The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width
01 Aug 1966-Jsme International Journal Series B-fluids and Thermal Engineering (The Japan Society of Mechanical Engineers)-Vol. 9, Iss: 35, pp 533-550
TL;DR: In this article, a theoretical analysis for the laminar flow of an incompressible fluid in a narrow gap between two parallel discs of which gap-width varies arbitrarily with time.
Abstract: A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid in a narrow gap between two parallel discs of which gap-width h (t) varies arbitrarily with time. An infinite set of the non-dimensional time-dependent parameters [numerical formula], …… is introduced providing that the function h (t) is continuously differentiable, and the exact solutions of the Navier-Stokes equations and the thermal energy equation are obtained as the "multifold"series of these non-dimensional parameters. As an application, a detailed numerical study has been made of the fundamental case when the walls perform reciprocating harmonic oscillations with finite amplitudes {h (t)=h0 (1+asinωt)}. The flow characteristics are governed by the two non-dimensional parameters a and Rω=(h02ω)/υ. As compared with the sinusoidal velocity of the gap-width change, (dh)/(dt)=aωh0cosωt, the varying hydrodynamical force acting on the wall surface becomes more distorted in wave form as a increases, and becomes more advanced in phase as Rω increases. Heat is generated in the fluid between the walls through viscous friction : when the fluid is cooled by only one wall surface the fluid temperature becomes very much higher than when the cooling is done by both the two walls.
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