Thermodynamics HW Solutions 393

Thermodynamics HW Solutions 393 - k = 0.72 W/m. ° C and α...

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Chapter 4 Transient Heat Conduction 4-124 A brick house made of brick that was initially cold is exposed to warm atmospheric air at the outer surfaces. The time it will take for the temperature of the inner surfaces of the house to start changing is to be determined. Assumptions 1 The temperature in the wall is affected by the thermal conditions at outer surfaces only, and thus the wall can be considered to be a semi-infinite medium with a specified outer surface temperature of 18 ° C. 2 The thermal properties of the brick wall are constant. Properties The thermal properties of the brick are given to be
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Unformatted text preview: k = 0.72 W/m. ° C and α = 0.45 × 10-4 m 2 /s. Analysis The exact analytical solution to this problem is T i = 5 ° C 15 ° C 30 cm Wall x ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = − − t x erfc T T T t x T i s i α ) , ( Substituting, ) /s m 10 45 . ( 2 m 3 . 01 . 5 15 5 1 . 5 2 6 ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ × = = − − − t erfc Noting from Table 4-3 that 0.01 = erfc(1.8215), the time is determined to be min 251 = = ⎯→ ⎯ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ × − s 070 , 15 8215 . 1 ) /s m 10 45 . ( 2 m 3 . 2 6 t t 4-104...
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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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