Living Reference Work Entry

Encyclopedia of Nanotechnology

pp 1-12

Date: Latest Version

Simulating Nanoscale Heat Transport

  • Giuseppe RomanoAffiliated withDepartment of Materials Science and Engineering, Massachusetts Institute of Technology Email author 
  • , Jean-Philippe M. PeraudAffiliated withDepartment of Mechanical Engineering, Massachusetts Institute of Technology
  • , Jeffrey C. GrossmanAffiliated withDepartment of Materials Science and Engineering, Massachusetts Institute of Technology

Synonyms

Modeling nanoscale heat transport

Introduction

Heat conduction has been modeled for almost two centuries by the well-known Fourier’s law. Jean-Baptiste Joseph Fourier stated that “the quantity of heat which flows uniformly, during unit of time, across unit of surface taken on any section whatever parallel to the sides, all other things being equal, is directly proportional to the difference of the extreme temperatures, and inversely proportional to the distance which separates these sides” [1]. Fourier’s law can be conveniently written in its local form:
$$ \mathbf{J}=-\kappa \nabla T, $$
(1)
where κ is the thermal conductivity (for silicon, it is about 150 Wm−1K−1), T is the lattice temperature, and J is the heat flux. Equation 1 together with the continuity equation for thermal flux ...
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