47
Substitution of the numerical expressions for the individual terms of
the energy balance (equation 2-55) and dividing by the cross-sectional
area normal to the z axis (dx*dy) yields
dWjCs
Tj,m-1-Tj,n
eft
Tj+l>n"Tj,n
dz-i
Tj-l,n Tj,n
n (5j+l,n"^j,n) (Tj+l,n+Tj,n)
+ ^wjcpwjDLj azj 2
n *j,n) (Tj-l,n+Tj,n)
+ ^wjcpwjDLj aij^[ 2
n (Pvj+l,n ^vj,n) (Tj+l,n+Tj,n)
+ cpvjDvj 3zj 2
^ (^vj-l,n /vj.n) (Tj-l,n+Tj,n)
+ CpvjDyj 2
- dwj (hfgjEjjn) (2-64)
The partial differential equation describing the diffusion of
water within the soil can be transformed to difference form in a
similar fashion as the energy equation. The change in water content
of a volume of soil for the jth node is caused by diffusion of water
from nodes j+1 and j-1 to node j less the amount of water changed to a
vapor phase. The numerical expression for the water continuity per
unit area becomes