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Thermodynamics HW Solutions 277

# Thermodynamics HW Solutions 277 - Chapter 3 Steady Heat...

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Unformatted text preview: Chapter 3 Steady Heat Conduction 3-166 Steam passes through a row of 10 parallel pipes placed horizontally in a concrete floor exposed to room air at 25 ° C with a heat transfer coefficient of 12 W/m2.°C. If the surface temperature of the concrete floor is not to exceed 40 ° C , the minimum burial depth of the steam pipes below the floor surface is to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer is two-dimensional (no change in the axial direction). 3 Thermal conductivity of the concrete is constant. Properties The thermal conductivity of concrete is given to be k = 0.75 W/m⋅°C. Analysis In steady operation, the rate of heat loss from the steam through the concrete floor by conduction must be equal to the rate of heat transfer from the concrete floor to the room by combined convection and radiation, which is determined to be & Q = hAs (Ts − T∞ ) = (12 W/m 2 .°C)[(10 m )(5 m )](40 − 25)°C = 9000 W Then the depth the steam pipes should be buried can be determined with the aid of shape factor for this configuration from Table 3-5 to be & Q = nSk (T1 − T2 ) ⎯ → S = ⎯ w= & 9000 W Q = = 10.91 m (per pipe) nk ( T1 − T2 ) 10(0.75 W / m. ° C)(150 − 40)° C a 10 m = = 1 m (center - to - center distance of pipes) n 10 S= 10.91 m = 10 m 2πL 2πz ⎞ ⎛ 2w ln⎜ sinh ⎟ w⎠ ⎝ πD 2π (5 m) ⎡ 2(1 m) 2πz ⎤ ln ⎢ sinh ⎥ (1 m) ⎦ ⎣ π (0.06 m) Room 25°C 40°C ⎯ ⎯→ z = 0.205 m = 20.5 cm 3-120 ...
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