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

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 gradi...

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