Abstract
Abstract
Highlights
The transient behaviour of fluids caused by impulsive change of boundary data is of great interest in fluid mechanics
We investigated the transient behaviour of a rarefied gas caused by an impulsive onset of the rotating motion of a sphere based on the linearized BGK equation and the diffuse reflection boundary condition
This problem can be viewed as an extension of the one-dimensional linearized Rayleigh problem to a three-dimensional axisymmetric flow
Summary
The transient behaviour of fluids caused by impulsive change of boundary data is of great interest in fluid mechanics. The linearized Rayleigh problem describes the propagation of the transverse momentum into the gas and contains both the free-molecular-like and the continuum-flow-like behaviours in a single problem. These characters have been revisited in recent mathematical studies (Kuo 2011, 2017). Unlike the one-dimensional Rayleigh problem for a planer boundary, the sphere radius appears as a quantity having a physical dimension of length in addition to the molecular mean free path in the present problem. Their quotient, known as the Knudsen number, plays an important role in characterizing unsteady response.
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