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hw4 - of the concrete at r = 0.0(center and 0.3 m(surface...

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ME 322 HW #4 11.03.2008 1. An aluminum can having the diameter of 6 cm and the height of 10 cm contains fruit juice at 1ºC . Using a lumped-capacity analysis, estimate the time required for the contents to warm to 15ºC when the can is placed in a room at 22ºC with a convection coefficient of 4 W/m 2 ºC. Assume the fruit juice has the same properties as water. Also validate the assumption of the lumped-capacity analysis employed. (ANSWER: 14400 s) 2. A concrete column (an infinite circular cylinder) with radius o r = 0.3 m initially has a uniform temperature of 30ºC. Now the atmospheric environment is suddenly changed to 20ºC. The convection heat transfer coefficient is estimated to be 5 W/m 2 ºC. What will be the temperatures
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Unformatted text preview: of the concrete at r = 0.0 (center) and 0.3 m (surface) after 24 hours? The properties of the concrete are as follows: α = 7 × 10 7 − m 2 /s and k = 1 W/mºC. (ANSWER: 23.2ºC, 21.7ºC) NOTE: For a cylinder with a convection boundary, the one-term approximation is given as follows: ) ( ) exp( 1 2 1 1 o o o i r r J F C T T T T ζ − = − − ∞ ∞ The values for Bessel function are given in Table B.4. 3. On a hot summer day a concrete driveway may reach a temperature of 50ºC. Suppose that a stream of water is directed on the driveway so that the surface temperature is suddenly lowered to 20ºC. How long will it take to cool the concrete to 30ºC at a depth of 5 cm from the surface? (ANSWER: 9620 s)...
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