Thermodynamics HW Solutions 388

Thermodynamics HW Solutions 388 - Chapter 4 Transient Heat...

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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 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 the watermelon are given to be k = 0.618 W/m. ° C, α = 0.15 × 10 -6 m 2 /s, ρ = 995 kg/m 3 and C p = 4.18 kJ/kg. ° C. Analysis The Fourier number is [] 252 . 0 m) 10 . 0 ( s/min 60 min) 40 60 (4 /s) m 10 15 . 0 ( 2 2 6 2 = × + × × = α = τ o r t Water melon T i = 35 ° C
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