3.3 Constitutive Equations

The basic constitutive equations relate the fluxes of heat, species, and momentum to the field variables and material properties. A simple molecular model is presented below to provide a qualitative estimate (on the order of magnitude) of the transport coefficients.

3.3.1 A Lattice Model

Diffusion stems from the random molecular walks of constituent particles. Figure 3-3 shows a simple Lattice model with an assumption that the movement of a molecule occurs only along any of the six directions. For a particle, the probability of moving in one direction is 1/6, assuming that the chance for movement in each direction is the same. The flux in the x direction, denoted as fx (which can be heat, species or momentum flux), ...

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