PROBLEMA 2.5

Prévia do material em texto

92
PROBLEM 2.5 
A solution with a boiling point of 82°C boils on the outside of a 2.5 cm tube with a No. 14 
BWG gauge wall. On the inside of the tube flows saturated steam at 4.2 bar (abs). The 
convective heat transfer coefficients are 8500 W/(m2 K) on the steam side and 6200 
W/(m2 K) on the exterior surface. Calculate the increase in the rate of heat transfer for a 
copper over a steel tube. 
GIVEN 
Tube with saturated steam on the inside and solution boiling at 82°C outside 
Tube specification: 2.5 cm No. 14 BWG gauge wall 
Saturated steam in the pipe is at 4.2 bar 
Convective heat transfer coefficients Steam side ( cih ) : 8500 W/(m
2 K) 
 Exterior surface ( coh ) : 6200 W/(m
2 K) 
FIND 
The increase in the rate of heat transfer for a copper over a steel tube 
ASSUMPTIONS 
The system is in steady state 
Constant thermal conductivities 
SKETCH 
 
PROPERTIES AND CONSTANTS 
From Appendix 2, Tables 10, 12, 13 and 42 
Temperature of saturated steam at 4.2 bar (Ts) = 144°C 
Thermal conductivities Copper (kc) = 390 W/(m K) at 127°C 
 1% Carbon steel (ks) = 43 W/(m K) at 20°C 
Tube inside diameter (Di) = 0.834 in. 
SOLUTION 
The thermal circuit for the tube is shown below 
 
The individual resistances are 
 Rci = 
1 1
ci i ci ih A h D L
 = 
2 �2
1 1
(8500 W/(m K)) (2.08 10 m)L
 = 
0.0018
L
 K/W 
 Rco = 
1 1
co o co ih A h D L
 = 
2 �2
1 1
(6200 W/(m K)) (2.5 10 m)L
 = 
0.00205
L
 K/W 
 
93
 Rkc = 
ln
2
o
i
c
r
r
Lk
 = 
�5
2.5cm
ln
7.5 102.08cm
2 (390W/(m K))L L
 K/W 
 Rks = 
ln
2
o
s
s
r
r
Lk
 = 
�4
2.5cm
ln
6.81 102.08 cm
2 (43W/(m K))L L
 K/W 
For the copper tube 
 c
q
L
 = 
(144 82)K
(0.0018 0.000075 0.00205) (K m)/W
 = 15800 W/m 
For the steel tube 
 s
q
L
 = 
(144 82)K
(0.0018 0.00068 0.00205)(K m)/W
 = 13690 W/m 
The increase in the rate of heat transfer per unit length with the copper tube is 
 = c s
q q
L L
 = 2110 W/m 
 % increase = 
2110
13690
 100 = 15.4% 
COMMENTS 
The choice of tubing material is significant in this case because the convective heat transfer 
resistances are small making the conductive resistant a significant portion of the overall thermal 
resistance. 
PROBLEM 2.6 
Steam having a quality of 98% at a pressure of 1.37 105 N/m2 is flowing at a velocity of 
1 m/s through a steel pipe of 2.7 cm OD and 2.1 cm ID. The heat transfer coefficient at 
the inner surface, where condensation occurs, is 567 W/(m2 K). A dirt film at the inner 
surface adds a unit thermal resistance of 0.18 (m2 K)/W. Estimate the rate of heat loss 
per meter length of pipe if; (a) the pipe is bare, (b) the pipe is covered with a 5 cm layer 
of 85% magnesia insulation. For both cases assume that the convective heat transfer 
coefficient at the outer surface is 11 W/(m2 K) and that the environmental temperature 
is 21°C. Also estimate the quality of the steam after a 3-m length of pipe in both cases. 
GIVEN 
A steel pipe with steam condensing on the inside 
Diameters Outside (Do) = 2.7 cm = 0.027 m 
 Inside (Di) = 2.1 cm = 0.021 m 
Velocity of the steam (V) = 1 m/s 
Initial steam quality (Xi) = 98% 
Steam pressure = 1.37 105 N/m2 
Heat transfer coefficients Inside (hci) = 567 W/(m
2 K) 
 Outside (hco) = 11 W/(m
2 K) 
Thermal resistance of dirt film on inside surface (Rf) = 0.18 (m
2 K)/W 
Ambient temperature (T ) = 21°C