Hot spots are local regions of high
temperature that are widely
considered to govern explosive initiation. Hot spot dynamics rests
on a delicate balance between heat generation due to chemical reactions
and heat loss through thermal conduction, making accurate determinations
of the conductivity under extreme conditions a key component of predictive
explosive models. We develop here an approach to directly determine
the thermal transport properties of explosive hot spots with realistic
initial structures through a combination of molecular dynamics (MD)
and diffusive heat equation (HEq) modeling. Effective thermal conductivity
values are determined by fitting HEq models to MD predictions of long
timescale hot spot relaxation. The approach is applied to model hot
spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene
(TATB) for a range of shock strengths and two limiting cases for impact
orientation. Isotropic and anisotropic HEq models yield similar results,
despite TATB exhibiting some of the largest and most anisotropic thermal
conductivity values for explosive near normal conditions. The conductivity
is found to be a strong function of density, which parametrically
captures dependence on temperature, pressure, and material state.
The associated root-mean-square errors of the fitted HEq models are
approximately 5% of MD predicted final equilibrium temperatures. The
conductivity values determined here for TATB hot spots are considerably
larger than those used in a prior hot spot criticality study, which
may significantly impact predictions for critical hot spot sizes.
The approach provides a convenient foundation for determining the
effective thermal conductivity for hot spot problems in other explosives
and directly yields information on reasonable approximations that
might be taken in higher-level models for those materials.