Page 76 - Modelling in Transport Phenomena A Conceptual Approach

3.5. TRANSPORT ANALOGIES 57

Reynolds further assumed that Pr = Sc = 1. Under these circumstances Eq. (3.5-9)
reduces to

(3.510)

which is known as the Reynolds analogy. Physical properties in Eq. (3.510) must
be evaluated at T = (T, + T,)/2.
The Reynolds analogy is reasonably valid for gas systems but should not be
considered for liquid systems.

3.5.2 The Chilton-Colburn Analogy
In the Chilton-Colburn analogy the relationships between the effective film thick-
nesses are expressed as
6 6
- = pr'l3 - = sc1/3 (3.51 1)
6t 6,
Substitution of Eq. (3.5-11) into Eq. (3.57) yields

(3.512)

and
I
(3.513)
j,
- = StM SC213
where jH and jM are the Colburn j-factors for heat and mass transfer, respec-
tively.
Physical properties in Eqs. (3.512) and (3.513) must be evaluated at T =
(T, + T,)/2. The Chilton-Colburn analogy is valid when 0.6 5 Pr 5 60 and
0.6 5 Sc 5 3000. Note that Eqs. (3.512) and (3.5-13) reduce to Reynolds analogy,
Eq. (3.5-lo), for fluids with Pr = 1 and Sc = 1.
As stated in Section 3.1, the drag force is the component of the force in the
direction of mean flow. In general, both viscous and pressure forces contribute to
this force5. In Eq. (3.1-3), only viscous force is considered in the evaluation of
the drag force. The reason for this is that the pressure always acts normal to the
surface of the flat plate and the component of this force in the direction of mean
flow is zero. In the case of curved surfaces, however, the component of normal
force to the surface in the direction of mean flow is not necessarily zero as shown
in Figure 3.8. Therefore, the friction factor for flow over flat plates and for flow
inside circular ducts includes only friction drag, whereas the friction factor for flow
around cylinders, spheres, and other bluff objects includes both friction and form
drags. As a result, f/2 term for flow around cylinders and spheres is greater than

5The drag force arising from viscous and pressure forces are called friction (or, skin) drag and
form drag, respectively.