A Flow Field between Two Oscillating Plates with Different Amplitudes and Frequencies

Shalom Sadik

《中國機械工程學刊》 38卷1期 (2017/02) Pp. 99-109

摘要

A linear physical cases extension of the Stokes second problem to a flow field between two oscillating plates with different amplitudes and frequencies for one homogenous fluid and two fluids is presented. The solution presented may be applicable to any number of fluids. As a first stage, a homogeneous fluid flow field between two oscillating plates were derived. The plates are oscillating with different amplitudes and frequencies. As a second stage a two fluids flow field between the oscillating plates was derived. The fluids are characterized by different viscosities. Actually, six problems solutions were received: a homogeneous fluid flow field between a bottom plate oscillating and an upper plate standing, a homogeneous fluid flow field between an upper plate oscillating and a bottom plate standing, a homogeneous fluid flow field between upper and bottom plate oscillating, a two fluids flow field between a bottom plate oscillating and an upper plate standing, a two fluids fluid flow field between an upper plate oscillating and a bottom plate standing and a two fluids fluid flow field between upper and bottom plate oscillating. It was shown that a physical superposition using leads to get a full solution. Complex numbers was used for solution, it was shown that in order to get an exact solution all the complex number parts, the real and the imaginary parts, has to fulfill the problem boundary conditions. Leading parameters influence was examined. It was shown that reduced fluids viscosity and increased plate frequency increases the velocity lines density.

關鍵字

oscillating plate ； flow field ； amplitude ； frequency