For an arbitrary scalar 
, Ansys Fluent solves
the equation
 | (1–8) |
where 
and 
are
the diffusion coefficient and source term you supplied for each of
the 
scalar equations. Note that 
is defined
as a tensor in the case of anisotropic diffusivity. The diffusion
term is therefore 
For isotropic diffusivity, 
could be written
as 
where I is the identity matrix.
For the steady-state case, Ansys Fluent will solve one of the three following equations, depending on the method used to compute the convective flux:
If convective flux is not to be computed, Ansys Fluent will solve the equation
(1–9)
where
and 
are
the diffusion coefficient and source term you supplied for each of
the 
scalar equations.If convective flux is to be computed with mass flow rate, Ansys Fluent will solve the equation
(1–10)
It is also possible to specify a user-defined function to be used in the computation of convective flux. In this case, the user-defined mass flux is assumed to be of the form
(1–11)
where
is the face vector area.