5. Oranges and grapes, when exposed to below-freezing temperatures when still growing on their plants, can...

 

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5. Oranges and grapes, when exposed to below-freezing temperatures when still growing on their plants, can sustain serious damage. A grape with mass if 1.4 g, originally at a uniform temperature of 7 °C, is suddenly exposed to very cold air during a cold, frosty night. The convection heat transfer coefficient between the air and grape surface is 12 W/m? K. After 20 minutes under these conditions, the center of the grape reaches 0 °C. At these same conditions, how long will it take for the center of a 10 cm (diameter) orange to reach 0 °C? For oranges and grapes, use density (940 kb/m3), specific heat capacity (3800 J/kg-K), thermal conductivity (0.6 W/m K). For full credit, if you use any equations which are the results of solving differential equations, you must first derive them starting from first principles, be logical in the derivation, and state any assumptions. If you use any charts, you must mark on your chart how it was used. See charts at the end. 5. Oranges and grapes, when exposed to below-freezing temperatures when still growing on their plants, can sustain serious damage. A grape with mass if 1.4 g, originally at a uniform temperature of 7 °C, is suddenly exposed to very cold air during a cold, frosty night. The convection heat transfer coefficient between the air and grape surface is 12 W/m? K. After 20 minutes under these conditions, the center of the grape reaches 0 °C. At these same conditions, how long will it take for the center of a 10 cm (diameter) orange to reach 0 °C? For oranges and grapes, use density (940 kb/m3), specific heat capacity (3800 J/kg-K), thermal conductivity (0.6 W/m K). For full credit, if you use any equations which are the results of solving differential equations, you must first derive them starting from first principles, be logical in the derivation, and state any assumptions. If you use any charts, you must mark on your chart how it was used. See charts at the end.

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