HW3 142 - surfaces (i.e., suppose that both ends are warmer...

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Problem Set #3 Due Thursday 4/22/10 1. It has been noted that, in the summertime, students in an air-conditioned classroom at 72ºF are quite comfortable in short pants, sandals and a tee shirt. By contrast, in the winter the same students are comfortable in a classroom at 75ºF while wearing long pants, long-sleeve shirts and sweaters. How can this apparent discrepancy be explained? 2. A cylindrical steel rod with diameter 1.75” and length 18” is connected to steel plates at the boiling point and freezing point of water, respectively (i.e., at 212ºF and 32ºF). The ambient air termperature is 72ºF. If the average heat transfer coefficient between the rod and the surrounding air is 1.8 BTU/hr.ft 2 .ºF, calculate and plot the radially-averaged temperature along the rod. Assume the conductivity of the steel is k=25Btu/hr.ft.ºF. 3. In Problem #2, suppose the purpose of the connecting rod is to remove heat from two hot
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Unformatted text preview: surfaces (i.e., suppose that both ends are warmer than ambient temperature). If the rod is too long, the temperature in the middle region becomes equal to the ambient temperature, and therefore makes a negligible contribution to the amount of heat removed. Assuming the desired condition is to have the entire rod be at a temperature greater than ambient, derive an estimate for what the rod length should be. Use order-of-magnitude reasoning to derive your estimate. 4. The surface of a large slab of material with thermal diffusivity = 0.005 cm 2 / s is suddenly raised from T to T 1 . Plot the temperature versus dimensional position after 1, 4, 8, and 12 hours. Interpret your result in terms of daily changes in temperature under the surface of the Earth. (T=72F) T=32F T=212F h=1.8Btu/hr.ft 2. F...
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