Problem 21-2 - Example 21-2 A river is covered with a layer of ice 1 ft thick at a temperature of 10F One spring day a warm wind at 50F blows over

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Example 21-2 A river is covered with a layer of ice 1 ft. thick at a temperature of 10 ° F. One spring day, a warm wind at 50 ° F blows over the ice. If h = 20 Btu /(hr . ft 2 ° F), how long will it be before the surface of the ice starts to melt? (Assume ice is semi-infinite) Solution: For a semi-infinite solid () 2 2 , 1e r f c 2 exp erfc 2 f if Tx t T x TT t hx h t x h t kk k t α αα ⎛⎞ =− ⎜⎟ ⎝⎠ ⎡⎤ ++ + ⎢⎥ ⎣⎦ At the surface of the ice, x = 0. Note from Table 11-4, that erfc 0 1 = The solution simplifies to 2 2 , exp erfc f ht h t k k = Btu k_('ice',10) 1.14 hr ft R k == 3 lbm rho_('ice',10) 57.43 ft ρ o Btu c_('ice',10) 0.473 lbm F p c 2 3o Btu 1.14 ft hr ft R 0.0419 lbm Btu hr 57.43 0.473 ft lbm F p k c ⋅⋅ =
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Substituting values 2 2 o 2 2 o Btu ft 20 0.0419 hr ft F hr 32 50 exp 10 50 Btu 1.14 hr ft R Btu ft 20 0.0419 hr ft F hr erfc Btu 1.14 hr ft R t t
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This homework help was uploaded on 04/07/2008 for the course MANE 4010 taught by Professor Kaminski during the Spring '08 term at Rensselaer Polytechnic Institute.

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Problem 21-2 - Example 21-2 A river is covered with a layer of ice 1 ft thick at a temperature of 10F One spring day a warm wind at 50F blows over

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