Heat transport by baroclinic acoustic streaming

Recently, Chini \emph{et al.} [\emph{J. Fluid Mech.}, Vol. 744 (2014)] and Michel \& Chini [\emph{J. Fluid Mech.}, Vol. 858 (2019)] demonstrated that strong acoustic streaming flows can be generated in gases subjected to an imposed cross-channel temperature gradient. In contrast with classic Rayleigh streaming, standing acoustic waves of $\mathit{O}(\epsilon)$ amplitude acquire vorticity owing to baroclinic torques acting throughout the domain rather than via viscous torques acting in Stokes boundary layers. More significantly, these baroclinically-driven streaming flows have a magnitude that is $\mathit{O}(\epsilon)$, i.e. comparable to that of the sound waves, leading to fully two-way wave/mean-flow coupling. The present investigation extends these earlier studies by relaxing the restriction to small aspect-ratio domains, thereby enabling the (forced) heat transport across the channel to be quantified as a function of aspect ratio. This extension requires the numerical solution of a two-dimensional eigenvalue problem for the sound-wave frequency and mode structure. Nevertheless, the resulting computations are orders of magnitude faster than DNS of the compressible Navier-Stokes equations. The prospect for using baroclinic acoustic streaming as a cooling technology is evaluated.