Homework_5_Solution

Homework_5_Solution - 4-17 A mother warms milk for her baby...

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4-17 A mother warms milk for her baby by placing it in a glass that is placed in a pot of hot water. The time it takes for the milk to reach a specified temperature is to be determined. Assumptions The milk can be treated as a lumped capacitance system since it is constantly being stirred and thus at uniform temperature, therefore the test for the Biot number is not necessary. The glass is cylindrical. Milk has the same properties as water. The heat transfer is constant and uniform over the glass. = + = × = = = = = = = = = = = - 2 2 3 4 2 o C 20 o C 20 3 C 20 o o o o 2 m 019 . 0 4 2 m 10 98 . 1 4 C W/m 0.602 C J/kg 33 . 4191 kg/m 67 . 996 C 38 C 3 C 60 C W/m 120 m 07 . 0 m 06 . 0 o o o D DL A L D V k c T T T h L D s p f i π π π ρ Known Unknown c L b t , , Property Relations and Laws mins 5.8 = × - - - = × - - - = = = = = × = = - s 60 min 1 s 0027 . 0 60 3 60 38 ln s 60 min 1 ln s 0027 . 0 m) C)(0.01 J/kg 33 . 4191 )( kg/m 67 . 996 ( C W/m 120 m 01 . 0 m 019 . 0 m 10 98 . 1 1 - 1 - o 3 o 2 2 3 4 b T T T T t L c h b A V L i f c p s c ρ Conclusion The solution makes sense. Interesting that lumped capacitance can be assumed for liquids being stirred.
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