Mesoscale Effects in Heat Conduction through Crystalline Solids

Heat conduction in crystalline solids occurs through the motion of molecular-scale vibrations, or phonons. At large enough time and length scales there are sufficient phonon-phonon interactions for local equilibrium to be established, and heat conduction is described by Fourier’s law. However, at length scales comparable to the mean-free path of the phonons, Fourier’s law becomes inaccurate, and more fundamental “mesoscale” descriptions of heat transfer are required. We are using the phonon Boltzmann Transport Equation (BTE) to describe heat conduction in the high-energy material ß-HMX. Using a recently derived Green’s function for the BTE, we calculate phonon distribution functions and temperature changes for stationary and moving heat sources. The results are interpreted in terms of continuum-scale simulations of crack formation following the shock-induced collapse of air-filled pores in ß-HMX. The latter simulations were performed by using an Arbitrary Lagrangian-Eulerian finite element method.