Thermodynamics HW Solutions 297

Thermodynamics HW Solutions 297 - temperature are = 62.22...

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Chapter 4 Transient Heat Conduction 4-19E A person shakes a can of drink in a iced water to cool it. The cooling time of the drink is to be determined. Assumptions 1 The can containing the drink is cylindrical in shape with a radius of r 0 = 1.25 in. 2 The thermal properties of the milk are taken to be the same as those of water. 3 Thermal properties of the milk are constant at room temperature. 4 The heat transfer coefficient is constant and uniform over the entire surface. 5 The Biot number in this case is large (much larger than 0.1). However, the lumped system analysis is still applicable since the milk is stirred constantly, so that its temperature remains uniform at all times. Milk 3 ° C Water 32 ° F Cola 75 ° F Properties The density and specific heat of water at room
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Unformatted text preview: temperature are = 62.22 lbm/ft 3 , and C p = 0.999 Btu/lbm. F (Table A-9E). Analysis Application of lumped system analysis in this case gives ft 04167 . ft) 12 / 25 . 1 ( 2 + ft) ft)(5/12 12 / 25 . 1 ( 2 ft) 12 / 5 ( ft) 12 / 25 . 1 ( 2 2 2 2 2 2 = = + = = o o o s c r L r L r A V L s 406 = = = = = = = = t e e T T T t T L C h V C hA b t bt i c p p s ) s 00322 . ( 1-1-3 2-1 32 80 32 45 ) ( s 00322 . h 583 . 11 ft) F)(0.04167 Btu/lbm. 999 . )( lbm/ft (62.22 F . Btu/h.ft 30 Therefore, it will take 7 minutes and 46 seconds to cool the canned drink to 45 F. 4-8...
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