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An aluminium saucepan containing 1 kg of water is heated by a hot plate as shown in the figure below. The pan has a cylindrical shape, with a radius of 15 cm. The thickness of the aluminium section at the bottom is 10 mm. The air temperature is 25 oC, and water temperature in the pan is uniform at 100 oC.
a. Calculate the heat transfer rate via convection at the water surface.
b. Calculate the heat transfer rate via conduction at the bottom of the pan if the hot plate temperature is uniform and is 150 oC. How does this compare with the heat loss rate in part a.?
c. Assuming that the transfers calculated in parts a. and b. are the only heat loss processes, how long would it take to evaporate all the water if the hot plate temperature stays at 150 oC?
Constants to consider: Latent heat of water: 2260 J/g, convection coefficient of air: 100 W/(m² K), and conduction coefficient of aluminium: 205 W/(m K)
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