Page 196 - Design and Operation of Heat Exchangers and their Networks

184 Design and operation of heat exchangers and their networks

. . .
m t p c,out n i,f,in f,in p in n i,v,in h v,in
h
c c,out
t
t int v

t f
.
t wc t t d f n i,int
t c,m wh .
. q l
q s,f q .
x i s,v
x i,int y i,int
y i

h
–d f 0 d v
. . .
h
h
m t p c,in n i,f,out f,out p out n i,v,out v,out
c c,in
Fig. 4.4 Heat and mass transfer in a cell.
∗
η ¼ 0 : y ¼ y i, int (4.224)
i
∗
η ¼ δ v : y ¼ y i (4.225)
i
where
_ n int ¼ _n 1, int + _n 2, int (4.226)
and “*” denotes the local value of y i . The solution of Eqs. (4.223), (4.224)
can be expressed as
∗
ð
y ¼ _n i, int =_n int + y i, int _n i, int =_n int Þe _n int η= c v D v Þ (4.227)
ð
i
Using the other boundary condition (4.225) and expressing the mass
transfer coefficient as
β ¼ D=δ (4.228)

we obtain

_ n i, int =_n int y i, int
_ n int ¼ β c v ln (4.229)
v
_ n i, int =_n int y i
where the concentration c of the mixture is given by
X
c ¼ ρ e M ¼ ρ n i M i (4.230)
e
i