Page 90 - Modelling in Transport Phenomena A Conceptual Approach

70 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

(4.2-1 1)
I nA (WL)(k) ICA, - CAW I I (4.212)

Engineering problems associated with the flow of a fluid over a flat plate are clas-
sified as follows:

Calculate the transfer rate; given the physical properties, the velocity of the
fluid, and the dimensions of the plate.

Calculate the length of the plate in the direction of flow; given the physical
properties, the velocity of the fluid, and the transfer rate.

Calculate the fluid velocity; given the dimensions of the plate, the transfer
rate, and the physical properties of the fluid.

Example 4.1 Water at 20 "C flows over a 2m long flat plate with a velocity of
3 m/ s. The width of the plate is 1 m. Calculate the drag force on one side of the
plate.
Solution

Physical properties
p = 999 kg/ m3
For water at 20°C (293K) :
~ = lool 10-6k~/~.

Assumption
1. Steady-state conditions prevail.

Analysis

To determine which correlation to .we for calculating the average friction factor
(f) , we must first determine the Reynolds number:

Therefore, both the laminar and the turbulent flow regions exist on the plate. The
use of Eq. (0) in Table 4.2 gives the fnction factor as

1743
0.074
-
(f) = - -
Rei/5 hL
- 0.074 --- -3x 10-3
-
(6 x 106)1/5 6 x lo6