Likewise, conservation of energy of the air/vapor mixture is obtained from the
differential control volume and yields,
d d
dz no ha +n ,- h, I + (nT'wra)hfg = -Ua(TL Ta)A + qHLad (3.11)
As in the liquid energy equation, Equation 3.11 can be simplified by utilizing the fact that
the air mass flow rate is held constant throughout the entire process such that:
d dha dh, d nv dh dT dh,- dT
(nz ha +nz, h,,) =n m +nz +h, ,-= CPa and = CPT
dz dz dz dz dz dz dz dz
Equation 3.11 then becomes,
dT d n,
a(nza C~a PT-)C,, = hL(a ~TL Ta)A + qua~d .
dz dz
(3.12)
Equation 3.12 can be simplified by noting that the CPmix, Specific heat of the mixture, is
evaluated as,
Cnnx 82aPa PTC (3.1
Recalling the evaluation of the latent heat of evaporization from the liquid conservation
equation, and combining Equations 3.12 and Equation 3.13 the gradient of air
temperature through the diffusion tower is evaluated as,
dT, 1 doi hL(, U~TL () 4quL
+ (3.1
dz 1+@i dz Cnx Pnx(+) d1m),n
3)
where d is the diameter of the diffusion tower and qm is the heat flux loss from the air.
Equation 3.14 is also a first order ordinary differential equation with dependent variable
Ta. Equations 3.6, 3.10, and 3.14 are a set of coupled ordinary differential equations that
when solved simultaneously give solutions for the distributions of humidity ratio, air
4)