Cooling by Baroclinic Acoustic Streaming

In the absence of natural convection, efficient heat transfers rely on externally forced flows. Generating such flows with acoustic waves rather than mechanical fans would enable remote locations to be cooled using virtually infinite-lifetime transducers. This outlook is reinforced by the recent discovery that standing acoustic waves drive streaming flows of much higher velocities if the background medium is inhomogeneous. This regime of streaming is investigated experimentally in a cavity filled with stably stratified air in which horizontal sound waves are found to significantly enhance heat transfers. The additional heat flux scales as the square of the input acoustic power for low-amplitude waves and increases with the air stratification. These two features qualitatively match theoretical predictions, although corrections possibly ascribed to gravity are observed.

Figure 1

Experimental setup. A speaker, driven by a harmonic signal of frequency $f$ and power ${\mathcal{P}}_{\mathrm{ac}}$, generates an acoustic wave of local amplitude $A_p$ measured at the opposite end. The cavity of height $H$ and length $L$ is heated at the top (power ${\mathcal{P}}_{\mathrm{th}}$, temperature $T_h$) and cooled at the bottom (temperature $T_c$). The width $\ell$ is not displayed. Gray areas represent dural samples and hatched areas represent thermal insulators.

Figure 2

Top to bottom temperature difference $T_h-T_c$ as a function of the forcing frequency $f$ for ${\mathcal{P}}_{\mathrm{ac}}=0.5\mathrm{W}$ and ${\mathcal{P}}_{\mathrm{th}}=8.8\mathrm{W}$. The corresponding temperature stratification $\mathrm{\Delta }{T}_0$ and streaming temperature drop $\mathrm{\Delta }T$ are also reported.

Figure 3

Relative temperature drop $\mathrm{\Delta }T/\mathrm{\Delta }{T}_0$ as a function of the injected power in the loudspeaker ${\mathcal{P}}_{\mathrm{ac}}$ for ${\mathcal{P}}_{\mathrm{th}}=8.8\mathrm{W}$.

Figure 4

Relative temperature drop $\mathrm{\Delta }T/\mathrm{\Delta }{T}_0$ as a function of the dimensionless temperature stratification $\mathrm{\Gamma }=\mathrm{\Delta }{T}_0/T_c$ for fixed power supplied to the loudspeaker ${\mathcal{P}}_{\mathrm{ac}}=0.5\mathrm{W}$ and various heating ${\mathcal{P}}_{\mathrm{th}}$. Note that $\mathrm{\Delta }T/\mathrm{\Delta }{T}_0$ would be constant if the streaming flow were independent of $\mathrm{\Gamma }$.

Figure 5

Function $F(\mathrm{\Gamma })$ associated with cooling by baroclinic streaming and the approximation for $\mathrm{\Gamma }<0.4$ used in the present study.