Thermodynamics HW Solutions 338

# Thermodynamics HW Solutions 338 - Chapter 4 Transient Heat...

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Unformatted text preview: Chapter 4 Transient Heat Conduction 4-64 An area is subjected to cold air for a 10-h period. The soil temperatures at distances 0, 10, 20, and 50 cm from the earth’s surface are to be determined. Assumptions 1 The temperature in the soil is affected by the thermal conditions at one surface only, and thus the soil can be considered to be a semi-infinite medium with a specified surface temperature. 2 The thermal properties of the soil are constant. Properties The thermal properties of the soil are given to be k = 0.9 W/m. ° C and α = 1.6 × 10-5 m 2 /s. Analysis The one-dimensional transient temperature distribution in the ground can be determined from ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = − − ∞ k t h t x erfc k t h k hx t x erfc T T T t x T i i α α α α 2 exp 2 ) , ( 2 2 Soil T i = 10 ° C Winds T ∞ =-10 ° C where 1138 7 . 33 7 . 33 C W/m. 0.9 ) s 3600 10 )( s / m 10 (1.6 C)...
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