Calculating the Thermal Conductivity

The sections on basics of heat transfer and adopting a molecular viewpoint provided some motivation for trying to calculate the thermal conductivity of materials from molecular simulation. We saw that for complicated real materials engineers need better tools to calculate these physical properties. Simple theories that employ severe approximations in order to achieve a closed-form equation (something you can write down with pencil and paper) are not enough. Molecular simulation has recently emerged as a powerful new tool for chemical engineers.

From the macroscopic theory we have the basic equation J = - k dT/dx (Fourier's law), and from the molecular dynamics simulation we can find out how the molecules move about and how the system will evolve in time. The remaining question is how we should use the MD simulation to calculate k? Think about this for a few minutes before reading the next part.