Page 124 - Modelling in Transport Phenomena A Conceptual Approach

104 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

Since the flow is laminar, Eq. (4.5-25) must be wed, i.e.,

Nu = 1.86 [RePr (D/,c)]~/~ (~/p,)"~~

Substitution of Eq. (8) into Eq. (7) yields

= (1519)(143) [ (12.4 x 10-3/9.3 x 10-3)-0-14 In (100 - 40)] 3/2

(4) (1.86) 100 - 60
= 2602
The tube length is then
L = (2602)(65 x = 169m
Example 4.16 Air at 20°C enters a circular pipe of 1.5cm internal diameter
with a velocity of 50 m/ s. Steam condenses on the outside of the pipe so as to keep
the surface temperature of the pipe at 150OC.
a) Calculate the length of the pipe required to increase air temperature to 90°C.
b) Discuss the eflect of surface roughness on the length of the pipe.
Solution
Physical properties

The mean bulk temperature is (20 + 90)/2 = 55OC
For air at 20 "C (293 K) : p = 1.2047kg/ m3
p = 19.8 x kg/ m. s
For air at 55OC (328K) : v = 18.39 x 10-6m2/s
{ Pr = 0.707
For air at 150 "C (423 K) : p = 23.86 x kg/ m. s
Analysis

a) System: Air in the pipe
The inventory rate equation for mass duces to
Rate of mass of air in = Rate of mass of air out = m (1)
Note that for compressible fluids like air, both density and average velocity depend
on temperature and pressure. Therefore, wing the inlet conditions