Page 91 - Modelling in Transport Phenomena A Conceptual Approach

4.2. FLOW PAST A FLAT PLATE 71

The drag force can then be calculated from Eq. (4.2-10) as

1
[::
= (1 x 2) -(999)(3)2 (3 x = 27~

Example 4.2 Air at a temperature of 25°C flows over a 30cm vide electric
resistance flat plate heater with a velocity of 13 m/ s. The heater dissipates energy
into the air at a constant rate of 2730W/m2. How long must the heater be in the
direction of flow for the surface temperature not to exceed 155"C?

Solution
Physical properties
The film temperature is (25 + 155)/2 = 90 "C.

v = 21.95 x m2/ s
For air at 90 "C (363 K) and 1 atm : lc = 30.58 x W/ m. K
{ Pr = 0.704
Assumptions

1. Steady-state conditions prevail.
2. Both the laminar and the turbulent flow regions exist over the plate.

Analysis
The average convection heat transfer coeficient can be calculated from Newton's
law of cooling as

- = 21 W/ m2. K
- 2730
155 - 25
To determine which correlation to use, it is necessary to calculate the Reynolds
number. However, the Reynolds number cannot be determined a priori since the
length of the heater is unknown. Therefore, a trial-and-emr procedure must be
used. Since we assumed that both the laminar and the turbulent flow regions exist
over the heater, the use of Eq. (E) in Table 4.2 gives

(NU) - (0.037Re4,/5 -871) Pr
(h)L
=
k