Page 128 - Modelling in Transport Phenomena A Conceptual Approach

108 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

4.5.3.3 Calculation of the mass transfer rate

Once the average mass transfer coefficient is calculated from correlations given by
Eqs. (4.531)-(4.533), then the rate of mass of species A transferred is calculated
1
as
[ hA = (nDL)(k) (ACA)LM MA (4.534)
where MA is the molecular weight of species d, and (AcA)~~, logarithmic mean
concentration difference, is defined by

(4.5-35)

The derivation of Eq. (4.534) is given in Section 9.5 in Chapter 9.

Example 4.17 A smooth tube with an internal diameter of 2.5cm is cast from
solid naphthalene. Pure air enters the tube at an average velocity of 9 m/ s. If the
average air pressure is 1 atm and the temperature is 40 "C, estimate the tube length
required for the average concentration of naphthalene vapor in the air to reach 25%
of the saturation value.

Solution
Physical properties

Diffusion weficient of naphthalene (d) in air (23) at 40°C (313K) :

= 6.61 x m2/ s

For air ut 40 "C (313 K) : v = 16.95 x m2/ s
The Schmidt number is
v
sc = -
DAB
- 16.95 x = 2.56
-
6.61 x
Assumptions

1. Steady-state conditions prevail.
2. The system is isothermal.