Thermodynamics HW Solutions 323

# Thermodynamics HW Solutions 323 - − = − − ∞ ∞ o o...

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Chapter 4 Transient Heat Conduction 4-47 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 one-dimensional 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 one- term 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. 4-14b we have 15 . 0 1 1 17 . 0 94 59 94 88 = = = = =
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Unformatted text preview: − = − − ∞ ∞ o o o o o hr k Bi r r r r T T T T Water 94 ° C Hot dog The Fourier number is determined from Fig. 4-14a 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 4-34...
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