Aspect-ratio-dependent heat transport by baroclinic acoustic streaming

TL;DR

This study investigates how aspect-ratio-dependent baroclinic acoustic streaming significantly enhances heat transfer in a confined gas, revealing potential for improved convective cooling through nonlinear acoustic effects.

Contribution

It introduces a theoretical framework and numerical analysis of acoustic streaming in a gas, highlighting the role of baroclinic vorticity and quantifying heat flux enhancement beyond classical conduction.

Findings

Heat fluxes nearly 100 times greater than conduction.

Aspect ratio and acoustic amplitude critically influence heat transfer.

Proper wave-flow coupling is essential for steady-state predictions.

Abstract

Standing acoustic waves have been known to generate Eulerian time-mean 'streaming' flows at least since the seminal investigation of Lord Rayleigh in the 1880s. Nevertheless, a recent body of numerical and experimental evidence has shown that inhomogeneities in the ambient density distribution lead to much faster flows than arise in classical Rayleigh streaming. The emergence of these unusually strong flows creates new opportunities to enhance heat transfer in systems in which convective cooling cannot otherwise be easily achieved. To assess this possibility, a theoretical study of acoustic streaming in an ideal gas confined in a rectangular channel with top and bottom walls maintained at fixed but differing temperatures is performed. A two time scale system of equations is utilized to efficiently capture the coupling between the fast acoustic waves and the slowly evolving streaming flow, enabling strongly nonlinear regimes to be accessed. A large suite of numerical simulations is carried out to probe the streaming dynamics, to highlight the critical role played by baroclinically generated wave vorticity and to quantify the additional heat flux induced by the standing acoustic wave. Proper treatment of the two-way coupling between the waves and mean flow is found to be essential for convergence to a self-consistent steady state, and the variation of the resulting acoustically enhanced steady-state heat flux with both the amplitude of the acoustic wave and the O(1) aspect ratio of the channel is documented. For certain parameters, heat fluxes almost two orders of magnitude larger than those realizable by conduction alone can be attained.