Practical 3: 2,3-d Steady-state Conduction + fins
Concept questions
C1 Give at least one examples each of 1-, 2- and 3-dimensional heat conduction.
C2 Consider a heat exchanger where furnace exhaust gases are used to heat water. The overall heat transfer coefficient for the heat exchanger is too low to achieve the desired heat transfer, and fins will be added to address this. Do you recommend adding the fins to the air side or the water side of the heat exchanger? Explain your answer.
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1. A motorbike uses 0.1 l/km of petrol when traveling at 100km/hr. The energy content of petrol is 32MJ/l. Only 40% of the energy released when the fuel is burnt in the engine is converted to work; the remainder is lost as heat. When the motorbike is traveling at 100km/hr, the heat transfer coefficient is high: 30 Wm-2K-1. The area available for heat loss from the engine is 3 m2.
Hint: start with an energy balance over the bike to determine how much heat needs to be removed from the engine!
a) What is the steady state rate of heat loss from the engine when the bike is travelling at 100 km h-1 in air at 25 oC?
b) In the absence of any fins, what would be the steady state temperature of the outside surface of the engine when the bike is travelling at 100 km h-1?
In practice, metal fins are used to increase the surface area available for air-cooling of the engine. Fins with efficiency of 85 %, covering one quarter of the surface area available for heat loss, can reduce the surface temperature of the engine to 300 oC when the bike is travelling at 100 kmh-1.
c) What is the heat loss through the fins under these conditions?
d) What is the total surface area of the fins?
e) Comment on your assumptions, and any limitations to your calculations.
f) If the fins described above are rectangular fins of length 1 cm and thickness 2 mm, estimate the heat transfer coefficient based on the efficiency specified above.
2. Radioactive wastes are temporarily stored in a spherical container, the centre of which is buried a distance of 10 m below the Earth’s surface. The outside diameter of the container is 2m, and 500 W of heat are released as a result of the radioactive decay process. If the bulk soil temperature is 20 oC, what is the outside temperature of the container under steady-state conditions?
3. Pressurized steam at 450K flows through a long, thin-walled pipe of 0.5 m diameter.
a) If the pipe is laid underground such that top of the pipe is 0.5 m deep (soil temperature 300 K), what will be the rate of heat loss per unit length of pipe?
Due to the high costs of burying a pipeline, an alternative option is being considered. The pipe is enclosed in a concrete casing, which is of square cross section (1.5 m x 1.5 m). The casing is exposed to the atmosphere air on all sides, with an air temperature of 300 K and coefficient of heat transfer of 10 Wm-2 K-1.
b) What is the rate of heat loss from the pipe under these conditions?
c) Compare the two options.
4. A steel pipeline, used for transport of crude oil in Alaska, is buried in earth at 0 oC such that its centerline is a distance of 1.5 m below the surface. The pipe has an outer diameter of 0.5m. Heated oil flows through the pipe line at a temperature of 120oC, and the earth C.
a) Determine the rate of heat loss per m of pipeline
b) What is the reduction in the rate of heat loss per m of pipeline, if the pipe is insulated with a layer of cellular glass 100 mm thick?
c) If the crude oil flows through the pipe at a rate of 4m3s-1, and has a density of 800 kgm-3, and heat capacity of 2.25 kJkg-1 K-1, approximately how far will the oil travel before the temperature has dropped by 10oC? Comment on this calculation, and the validity of the assumptions made in parts a) and b).
5. An igloo is built in the shape of a hemisphere, with an inner radius of 1.8 m and walls of compacted snow that are 0.5 m thick. The heat transfer coefficient for convection from the air inside the igloo to the surface of the walls and floors is 6 Wm-2K-1. The temperature of the ice cap on which the igloo sits is -20oC, and has the same thermal conductivity of the surrounding snow. The air outside the igloo is at -40oC. Under normal conditions, the igloo is occupied by 6 people, and their combined body heat provides a continuous source of 320 W within the igloo.
a) What will be the steady state temperature of the igloo under normal weather conditions, when the heat transfer coefficient for convection from the outside of the igloo to the air is 15 Wm-2K-1?
b) What percentage of the total heat loss from the igloo occurs through the floor? Explain why this is so.
c) In big storms, the coefficient for heat transfer outside the igloo can double; what will be the inside temperature of the igloo under these conditions? Explain your answer.
d) At certain times of years, lots of relatives visit each other; if the number of people inside this igloo doubles, what will be the new steady state temperature inside the igloo?
e) From a heat transfer perspective, what should you do when visitors come to stay? Let them stay in your igloo, build another igloo, or move to a larger igloo?
(Hint: if you set out your calculations well in part a, Parts b-d will be easy)
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