Ballistic-diffusive model for heat transport in superlattices and the minimum effective heat conductivity

Abstract

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.

arXiv comment14 pages, 3 figures

References in corpus (6)

• Minimum Thermal Conductivity of Superlattices
• Generalized heat conduction in heat pulse experiments
• Universal heat conduction -- the thermodynamics of some weakly nonlocal theories
• Guyer-Krumhansl-type heat conduction at room temperature
• Models of ballistic propagation of heat at low temperatures
• On the rarefied gas experiments

Cited by in corpus (3)

• Lagging Heat Models in Thermodynamics and Bioheat Transfer: a Critical Review
• Generalized ballistic-conductive heat conduction in isotropic materials
• Spectral properties of dissipation