TABLE OF CONTENTS Fourier's law and the associated heat diffusion equation comprise one of the most celebrated models in mathematical physics. Joseph Fourier in 1824 wrote: Heat, like gravity, penetrates every substance of the universe; its rays occupy all parts of space . The theory of heat will hereafter form one of the most important branches of general physics. Soon afterward, heat transfer also became an important engineering field, essential to the second industrial revolution and the development of modern technologies.
Recall the discussion of heat interaction and heat transfer in Chap. 2. We have treated heat conduction as a diffusion process based on the concept of local thermal equilibrium. This allows us to define and determine the equilibrium temperature at each location in a body instantaneously, under the continuum assumption described in Chap. 1. The local-equilibrium condition breaks down at the microscale when the characteristic length L is smaller than a mechanistic length scale, such as the mean free path ?. For conduction by molecules, consider a rarefied gas between two parallel plates at different temperatures. If the mean free path is much greater than the separation distance, i.e., the Knudsen number Kn = ?/ L >> 1, the gas is in the free molecule regime and its velocity distribution cannot be described by Maxwell's distribution function. Furthermore, the transport becomes ballistic rather than diffusive. Nonequilibrium energy transfer refers to the situation when the assumption of local equilibrium does not hold. This can occur...
