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Lumped Parameter Description of Thermovisous Acoustics in Tubes with Equilateral Triangular Cross-Sections

An accurate acoustic model of a tube in the millimeter or submillimeter
size should include the losses that occur due to viscosity
and thermal conduction, collectively termed thermoviscous
losses. These losses are prominent in a boundary layer near
the tube walls. Under the assumption that the boundary layer is
thick compared to a characteristic geometry length, such as the
radius for a circular cross-section, and fills out the entire crosssection,
the tube can be described via a lumped parameter model.
The lumped parameters have been known for several decades for
a tube with circular cross-section, but the equilateral triangular
tube has only been investigated in terms of transmission line parameters.
The lumped parameters have here been established for
the equilateral triangular tube as a truncated series solution of
the transmission line parameters. One result observed is that the
lumped parameter model for a triangular tube has 38% more viscous
loss than a circular tube for a given area.

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