Thermoacoustic streaming in a resonant channel: The time-averaged temperature distribution

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Abstract
The problem of thermoacoustic streaming in a plane parallel resonant channel, representative of the stack in a thermoacoustic engine, has been developed in a general dimensionless form. The utility of such a formulation and its wide ranging applicability to different solid–fluid combinations is demonstrated by which a consistent account of all the energy-exchange mechanisms can be made. Certain (wide-gap, thick-wall) simplifications are initially made to arrive at more manageable forms of the time-averaged temperature distributions of interest in both the fluid gap, and the channel walls. These simplifications clarify the origin of the thermoacoustic effect and provide a description of the responsible physical mechanisms based on which the validity of the “bucket-brigade” model is examined. The unexpected role of a little-known second-order thermal expansion coefficient is pointed out. It is shown that the conjugate wall–fluid coupling is crucial in yielding the large time-averaged axial temperature gradients that can be induced in the channel. In particular, the heat transfer rates at the ends of the channel are found to play an important role in determining the magnitude of these time-averaged gradients. The more general and practically useful case of arbitrary channel gap widths is also treated and it is found that for ideal gas working fluids there is an optimum channel gap width for which the axial thermal stratification in the channel is maximized. A comparison of the predictions from this study with available experimental data shows very good agreement.

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