Unformatted text preview: Chapter 3 Steady Heat Conduction
3166 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 twodimensional (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 35 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 3120 ...
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, Thermal conductivity

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