  The coupling between mechanical and thermal properties due to thermal
expansion complicates the problem of measuring frequency-dependent
thermoviscoelastic properties, in particular for highly viscous liquids. A
simplification arises if there is spherical symmetry where - as detailed in the
present paper - the thermoviscoelastic problem may be solved analytically in
the inertia-free limit, i.e., the limit where the sample is much smaller than
the wavelength of sound waves at the frequencies of interest. As for the
one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E
75, 041502 (2007)], the solution is conveniently formulated in terms of the
so-called transfer matrix, which directly links to the boundary conditions that
can be experimentally controlled. Once the transfer matrix has been calculated,
it is fairly easy to deduce the equations describing various experimentally
relevant special cases (boundary conditions that are adiabatic, isothermal,
isochoric, etc.). In most situations the relevant frequency-dependent specific
heat is the longitudinal specific heat, a quantity that is in between the
isochoric and isobaric frequency-dependent specific heats.
