Thermodynamics HW Solutions 378

Thermodynamics HW Solutions 378 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-111 The trunks of some dry oak trees are exposed to hot gases. The time for the ignition of the trunks is to be determined. Assumptions 1 Heat conduction in the trunks is one-dimensional since it is long and it has thermal symmetry about the center line. 2 The thermal properties of the trunks 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 the trunks are given to be k = 0.17 W/m. ° C and α = 1.28 × 10 -7 m 2 /s. Analysis We treat the trunks of the trees as an infinite cylinder since heat transfer is primarily in the radial direction. Then the Biot number becomes 24 . 38 ) C W/m. 17 . 0 ( ) m 1 . 0 )( C . W/m 65 ( 2 = ° ° = = k hr Bi o The constants λ 1 and A 1 corresponding to this Biot number are, from Table 4-1, 5989 . 1 and 3420 . 2 1 1 = = A The Fourier number is 184 . 0
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