Wave Characteristics of Heat Conduction Using a Discrete Microscopic Model

The wave properties of heat conduction are studied using a discrete velocity microscopic model. In this model, molecules move with two possible speeds along one of six allowable directions, and the molecular dynamics are governed by the Boltzmann transport equation. Macroscopic quantities such as temperature and density are extracted from the distribution of molecules among various possible states. It is found that at a low degree of rarefaction (low Knudsen number), an initial temperature pulse simply spreads out with time without exhibiting any wavelike behavior. But at a high degree of rarefaction (high Knudsen number), an initial temperature pulse propagates as a highly damped temperature ripple at almost constant speed. The thermal propagation speed thus obtained agrees with the value predicted from macroscopic equations. This propagation of temperature pulse is then compared with the propagation of density disturbance (sound wave) using the same model.