ABSTRACT
This chapter presents a variation of the transient methods where two separate blocks are equilibrated at different temperatures before the approach-to-equilibrium is monitored to extract a characteristic decay time. In parallel, the heat equation is solved analytically under the same conditions of periodicity and initial temperature profile. It is shown that the temperature profile obtained by molecular dynamics (MD) has the spatial and temporal form of the Fourier series solution of the heat equation. The chapter presents a novel computational approach, to obtain the thermal conductivity of real materials from molecular dynamics simulations of temperature transients. The approach-to-equilibrium is monitored, and a characteristic decay time is obtained. The temperature profile has a spatial and temporal evolution that closely follows the solution of the heat equation, as can be shown if the latter is written and solved under the same conditions of the molecular dynamics simulation, namely: 1D heat current, periodic boundary conditions and step-like initial temperature profile.
