Chapter 4 - Analysis of Energy Transport Equations at Micro/Nanoscales

Abstract

Heat equation is expressed through the electron kinetic theory, which is based on the probabilistic approach. The importance and limitations of hyperbolic heat equations are discussed, and mathematical formulations of hyperbolic heat equation and electron kinetic theory approach are presented. The mathematical analysis for the equation of phonon radiative transport is incorporated, and the equation for phonon radiative transport is deduced from the Boltzmann transport equation. The modified form of the equation for phonon transport is introduced and its similarity with the two-equation model for heating is discussed. The limitations of phonon radiative transport equation is included and analogies related to large thickness films and longer transport durations are provided. In metallic thin films, electron resistance to the transport characteristics is also presented. Introduction to cross-plane transport of phonons is briefly discussed and possible boundary conditions resembling the thermal disturbance across the thin film are provided. Finally, thermal stress analysis due to micro/nanoscale thermal transport is presented and a case study related to laser short-pulse heating and thermal development in the irradiated region is provided.