The response of a confined gas to a thermal disturbance: rapid boundary heating

Abstract

Summa~An inert compressible gas confined between infinite parallel planar walls is subjected to significant heat addition at the boundaries. The wall temperature is increased during an interval which is scaled by the acoustic time of the container, defined as the passage time of an acoustic wave across the slab. On this time scale heat transfer to the gas occurs in thin conductive boundary layers adjacent to the walls. Temperature increases in these layers cause the gas to expand such that a finite velocity exists at the boundary-layer edge. This mechanical effect, which is like a time-varying piston motion, induces a planar linear acoustic field in the basically adiabatic core of the slab. A spatially homogeneous pressure rise and a bulk velocity field evolve in the core as the result of repeated passage of weak compression waves through the gas. Eventually the thickness of the conduction boundary layers is a significant fraction of the slab width. This occurs on the condition time scale of the slab which is typically a factor of 106 larger than the acoustic time. The further evolution of the thermomechanical response of the gas is dominated by a conductive-convective balance throughout the slab. The evolving spatially-dependent temperature distribution is affected by the homogeneous pressure rise (compressive heating) and by the deformation process occurring in the confined gas. Superimposed on this relatively slowly-varying conduction-dominated field is an acoustic field which is the descendent of that generated on the shorter time scale. The short-time-scale acoustic waves are distorted as !hey propagate through a slowly-varying inhomogeneous gas in a finite space. Solutions are developed in terms of asymptotic expansions valid when the ratio of the acoustic to conduction time scales is small. The results provide an explicit expression for the piston analogy of boundary heat addition.

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

“…Rayleigh [1] first approached the idea that a slight variation in temperature can create a mechanical reaction in the form of an acoustic wave in the rest of the fluid. The resulted fluid motion from rapid heating, termed as thermoacoustic convection [2], was numerically investigated by Ozoe et al Through use of matched asymptotic expansions and multiple-time-scale technique, Kassoy [3] and Radhwan and Kassoy [4] conducted pioneering studies on the thermoacoustic interaction in a confined perfect gas under slow and rapid boundary heating. Their results showed that the process is dominated by two physical regimes, which feature, respectively, thermomechanical convection on the acoustic timescale, and strong conductive-convective coupling on the typical timescale of thermal diffusion.…”

Gas-flow animation by unsteady heating in a microchannel

“…The problem of unsteady heating has been studied in the context of continuum gas dynamics in a series of papers 6,7 under the assumption of gradual changes in wall thermal states. To satisfy the continuum assumption, a heating time scale longer than some modest multiple of the molecular collision time has been assumed.…”

The response of a compressible gas to extremely rapid transient, spatially resolved energy addition: an asymptotic formulation

“…A more systematic approach to thermomechanical problems involving transient, spatially resolved heat addition and the mechanical waves generated subsequently by localized gas expansion has been developed by Kassoy and co-workers (e.g., [18,19], [26][27][28][29][30]). Asymptotic procedures are used to identify equations that describe energy addition on explicit time scales to finite gas volumes, and the resulting gasdynamic waves.…”