Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties

Abstract

Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties induced by a sudden start-up of one of the walls is studied based on kinetic theory. The linearized Boltzmann equation for a hard sphere molecular gas is analyzed under the assumptions that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary. The initial and boundary value problem is solved numerically by using a modified hybrid scheme of characteristic coordinate and finite difference methods, to describe the discontinuities in the velocity distribution function correctly. The time evolution of the flow and the approach to the final time-independent state are studied over a wide range of the mean free paths and the accommodation coefficient of the boundary. In the transient process, the shear force acting on the moving wall depends on which wall moves. In contrast, the shear force acting on the wall at rest is independent of which wall moves; this property is a consequence of the symmetric relation of the Boltzmann equation [S. Takata, “Symmetry of the unsteady linearized Boltzmann equation in a fixed bounded domain,” J. Stat. Phys. 140, 985 (2010)]. The speed of approach to the time-independent state is fastest at an intermediate value of the mean free path. The behavior of the gas in the final time-independent state, including the heat flow in the isothermal gas, is also discussed.

Transient behaviour of a rarefied gas around a sphere caused by impulsive rotation

“…The present problem is expected to provide fundamental information on the unsteady behaviour of rarefied gas if combined with recent results focusing on oscillatory shear-driven flows (e.g. Park, Bahukudumbi & Beskok 2004;Hadjiconstantinou 2005;Sharipov & Kalempa 2008;Doi 2010;Yap & Sader 2012, 2016.…”

“…Sone & Sugimoto 1990; Aoki et al. 1991; Doi 2016). However, most of the studies are limited to spatially one-dimensional problems.…”

“…Later on, flows caused by a sudden change of boundary data have been investigated in various situations (e.g. Sone & Sugimoto 1990;Aoki et al 1991;Doi 2016). However, most of the studies are limited to spatially one-dimensional problems.…”

Flows of a Rarefied Gas between Coaxial Circular Cylinders with Nonuniform Surface Properties

“…In the heat transfer problem, similarly, the distribution function φ is an even function with respect to θ ζ . By using the conservation laws (23) and the boundary condition (13) or (14), we obtain…”

“…Examples of the flows between plane parallel walls with unequal surface properties are studied, e.g., in Refs. [8]- [13]. Flows between parallel walls with nonuniform surface properties along the wall surface are studied, e.g., in Refs.…”