Page 129 - Modelling in Transport Phenomena A Conceptual Approach

4.5. FLOW ZN CIRCULAR PIPES 109

Analysis
System: Air in the naphthalene tube

If naphthalene is designated as species A, then the rate equation for the conservation
of species A becomes

Rate of moles of A in = Rate of moles of A out (1)
The tern in Eq. (1) are expressed by

Rate of moles of A in = TDL(~,)(AcA)LM (2)
Rate of moles of A out = e(CAb)out = (7rD2/4)(v)(C~b)out (3)
Since the concentration at the wall is constant, the expression for (ACA)LM,
Eq.
(4.5-35), becomes
(CA, )out
(ACA)LM (4)
=

Substitution of Eqs. (i!)-(4) into Eq. (1) gives
CAW ]
1 (4
L 4 (kc) [ (cA, )mt
In l--
D
-
__-- (') In (1 - 0.25) = 0.072
4 (kc)
Note that Eq. (5) can also be expressed in the form

The value of L depends on the correlations as follows:

Chilton-Colburn analogy

Substitution of Eq. (3.5-13) into Eq. (6) gives
L 2
- = 0.072 - Sc2I3
D f
The Reynolds number is

- (2-5 10-2)(9) = 13,274 =+ Turbulent flow
-
16.95 x