Thermodynamics HW Solutions 390

Thermodynamics HW Solutions 390 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-121 A cold cylindrical concrete column is exposed to warm ambient air during the day. The time it will take for the surface temperature to rise to a specified value, the amounts of heat transfer for specified values of center and surface temperatures are to be determined. Assumptions 1 Heat conduction in the column is one-dimensional since it is long and it has thermal symmetry about the center line. 2 The thermal properties of the column are constant. 3 The heat transfer coefficient is constant and uniform over the entire surface. 4 The Fourier number is τ > 0.2 so that the one- term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Properties The properties of concrete are given to be k = 0.79 W/m. ° C, α = 5.94 × 10 -7 m 2 /s, ρ = 1600 kg/m 3 and C p = 0.84 kJ/kg. ° C Analysis ( a ) The Biot number is 658 . 2 ) C W/m. 79 . 0 ( ) m 15 . 0 )( C . W/m 14 ( 2 = ° ° = = k hr Bi o The constants
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