A Similarity Solution for Flow in a Narrow Channel of Varying Gap

J. A. Tichy; P. Bourgin

doi:10.1115/1.3171885

Journal of Applied Mechanics | Volume 53 | Issue 4 | Research Paper

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A Similarity Solution for Flow in a Narrow Channel of Varying Gap

J. A. Tichy and P. Bourgin

[+] Author and Article Information

J. A. Tichy

Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

P. Bourgin

Laboratoire de Mécanique des Fluides, Ecole Centrale de Lyon, Ecully, France 69130

J. Appl. Mech 53(4), 943-946 (Dec 01, 1986) (4 pages) doi:10.1115/1.3171885 History: Received April 17, 1986; Online July 21, 2009

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Abstract

A similarity solution may be obtained for the case of a narrow channel where the gap h varies, according to (a + bx) m . The lower surface may slide in either direction and there may be suction or injection at either surface which must vary as h −1 . Asymptotic solutions are found for large and small values of a modified Reynolds number which is based on the sliding velocity or the suction/injection rate. Boundary layer behavior may be exhibited at high Reynolds number. The present solution, being “exact” for all Reynolds numbers once the thin film assumptions have been invoked, may be of value to hydrodynamic lubrication workers to test approximations for the fluid inertia effect.

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Tichy JA, Bourgin PP. A Similarity Solution for Flow in a Narrow Channel of Varying Gap. ASME. J. Appl. Mech. 1986;53(4):943-946. doi:10.1115/1.3171885.

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A Similarity Solution for Flow in a Narrow Channel of Varying Gap

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