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Unformatted text preview: Chapter 18 Transient Heat Conduction 1847 A hot dog is dropped into boiling water, and temperature measurements are taken at certain time intervals. The thermal diffusivity and thermal conductivity of the hot dog and the convection heat transfer coefficient are to be determined. Assumptions 1 Heat conduction in the hot dog is onedimensional since it is long and it has thermal symmetry about the centerline. 2 The thermal properties of the hot dog 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 oneterm approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Properties The properties of hot dog available are given to be ρ = 980 kg/m 3 and C p = 3900 J/kg. ° C. Analysis ( a ) From Fig. 1814b we have 15 . 1 1 17 . 94 59 94 88 = = = = = = ∞ ∞ o o o o o hr k Bi r r r r T T T T The Fourier number is determined from Fig. 1814a to be 20 . 47 . 94 20 94 59 15 . 1 2 = = = = = = ∞ ∞ o i o o r t T T T T hr k Bi α τ The thermal diffusivity of the hot dog is determined to be /s m 10 2.017 2 7 × = = = α → = α s 120 m) 011 . )( 2 . ( 2 . 20 . 2 2 2 t r r t o o ( b ) The thermal conductivity of the hot dog is determined from C W/m. 0.771 ° = ° × = αρ = C) J/kg. )(3900 kg/m /s)(980 m 10 017 . 2 ( 3 2 7 p C k ( c ) From part ( a ) we have 15 . 1 = = o hr k Bi . Then, m 0.00165 m) 011 . )( 15 . ( 15 . = = = r h k Therefore, the heat transfer coefficient is C . W/m 467 2 ° = ° = → = m 0.00165 C W/m. 771 . 00165 . h h k 1834 Water 94 ° C Hot dog Chapter 18 Transient Heat Conduction 1848 Using the data and the answers given in Prob. 1843, the center and the surface temperatures of the hot dog 4 min after the start of the cooking and the amount of heat transferred to the hot dog are to be determined. Assumptions 1 Heat conduction in the hot dog is onedimensional since it is long and it has thermal symmetry about the center line. 2 The thermal properties of the hot dog 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 oneterm approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Properties The properties of hot dog and the convection heat transfer coefficient are given or obtained in P1847 to be k = 0.771 W/m. ° C, ρ = 980 kg/m 3 , C p = 3900 J/kg. ° C, α = 2.017 × 107 m 2 /s, and h = 467 W/ m 2 . ° C. Analysis The Biot number is 66 . 6 ) C W/m. 771 . ( ) m 011 . )( C . W/m 467 ( 2 = ° ° = = k hr Bi o The constants λ 1 1 and A corresponding to this Biot number are, from Table 181, 5357 . 1 and 0785 . 2 1 1 = = A λ The Fourier number is 2 . 4001 ....
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 Spring '08
 Chung
 Heat Transfer, TI, Thermal conductivity, transient heat conduction, T

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