Thermodynamics HW Solutions 317

Thermodynamics HW Solutions 317 - Biot number are, from...

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Chapter 4 Transient Heat Conduction 4-42 A long cylindrical wood log is exposed to hot gases in a fireplace. The time for the ignition of the wood is to be determined. Assumptions 1 Heat conduction in the wood is one-dimensional since it is long and it has thermal symmetry about the center line. 2 The thermal properties of the wood 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 wood are given to be k = 0.17 W/m. ° C, α = 1.28 × 10 -7 m 2 /s Analysis The Biot number is 00 . 4 ) C W/m. 17 . 0 ( ) m 05 . 0 )( C . W/m 6 . 13 ( 2 = ° ° = = k hr Bi o The constants λ 1 and A 1 corresponding to this
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Unformatted text preview: Biot number are, from Table 4-1, 4698 . 1 and 9081 . 1 1 1 = = A Once the constant is determined from Table 4-2 corresponding to the constant J 1 =1.9081, the Fourier number is determined to be 10 cm Wood log, 10 C Hot gases 700 C 251 . ) 2771 . ( ) 4698 . 1 ( 500 10 500 420 ) / ( ) , ( 2 2 1 ) 9081 . 1 ( 1 1 = = = e r r J e A T T T t r T o o i o which is above the value of 0.2. Therefore, the one-term approximate solution (or the transient temperature charts) can be used. Then the length of time before the log ignites is min 81.7 = = = = s 4904 /s) m 10 28 . 1 ( m) 05 . )( 251 . ( 2 7 2 2 o r t 4-28...
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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