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chap83_ex

# chap83_ex - 600 573.8 623.2 506.8 697 undefined value ±...

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1 Radiation Example Given : •Three infinite parallel plates. • Plate 1 is a blackbody ( ε 1 = 1.0). • Plate 2 is polished aluminum ( ε 2 = 0.1). • The shape factor between plates 2 and 3 is F =0.05. σ =5.67x10 -8 W/m 2 /K 4 T 1 =400 K T 2 T 3 =750 K Find the temperature of Plate 2 under steady-state conditions. Solution: ) K in ; (W/m ) 750 ( 05 . 0 ) ( 2 2 4 2 4 4 2 4 3 2 3 T T T T F f = = σ σ ( ) ( ) K 7 . 591 ) 400 ( 1 1 1 2 4 4 2 2 1 1 2 2 3 = + = = T T f f ε ε σ

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2 Radiation Example: Numerical Approach Let’s try to solve the same problem with the direct substitution method. ) 400 ( 0.1 ) .05(750 0 4 4 2 4 2 4 1 2 2 3 = = T T f f Assuming a starting temperature of T 2 =600 K on the right: K 8 . 573 11 08 . 2 ) 400 600 ( 2 ) (750 2 4 4 4 2 4 = = = T E T Substituting the new value of T 2 on the right and recalculating T 2 and continuing this way, we obtain the following series of values:
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Unformatted text preview: 600, 573.8, 623.2, 506.8, 697, undefined value. ± Hence, the solution diverges because the fourth power of a variable is very sensitive to small changes in the value of the variable. ± Problem 8.10 converges if the temperature value in the radiation term is assumed. 3 Conduction Example 100 ° C T 15 mm k=0.6 W/m/ C ± Compute the temperature T of the left surface of the plate if there is a heat conduction rate (flux) of 6000 W/m 2 through the plate to the right. ± Solution: C 250 015 . 100 6000 o = ⇒ − = = T T k q...
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