  We present an effective thermoviscous theory of acoustofluidics including
pressure acoustics, thermoviscous boundary layers, and streaming for fluids
embedded in elastic cavities. By including thermal fields, we thus extend the
effective viscous theory by Bach and Bruus, J. Acoust. Soc. Am. 144, 766
(2018). The acoustic temperature field and the thermoviscous boundary layers
are incorporated analytically as effective boundary conditions and
time-averaged body forces on the thermoacoustic bulk fields. Because it avoids
resolving the thin boundary layers, the effective model allows for numerical
simulation of both thermoviscous acoustic and time-averaged fields in 3D models
of acoustofluidic systems. We show how the acoustic streaming depends strongly
on steady and oscillating thermal fields through the temperature dependency of
the material parameters, in particular the viscosity and the compressibility,
affecting both the boundary conditions and spawning additional body forces in
the bulk. We also show how even small steady temperature gradients (1 K/mm)
induce gradients in compressibility and density that may result in very high
streaming velocities (1 mm/s) for moderate acoustic energy densities (100
J/m^3).
