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
Tj,n+l-Tj,n Tj+l,n-Tj,n Tj-1,n Tj,n
dwjCs dt= J dz- + dzj_
(Oj+1,n-0j,n) (Tj+l,n+Tj,n)
+ PwjCpwjDLj dzj 2
(0j-i,n 0j,n) (Tj-l,n+Tj,n)
+ PwjcpwjDLj dzj- 2
(Pvj+1,n Pvj,n) (Tj+1,n+Tj,n)
+ cpvjDvj dzj 2
(Pvj-l,n Pvj,n) (Tj-l,n+Tj,n)
+ cpvjDvj dzj-. 2
dwj (hfg,jEj,n) (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