230 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
The general solution of equation (i) is:
CADAcoshayCBsinhay ii
whereAandBare constants.
The boundary conditions are:
AtyDL, CAD 0 iii
AtyD 0 ,CADCAi iv
Substituting equation (iii) in equation (ii):
0 DAcoshaLCBsinhaL
and substituting equation (iv) in equation (ii):
CAiDAC0andADCAiand
BDCAicoshaL/sinhaL
∴ CADCAicoshayCAi
coshaL
sinhaL
sinhay
D
CAi
sinhaL
coshaysinhaLcoshaLsinhay
D
CAisinhaLy
sinhaL
DCAi
sinhaLy
sinhaL
DCAi
sinh
p
k/DLy
sinh
p
k/DL
Rate of absorption: NADD
(
dCA
dy
)
yD 0
AssumingCAto be small so that bulk flow can be neglected, then:
NADD
d
dy
(
sinhaLy
sinhaL
)
D
DCAiacoshaL
sinhaL
DDCAia/tanhaLDDCAiaL/LtanhaL
kLDD/L
ˇD
√
Dk/kLD
√
k/D LDaL
∴ NAD
kLCAiˇ
tanhˇ
PROBLEM 10.14
The diffusivity of the vapour of a volatile liquid in air can be conveniently determined
by Winkelmann’s method, in which liquid is contained in a narrow diameter vertical tube