Heat Chap04-105

Heat Chap04-105 - Chapter 4 Transient Heat Conduction...

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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 ) C W/m. 43 ( ) m 02 . 0 )( C . W/m 40 ( m 02 . 0 2 < = ° ° = = = = = k hL Bi L A V L c s c Since Bi < 0.1 , the lumped system analysis is applicable. Therefore, 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 . 0 ( 1 - 3 6 2 -1 50 15 50 0 ) ( s 000544 . 0 m) (0.02 ) C . J/m 10 675 . 3 ( C . W/m 40 ρ where C . J/m 10 675 . 3 /s m 10 17 . 1 C W/m. 43 3 6 2 5 ° × = × ° = α = ρ - k C p Alternative solution: This problem can also be solved using the transient chart Fig. 4-13a, 2 . 0 15 769 . 0 50 15 50 0 6 . 52 019 . 0 1 1 2 = = = - - - = - - = = o i o r t T T T T Bi α τ Then, s 513 = × = α τ = - /s) m 10 17 . 1 ( m) 02 . 0 )( 15 ( 2 5 2 2 o r t The difference is due to the reading error of the chart. 4-84 Steel plates T i = -15 ° C Hot gases T = 50 ° C
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Chapter 4 Transient Heat Conduction 4-106 A curing kiln is heated by injecting steam into it and raising its inner surface temperature to a specified value. It is to be determined whether the temperature at the outer surfaces of the kiln changes during the curing period. Assumptions 1 The temperature in the wall is affected by the thermal conditions at inner surfaces only and the convection heat transfer coefficient inside is very large. Therefore, the wall can be considered to be a semi-infinite medium with a specified surface temperature of 45 ° C. 2 The thermal properties of the concrete wall are constant. Properties The thermal properties of the concrete wall are given to be k = 0.9 W/m. ° C and α = 0.23 × 10 -5 m 2 /s. Analysis We determine the temperature at a depth of x = 0.3 m in 3 h using the analytical solution, = - - t x erfc T T T t x T i s i α 2 ) , ( Substituting, C 9.1 ° = = = × × = - - - ) , ( 1782 . 0 ) 952 . 0 ( ) s/h 3600 h 3 )( /s m 10 23 . 0 ( 2 m 3 . 0 5
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Heat Chap04-105 - Chapter 4 Transient Heat Conduction...

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