Gas-flow animation by unsteady heating in a microchannel

Abstract

We study the flow-field generated in a one-dimensional wall-bounded gas layer due to an arbitrary small-amplitude time variation in the temperature of its boundaries. Using the Fourier transform technique, analytical results are obtained for the slip-flow/Navier-Stokes limit. These results are complemented by low-variance simulations of the Boltzmann equation, which are useful for establishing the limits of the slip-flow description, as well as for bridging the gap between the slip-flow analysis and previously developed free-molecular analytical predictions. Results are presented for both periodic ͑sinusoidal͒ and nonperiodic ͑step-jump͒ heating profiles. Our slip-flow solution is used to elucidate a singular limit reported in the literature for oscillatory heating of a dynamically incompressible fluid.

The response of a confined rarefied gas to non-periodic acoustic excitation

“…This can be traced back to the ratio between advective (∼ L * /U * th ) and diffusive (∼ L * 2 /ν * ) time scales, governing relaxation processes in collisionless and continuum conditions, respectively. A similar result was found in a previous set of studies, where the thermoacoustic response of a gas to instantaneous (step-jump) change in the temperature of its boundaries was analyzed [14,15]. It therefore appears of interest to investigate the combined effects of thermal and mechanical excitations on the propagation of sound waves in a rarefied medium.…”

Active noise control of a vibrating surface: Continuum and non-continuum investigations on vibroacoustic sound reduction by a secondary heat-flux source

“…Yet, a thin-layer response of a confined system to high-frequency excitations (by direct variation in the boundary temperature) has been previously reported (see Refs. [22,23]). All of the above, together with the close agreement of our results with numerical predictions by the DSMC method, lend support of the validity of the present findings.…”

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

“…Recently, some efforts to describe a gas flow induced by unsteady heating boundaries have been made in the works (Manela and Hadjiconstantinou, 2008;Manela and Hadjiconstantinou, 2010) based on both collisionless Boltzmann equation and Monte Carlo method. An approach based on the linearized Boltzmann equation to describe the energy and momentum transfer in a gas subjected to an unsteady heating on the boundary is presented in Doi (2011).…”