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Unformatted text preview: Chapter 4 Transient Heat Conduction 4-118 Internal combustion engine valves are quenched in a large oil bath. The time it takes for the valve temperature to drop to specified temperatures and the maximum heat transfer are to be determined. Assumptions 1 The thermal properties of the valves are constant. 2 The heat transfer coefficient is constant and uniform over the entire surface. 3 Depending on the size of the oil bath, the oil bath temperature will increase during quenching. However, an average canstant temperature as specified in the problem will be used. 4 The Biot number is Bi < 0.1 so that the lumped system analysis is applicable (this assumption will be verified). Properties The thermal conductivity, density, and specific heat of the balls are given to be k = 48 W/m. C, = 7840 kg/m 3 , and C p = 440 J/kg. C. Analysis ( a ) The characteristic length of the balls and the Biot number are 1 . 024 . ) C W/m. 48 ( ) m 0018 . )( C . W/m 650 ( m 0018 . 8 m) 008 . ( 8 . 1 8 8 . 1 2 ) 4 / ( 8 . 1 2 2 < = = = = = = = = k hL Bi D DL L D A V L c s c Therefore, we can use lumped system analysis. Then the time for a final valve temperature of 400 C becomes s 7.2 = =-- =-- = = = =-- t e e T T T t T D C h V C hA b bt i p p s )t s 10468 . ( 1- 3 2-1 45 800 45 400 ) ( s 10468 . m) C)(0.008 J/kg. 440 )( kg/m 1.8(7840 C) . W/m 650 ( 8 8 . 1 8 ( b ) The time for a final valve temperature of 200 C is s 15.1 = =-- =---- t e e T T T t T bt i )t s 10468 . (-1 45 800 45 200 ) ( ( c ) The time for a final valve temperature of 46 C is s 63.3 = =-- =---- t e e T T T t T bt i )t s 10468 . (-1 45 800 45 46 ) ( ( d ) The maximum amount of heat transfer from a single valve is determined from ) (per valve = J 564 , 23 C ) 45 800 )( C J/kg. 440 )( kg 0709 . ( ] [ kg 0709 . 4 m) 10 . ( m) 008 . ( 8 . 1 ) kg/m 7840 ( 4 8 . 1 2 3 2 kJ 23.56 = - =- = = = = = i f p T T mC Q L D V m 4-98 Oil T = 45 C Engine valve T i = 800 C Chapter 4 Transient Heat Conduction 4-119 A watermelon is placed into a lake to cool it. The heat transfer coefficient at the surface of the watermelon and the temperature of the outer surface of the watermelon are to be determined. Assumptions 1 The watermelon is a homogeneous spherical object. 2 Heat conduction in the watermelon is one-dimensional because of symmetry about the midpoint. 3 The thermal properties of the watermelon are constant. 4 The heat transfer coefficient is constant and uniform over the entire surface. 5 The Fourier number is > 0.2 so that the one-term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified)....
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