Page 336 - Bird R.B. Transport phenomena

320 Chapter 10 Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow

PROBLEMS IOA.1. Heat loss from an insulated pipe. A standard schedule 40, 2-in. steel pipe (inside diameter
2.067 in. and wall thickness 0.154 in.) carrying steam is insulated with 2 in. of 85% magnesia
covered in turn with 2 in. of cork. Estimate the heat loss per hour per foot of pipe if the inner
surface of the pipe is at 250°F and the outer surface of the cork is at 90°F. The thermal
conductivities (in Btu/hr • ft • F) of the substances concerned are: steel, 26.1; 85% magnesia,
0.04; cork, 0.03.
Answer: 24 Btu/hr • ft
10.A.2. Heat loss from a rectangular fin. Calculate the heat loss from a rectangular fin (see Fig. 10.7-1)
for the following conditions:

Air temperature 350°F
Wall temperature 500°F
Thermal conductivity of fin 60 Btu/hr-ft-F
Thermal conductivity of air 0.0022 Btu/hr • ft • F
2
Heat transfer coefficient 120 Btu/hr- ft -F
Length of fin 0.2 ft
Width of fin 1.0 ft
Thickness of fin 0.16 in.
Answer: 2080 Btu/hr
10A.3. Maximum temperature in a lubricant. An oil is acting as a lubricant for a pair of cylindrical
surfaces such as those shown in Fig. 10.4-1. The angular velocity of the outer cylinder is 7908
rpm. The outer cylinder has a radius of 5.06 cm, and the clearance between the cylinders is
0.027 cm. What is the maximum temperature in the oil if both wall temperatures are known to
be 158°F? The physical properties of the oil are assumed constant at the following values:
Viscosity 92.3 cp
Density 1.22 g/cm 3
Thermal conductivity 0.055 cal/s • cm •
Answer: 174°F

10A.4. Current-carrying capacity of wire. A copper wire of 0.040 in. diameter is insulated uni-
formly with plastic to an outer diameter of 0.12 in. and is exposed to surroundings at 100°F.
The heat transfer coefficient from the outer surface of the plastic to the surroundings is 1.5
Btu/hr • ft 2 • F. What is the maximum steady current, in amperes, that this wire can carry
without heating any part of the plastic above its operating limit of 200°F? The thermal and
electrical conductivities may be assumed constant at the values given here:
1
1
к (Btu/hr •ft •F) k (ohm cm" )
e
Copper 220 5.1 X 10 5
Plastic 0.20 0.0
Answer: 13.7 amp

10A.5. Free convection velocity.
(a) Verify the expression for the average velocity in the upward-moving stream in Eq. 10.9-16.
(b) Evaluate /3 for the conditions given below.
(c) What is the average velocity in the upward-moving stream in the system described in Fig.
10.9-1 for air flowing under these conditions?
Pressure 1 atm
Temperature of the heated wall 100°C
Temperature of the cooled wall 20°C
Spacing between the walls 0.6 cm
Answer: 2.3 cm/s