Page 423 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 403

The chain rule of differentiation gives

(9.5-119)

- urn, 61f (9.5120)
---
~DAB~
d9'
Substitution of Eqs. (9.5119) and (9.5120) into Eq. (9.5113) yields

(9.5121)
The boundary conditions associated with Eq. (9.5121) are

at Q=O q5=1 (9.5-122)

at Q=oo c#=O (9.5-123)
The integrating factor for Eq. (9.5-121) is exp(Q2). Multiplication of Eq. (9.5-121)
by the integrating factor gives \y2 df ...J=o

"(e (9.5124)
dQ
which implies that
(9.5-125)

Integration of Eq. (9.5-125) leads to

(9.5-126)

where u is a dummy variable of integration. Application of the boundary condition
defined by Eq. (9.5-122) gives K2 = 1. On the other hand, the use of the boundary
condition defined by Eq. (9.5-123) gives
2
K1= - 1 - --- (9.5-127)
1- e- ua du fi

Therefore, the solution becomes

e- "2 du (9.5128)