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exam2_sol - ME 410 Name Spring 2008 Exam 2 Exam is open...

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ME 410 Spring 2008 Name Exam 2 Exam is open notes, open book. Problems have indicated point value. Problem 1 (30 pts) Often a watermelon is cut in half and put into the freezer to cool it quickly. If it is left in the freezer to long, a frozen layer will appear on top. To avoid this, determine how long to keep one half of a 30 cm diameter spherical watermelon in a freezer at -12°C such that the center of the outer flat surface is at 3°C. The watermelon is initially at 25°C and the freezer has a convection coefficient of 30 W/m 2 K. Assume the watermelon to have the properties of water. h = 30 W/m 2 ˚C, T =-12˚C, T i =25˚C, r = .15m Properties of H 2 O taken at T average ~ 285 K Cp = 4189 J/kgK, k = 0.590 W/mK, v = 0.001 m 3 /kg α = 1.41E-7 m 2 /s Check LCM r r r A V L k r h k hL Bi s c c 3 2 3 4 2 1 1 . 0 08475 . 5 3 2 2 3 = = = = = = π π , not valid Fourier number is unknown, looking to cool something quickly, so assume short time and model with semi-infinite. Also, unclear how to map to 1 st term geometry which requires symmetry. Use semi-infinite for convective condition at the surface
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