MIDTERM QUIZ 1 KEY ANSWERS
COVERAGE: HEAT CONDUCTION THROUGH SPHERES AND CYLINDERS
1. A liquid flows through a cast steel pipe (k = 50 W/m.K) with an outer diameter of 52 mm and 1
mm wall thickness.
i) Calculate the heat loss per meter length of uninsulated pipe when the water temperature is
15◦C, the outside air temperature is -10◦C, the water side heat transfer coefficient is 15 kW/m2.K
and the outside heat transfer coefficient is 10 W/m2.K.
ii) Calculate the corresponding heat loss when the pipe is lagged with insulation having an outer
diameter of 150 mm, and thermal conductivity of 0.05 w/m.K.
Answer:
i)
40.8040 W/m
ii)
6.9737 W/m
2. A spherical vessel of ID 0.3 m and thickness of 20 mm is made of steel with a conductivity of 40
W/m.K. The vessel is insulated with two layers of 60 mm thickness each of conductivity of 0.05 and
0.15 W/m.K. The inside surface is at 196°C. The outside is exposed to air at 30°C with convection
coefficient of 35 W/m2.K. There is a contact resistance of 1x10-3 °C/W between the two insulations.
Determine the heat gain and also the surface temperatures and the overall heat transfer coefficient
based on the inside surface of the metallic vessel.
Answer:
Rsteel=1.5603 x 10-3 K/W
R (1st insulation layer)=2.4423 K/W
R contact b/n insulation=1x10-3 °C/W
R (2nd insulation layer)=0.4772 K/W
R conv,o =0.0270 K/W
Q= 56.2891 W
Surface Temperatures:
T1(inside surface)= 196°C
T2=195.9122 °C
T3=58.4373 °C
T4=58.3810°C
T5=31.5198°C
Overall heat transfer coefficient based on inside area( Ui) = 1.1993 W/m2K
3. The end of a very long cylindrical stainless steel rod is attached to a heated wall and its surface
is in contact with a cold fluid.(ID=2.067”, OD = 2.375”). Neglecting convection heat transfer, if the
rod were made of constantan(k= 27 W/m.K), by what percentage would the heat transfer rate
change from that of the stainless steel(k=17 W/m.K).
Answer:
58.8234%