Flow past a stretching sheet, Z. Angew. Math. Phys., Volume 21 (1970), pp. 645-647

[3] P.D. Weidman Flows induced by flat surfaces sheared in their own plane, Fluid Dyn. Res., Volume 45 (2013)

[4] P.D. Weidman The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid, Acta Mech., Volume 226 (2015), pp. 3307-3316

[5] P.D. Weidman; S. Mansur; A. Ishak Biorthogonal stretching and shearing of an impermeable surface in a uniformly rotating fluid, Meccanica (2016) (in press) | DOI

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