The diffusion process is governed by the first Fick's law:
 | (9–1) |
It is also governed by the mass balance equation:
 | (9–2) |
where:
| {J} = diffusion flux vector |
|
| Dxx, Dyy, and Dzz = the diffusivity coefficients in the element's X, Y, and Z directions, respectively (input as DXX, DYY, DZZ on MP command) |
| C = C(x,y,z,t) = concentration (CONC degree of freedom) |
| {v} = transport velocity vector (input as VELO on BF command for PLANE238, SOLID239, and SOLID240 only) |
| G = diffusing substance generation rate per unit volume (input as DGEN on BF or BFE commands) |
|
 = divergence operator |
| t = time |
Substituting Equation 9–1 into Equation 9–2 produces the second Fick’s law augmented with the transport term:
 | (9–3) |
The applicable boundary conditions and loads are:
Specified concentration (input as CONC on D, DA, DK, DL commands). Initial concentration can also be applied using the CONC label with the IC command.
Specified diffusion flux
acting on a surface (input as DFLUX on SF or
SFE commands):
(9–4)
where:
{n} = unit outward normal vector {r} = diffusion flow vector Diffusing substance generation rate G (input as DGEN on BF or BFE commands).
Transport velocity vector {v} (input as VELO on BF command for PLANE238, SOLID239, and SOLID240 only).