Page 197 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 185

and the mass transfer coefficient can be evaluated by the Lewis relationship

2=3
β ¼ αLe = ρc p (4.231)
with the Lewis number

Le ¼ Sc=Pr ¼ a=D (4.232)
The similar method can be applied to the liquid region, which yields

_ n i, int =_n int x i
_ n int ¼ β c f ln (4.233)
f
_ n i, int =_n int x i, int
Newton’s method can be used to solve Eqs. (4.229), (4.233) for
unknown _n int and _n i, int . Let

(4.234)
φ ¼ _n 1, int =_n int
φ y i, int φ x 1
f φðÞ ¼ β c v ln β c f ln (4.235)
f
v
φ y i φ x 1, int
φ 0 ¼1.01 and φ 1 ¼1.0. For any iteration point φ k , the next iteration point
will be
φ φ
φ ¼ φ f φðÞ k k 1 (4.236)
k +1 k k f φðÞ f φ k 1 Þ
ð
k
With the calculated molar flow rates of the components, the latent heat
flux at the liquid-vapor interface can be expressed as
!
X
ð
_ q ¼ _ n j, int M j ½ h v,mix t int , p, y int Þ h f ,mix t int , p, x int ފ (4.237)
ð
e
l
j
The heat flux in the vapor region is given by
X dt
_ q ¼ e ð (4.238)
s,v _ n j, int M j c p,v, j t t int Þ + λ v dη
j
(4.239)
η ¼ 0 : t ¼ t int
(4.240)
η ¼ δ v : t ¼ t v
The solution of Eqs. (4.238), (4.239) can be expressed as
δ v _q s,v
∗
t ¼ t int + 1 e Co v η=δ v (4.241)
λ v Co v