The original name for the code was FRAC3DVS, which was created by René Therrien in 1992. [1992] is given by:
(
q
w
c
w
T
(
k
b
+
c
b
b
D
)
T
)
+
o
Q
T
see here
=
b
c
b
T
t
{\displaystyle -\nabla \cdot {\Big (}{\textbf {q}}\rho _{w}c_{w}T-(k_{b}+c_{b}\rho _{b}{\textbf {D}})\nabla T{\Big )}+\Omega _{o}\pm Q_{T}={\frac {\partial \rho _{b}c_{b}T}{\partial t}}}
where
{\displaystyle \rho }
is the density,
c
{\displaystyle c}
is the heat capacity,
T
{\displaystyle T}
is the temperature of the bulk subsurface,
k
{\displaystyle k}
is the thermal conductivity,
D
{\displaystyle D}
is the thermal dispersion term,
Q
T
{\displaystyle Q_{T}}
is the thermal source/sink,
o
{\displaystyle \Omega _{o}}
is the thermal interactions between the surface and subsurface, and
Q
T
{\displaystyle Q_{T}}
is the external thermal interactions. .