TITLE:
Flows of a Rarefied Gas between Coaxial Circular Cylinders with Nonuniform Surface Properties
AUTHORS:
Toshiyuki Doi
KEYWORDS:
Rarefied Gas Flow, Micro Flow, Boltzmann Equation, Gas-Surface Interaction, Reciprocity Relations
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.9 No.1,
February
15,
2019
ABSTRACT: Flows of a rarefied gas between coaxial circular cylinders with nonuniform
surface properties are studied on the basis of kinetic theory. It is assumed that
the outer cylinder is a diffuse reflection boundary and the inner cylinder is a
Maxwell-type boundary whose accommodation coefficient varies in the circumferential
direction. Three fundamental flows are studied: 1) a flow caused
by the rotation of the outer cylinder (Couette flow), 2) a flow induced between
the cylinders at rest kept at different temperatures (heat transfer problem),
and 3) a flow induced by the circumferential temperature distribution
along the cylindrical surfaces (thermal creep flow). The linearized ES-BGK
model of the Boltzmann equation is numerically analyzed using a finite difference
method. The time-independent behavior of the gas is studied over a
wide range of the gas rarefaction degree, the radii ratio, and a parameter characterizing
the distribution of the accommodation coefficient. Due to an effect
of nonuniform surface properties, a local heat transfer occurs between
the gas and the cylindrical surfaces in Couette flow; a local tangential stress
arises in the heat transfer problem. However, the total heat transfer between
the two cylinders in Couette flow and the total torque acting on the inner cylinder
in the heat transfer problem vanish irrespective of the flow parameters.
Two nondegenerate reciprocity relations arise due to the effect of nonuniform
surface properties. The reciprocity relations among the above-mentioned three
flows are numerically confirmed over a wide range of the flow parameters.
The force on the inner cylinder, which also arises due to the effect of nonuniform
surface properties in Couette flow and the heat transfer problems, is
studied.