Page 103 - Modelling in Transport Phenomena A Conceptual Approach

4.3. FLOW PAST A SINGLE SPHERE 83

Solution

Physical properties

f p = 1000 kg/ m3
p = 1304 x kg/ m. s
For water at 10 "C (283 K) :
= 587 lo-3 w, m.
Pr = 9.32
For water at 32 "C (305 K) : p = 769 x kg/ m. s

Analysis
System: Protective shell

Under steady conditions, the electrical power dissipated is equal to the rate of heat
loss from the shell surface to river. The rate of heat loss is given by

Q = (TD;) (h) (Tu - T,) (1)
To determine (h)7 it is necessary to calculate the Reynolds number

DPV,P
Rep = -
CL
- (5 x 10-2)(1.2)(1000)
- = 4.6 x io4
1304 x
The Whitaker correlation, Eq. (4.3-3U)7 gives

NU = 2 + ( 0.4 Rey + 0.06 Re?) (~,/CL~)~'~

[
Nu = 2 + 0.4 (4.6 x 104)1/2 + 0.06 (4.6 x 104)2/3] (9.32)0.4

The average heat transfer coeficient is

= (456) ( 5~xx1~%") = 5353 W/ m2. K

Therefore, the rate of heat loss is calculated from Eq. (1) as
Q = [~(5 10-2)2] (5353)(32 - 10) = 925 W
x