Page 327 - Modelling in Transport Phenomena A Conceptual Approach

8.5. MASS TRANSPORT WTH CONVECTION 307

where Do and DL are the tank diameters at z=O and z= L, respectively. There-
fore, the variation of the cross-sectional area is

7r D2(Z)
A(z) = -
4
Do
='bo-( - DL )z] 2
4
Substitution of Eq. (2) into Eq. (8.5-17) and integration gives the molar rate of
evaporation as
-
DL)
nA = - ~~CVDAB(D~ ln(1- XA,) (3)

The numerical values are

Do = 2m
DL = 1.5m
L = 0.5m
pTt 58.6
-
-
XA, = - -
= 0.077
P 760
c=-- P 1 = 41 x kmol/ m3 = 41 mol/ m3
RT - (0.08205)(25 + 273)
Substitution of these values into Eq. (3) gives

n(41)(1.35 x lo-')@ - 1.5) ln(1 - 0.077) 21 2.1
nA = - mol,s

Comment: When DL 3 Do, application of L'Hopital's de gives

and Eq. (3) reduces to

(nD:/4)cvAB
nA = -
L In( 1 - XA,)
which is Eq. (4) of Example 8.14.