Thermodynamics HW Solutions 342

Thermodynamics HW Solutions 342 - t h k hx t x erfc T T T t...

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Chapter 4 Transient Heat Conduction 4-67 A thick wood slab is exposed to hot gases for a period of 5 minutes. It is to be determined whether the wood will ignite. Assumptions 1 The wood slab is treated as a semi-infinite medium subjected to convection at the exposed surface. 2 The thermal properties of the wood slab are constant. 3 The heat transfer coefficient is constant and uniform over the entire surface. Properties The thermal properties of the wood are k = 0.17 W/m. ° C and α = 1.28 × 10 -7 m 2 /s. Analysis The one-dimensional transient temperature distribution in the wood can be determined from + + = k t h t x erfc k
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Unformatted text preview: t h k hx t x erfc T T T t x T i i 2 exp 2 ) , ( 2 2 where L =0.3 m Wood Slab T i = 25 C Hot gases T = 550 C x 0 628 . 1 276 . 1 276 . 1 C W/m. 0.17 ) s 60 5 )( s / m 10 (1.28 C) . W/m 35 ( 2 2 2 2 2-7 2 = = = = = k t h k t h k t h Noting that x = 0 at the surface and using Table 4-3 for erfc values, 630 . ) 0727 . )( 0937 . 5 ( 1 ) 276 . 1 ( ) 628 . 1 exp( ) ( 25 550 25 ) , ( = = + + = erfc erfc t x T Solving for T ( x, t ) gives C 356 = ) , ( t x T which is less than the ignition temperature of 450 C. Therefore, the wood will not ignite. 4-53...
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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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