temperature, Ti. The interfacial temperature is found by recognizing that the energy
convected from the liquid is the same as that convected to the gas,
1,7L 71L G U(71 Ta) (3.7)
where UL and UG; are the heat transfer coefficients of liquid and gas respectively. The
interfacial temperature is obtained by solving Equation 3.7 and is,
T7 = TL G L(3.8)
The conservation of energy on the liquid side of the differential volume yields the
following,
d(mL hL) dnwp)h +Ua(TL -T)A, (3.9)
dz dz f
where h is the enthalpy, U is the overall heat transfer coefficient, and hfg is the latent heat
of evaporation. Equation 3.9 can be further manipulated by utilizing the following:
d d nL dhL
dhL= CpdT~and (nLhL)-=hL- 9 2L ,and h g(, )=h(,(()- hL (7,). The
PLdz dz dz
gradient of the liquid temperature, TL, then reduces to the following,
dT TL G d co (h~ hL) L~T -,
+ (3.10)
dz L dz C C~L
where L = -I4 is the liquid mass flux, CP is the specific heat, and a is the overall specific
area of the packing material. Equation 3.10 is also a first order ordinary differential that
when solved will yield the temperature distribution of the water throughout the diffusion
tower.