A Discussion of Nano-Length Scale Heat Conduction by Comparing the Ballistic-Diffusive Equation and Molecular Dynamics Simulation

A discussion of two methods, the Ballistic-Diffusive, Chen [1,2], and Molecular Dynamics simulation, for solving heat conduction in the nano-length regime is presented. Using data from Chen [1,2], a solution to the Ballistic Diffusive equation is rescaled and compared with the Fourier solution. Results imply that care must be taken when rescaling and comparing equations used in the different length scale regimes because physical definitions (i.e. temperature) are not identical in the two regions (nano and macro length). Analysis of the molecular dynamics simulation shows its inadequacy to describe conductive heat transfer in the nanoscale. Based on the discussion, a modified energy transport map is devised.