  In this paper, we theoretically analyse wave propagation in two canonical
problems of interest: fluid-filled thermo-visco-elastic slits and fluid-loaded
thermo-visco-elastic plates. We show that these two configurations can be
studied via the same pair of dispersion equations with the aid of the framework
developed in [https://doi.org/10.1098/rspa.2022.0193], which incoporates
thermal effects. These two problems are further interrelated, since in the
short wavelength limit (relative to the slit/plate width) the respective modes
are governed by the same dispersion equation, commonly known as the
Scholte--Stoneley equation. It is the Scholte-type modes that are mainly
analyzed in this paper. We illustrate results when the fluid is water, although
the theory is valid for any Newtonian fluid. Both `hard' and `soft' solids are
compared, with the emphasis being placed on the importance of
thermo-viscoelastic effects, particularly when stress relaxation is considered.
Two main recent works are discussed extensively, namely
[https://doi.org/10.1121/1.5078528] for slits and
[https://doi.org/10.1103/PhysRevE.103.063002] for loaded plates, both of which
do not incorporate viscoelastic mechanisms. We show how the consideration of
viscoelasticity can extend the results discussed therein, and explain the
circumstances under which they arise.
