Xj
qcj+l,n= (Tj+i,n- Tj,n) (2-57)
qcj-l,n= (Tj-l,n- Tj,n) (2-58)
dzj-1
noting that dzj represents the difference between the depth of nodes
j+1 and j.
In developing the differential equations for this model, it is
assumed that mass movement is due to diffusion and obeys Fick's law of
diffusion. Therefore, the heat transferred by diffusion of water and
water vapor from node j+1 to j is expressed as
S(Oj+,n- Oj,n) (Tj+1,n+ Tj,n)2
qLj+l,n = PwCpwjDLj dz2 (2-59)
(Pvj+,n Pvj,n) (Tj+1,n+Tj,n)
qvj+1,n = cpvjDvj dz 2 (2-60)
and similarly for the heat flux transferred by mass diffusion from node
j-1 to node j as
(0j-l,n 1j,n) (Tj-l,n+Tj,n)
qLj-l,n = PwjCpwjDLj dzj-1 2 (2-61)
S(Pvj-l,n Pvj,n) (Tj-l,n+Tj,n)
qvj-l,n = cpvjDvj dzj- 2 (2-62)
The latent heat associated with the phase change of water for the
current time step (Ej,n) must be transferred per unit volume of soil
associated with node j and is determined by
hfgjEj,n
(2-63)
qej,n =