(190l) 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 Fourierâ??s law. However, at length scales comparable to the mean-free path of the phonons, Fourierâ??s law becomes inaccurate, and more fundamental â??mesoscaleâ? descriptions of heat transfer are required. We are using the phonon Boltzmann Transport Equation (BTE) to describe heat conduction in the high-energy material Ã?-HMX. Using a recently derived Greenâ??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 Ã?-HMX. The latter simulations were performed by using an Arbitrary Lagrangian-Eulerian finite element method.