  There has been much interest in semiconductor superlattices because of
showing very low thermal conductivities. This makes them especially suitable
for applications in a variety of devices for thermoelectric generation of
energy, heat control at the nanometric length scale, etc. Recent experiments
have confirmed that the effective thermal conductivity of superlattices at room
temperature have a minimum for very short periods (in the order of nanometers)
as some kinetic calculations had anticipated previously. This work will show
advances on a thermodynamic theory of heat transport in nanometric 1D
multilayer systems by considering the separation of ballistic and diffusive
heat fluxes, which are both described by Guyer-Krumhansl constitutive
equations. The dispersion relations, as derived from the ballistic and
diffusive heat transport equations, are used to derive an effective heat
conductivity of the superlattice and to explain the minimum of the effective
thermal conductivity.
