With the recent advances in nanosciences, micro/nanoscale engineering applications are bound to be more common, complex and challenging. Further understanding of thermal transport down to nanometer scales will be crucial for the design and operation of new devices, which is possible only with the use of better theoretical and numerical models of energy transfer mechanisms involving photons, electrons, and phonons. The focus of this monograph is on thermal transport modeling at time and length scales ranging from micro- to nanoscale levels. It is not designed as a comprehensive text, but is intended to serve as a handy reference for students and researchers who work on numerical and theoretical aspects of thermal transport phenomena at micro- and nanoscales. The equations and the solution methodologies presented here are general, as they can be used for multi-scale problems and can be extended to bulk systems. Yet, the presentation is tailored specifically for the electron-beam based machining applications. The treatise starts with an overview of the field, after that particle models based on the Boltzmann transport equation are introduced. The details for the electron-beam transport equation, the radiative transfer equation, and the phonon radiative transport equation are outlined and Monte Carlo methods specific to the solution of the electron and phonon transport problems are discussed. Governing equations for electron-phonon systems, including two-temperature and electron-phonon hydrodynamic models are given. Following that molecular dynamics simulations are summarized for potential melting/evaporation problems and a general discussion is provided on parallel solution algorithms.

Transport Equations