Chapter 2
Heat Conduction Equation
2131E
The concrete slab roof of a house is subjected to specified temperature at the bottom surface and
convection and radiation at the top surface. The temperature of the top surface of the roof and the rate of
heat transfer are to be determined when steady operating conditions are reached.
Assumptions
1
Steady operating conditions are reached.
2
Heat transfer is onedimensional since the roof
area is large relative to its thickness, and the thermal conditions on both sides of the roof are uniform.
3
Thermal properties are constant.
4
There is no heat generation in the wall.
Properties
The thermal conductivity and emissivity are given to be
k
= 1.1 Btu/h
⋅
ft
⋅
°F and
ε
= 0.9.
Analysis
In steady operation, heat conduction through the roof must be equal to net heat transfer from the
outer surface. Therefore, taking the outer surface temperature of the roof
to be
T
2
(in
°
F),
]
)
460
[(
)
(
4
sky
4
2
2
2
1
T
T
A
T
T
hA
L
T
T
kA
−
+
+
−
=
−
∞
σε
x
T
∞
h
T
o
L
T
sky
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Radiation, Heat Transfer, °F, Steady operating conditions

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