48
(0j,n+l- Oj,n) 0 +1,n- 0j,n (Oj-l,n- Oj,n)
dwJ dt DLj dzj + dzj-l
Ej,n
dwj (2-65)
Pw,j
Similarly, the differential equation describing the conservation of
mass in the vapor state is transformed as
(Pvj,n+1 Pvj,n) (Pvj+l,n Pvj,n)
S- dt Dvj dzj
(2-66)
(Pvj-l,n Pvj,n) dwj Ej,n
+ -Dv dzj-1 + (Sj j,n)
Equations (2-64), (2-65), and (2-66) constitute the numerical
equivalents for the partial differential equations describing the
conservation of thermal energy and mass in the soil profile. However,
the conservation relationships have yet to be developed for the
boundaries at the soil surface and the bottom of soil profile. Since
there is no volume associated with the surface node (Fig. 2-1), there
is no storage capacity for energy or mass. Therefore, the flux of mass
or energy from the node directly below the surface (j=2) to the surface
added to the net flux due to solar radiation onto the surface and the
heat flux due to convection from the air to the surface must be zero.
This can be expressed directly in difference form as follows.