Page 86 - Modelling in Transport Phenomena A Conceptual Approach

4.2. FLOW PAST A FLAT PLATE 67

and
(4.1-5)

where subscript w represents the conditions at the surface or the wall.

4.2 FLOW PAST A FLAT PLATE

Let us consider a flat plate suspended in a uniform stream of velocity v, and
temperature T, as shown in Figure 3.3. The length of the plate in the direction
of flow is L and its width is W. The local values of the friction factor, the Nusselt
number and the Sherwood number are given in Table 4.1 for both laminar and
turbulent flow conditions. The term Re, is the Reynolds number based on the
distance x and defined by

(4.2-1)

Table 4.1 The local values of the friction factor, the Nusselt number and the
Sherwood number for flow over a flat plate.

Laminar Turbulent

f, 0.664 Re,''' (A) 0.0592 Re,1/5 (D)
Nu, 0.332 Re:/2 Pr1j3 (B) 0.0296 Re:/5 Pr1l3 (E)
Sh, 0.332 Re:/z Sc1j3 (C) 0.0296 Sc1l3 (F)
Re, 5 500,000 5 x lo5 < Re, < lo7

0.6 5 Pr 5 60 0.6 5 Sc 5 3000

The expression for the friction factor under laminar flow conditions, Eq. (A)
in Table 4.1, can be obtained analytically from the solution of the equations of
change. Blausius (1908) was the first to obtain this solution using a mathematical
technique called the similarity solution or the method of combination of variables.
Note that Eqs. (B) and (C) in Table 4.1 can be obtained from Eq. (A) by using the
Chilton-Colburn analogy. Since analytical solutions are impossible for turbulent
flow, Eq. (D) in Table 4.1 is obtained experimentally. The use of this equation in
the Chilton-Colburn analogy yields Eqs. (E) and (F).
The average values of the friction factor, the Nusselt number and the Sherwood
number can be obtained from the local values by the application of the mean value
theorem. In many cases, however, the transition from laminar to turbulent flow
will occur on the plate. In this case, both the laminar and turbulent flow regions
must be taken into account in calculating the average values. For example, if the