Thermodynamics HW Solutions 373

Thermodynamics HW Solutions 373 - C W/m. 43 ( ) m 02 . )( C...

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Chapter 4 Transient Heat Conduction Review Problems 4-105 Two large steel plates are stuck together because of the freezing of the water between the two plates. Hot air is blown over the exposed surface of the plate on the top to melt the ice. The length of time the hot air should be blown is to be determined. Assumptions 1 Heat conduction in the plates is one-dimensional since the plate is large relative to its thickness and there is thermal symmetry about the center plane. 3 The thermal properties of the steel plates 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 thermal properties of steel plates are given to be k = 43 W/m. ° C and α = 1.17 × 10 -5 m 2 /s Analysis The characteristic length of the plates and the Biot number are 1 . 0 019 . 0 )
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Unformatted text preview: C W/m. 43 ( ) m 02 . )( C . W/m 40 ( m 02 . 2 < = = = = = = k hL Bi L A V L c s c Since , the lumped system analysis is applicable. Therefore, Bi < 0.1 min 8.0 s 482 = = = = = = = = t e e T T T t T L C h V C hA b bt i c p p s )t s 000544 . ( 1-3 6 2-1 50 15 50 ) ( s 000544 . m) (0.02 ) C . J/m 10 675 . 3 ( C . W/m 40 Steel plates T i = -15 C Hot gases T = 50 C where C . J/m 10 675 . 3 /s m 10 17 . 1 C W/m. 43 3 6 2 5 = = = k C p Alternative solution: This problem can also be solved using the transient chart Fig. 4-13a, 2 . 15 769 . 50 15 50 6 . 52 019 . 1 1 2 > = = = = = = o i o r t T T T T Bi Then, s 513 = = = /s) m 10 17 . 1 ( m) 02 . )( 15 ( 2 5 2 2 o r t The difference is due to the reading error of the chart. 4-84...
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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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