Thermal effects on acoustic streaming in standing waves.

Acoustic streaming generated by standing waves in channels of arbitrary width is investigated analytically. In a previous paper by the authors [J. Acoust. Soc. Am. 113, 153-160 (2003)], a purely viscous fluid in a two-dimensional channel was considered. That analysis is extended here to a gas in which heat conduction and dependence of the viscosity on temperature are taken into account. Calculations are presented for typical working gases used in thermoacoustic engines at standard temperature and pressure. In channels that are very wide in comparison with the viscous penetration depth, which is the Rayleigh streaming regime, the influence of the two thermal effects is comparable but small. The same is true in very narrow channels, having widths on the order of the viscous penetration depth. In channels having intermediate widths, 10-20 times the viscous penetration depth, the effect of heat conduction can be substantial. The analysis is performed for cylindrical tubes as well as two-dimensional channels, and the results are found to be qualitatively the same.