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Chapter 2
Heat Conduction Equation
243
A spherical shell of inner radius
, outer radius
, and thermal conductivity
k
is considered. The
outer surface of the shell is subjected to radiation to surrounding surfaces at
T
. Assuming no convection
and steady onedimensional conduction in the radial direction, the radiation boundary condition on the
outer surface of the shell can be expressed as
r
1
r
2
surr
r
1
r
2
T
surr
k
ε
−=
−
k
dT r
dr
Tr
T
()
2
2
4
εσ
surr
4
244
A spherical container consists of two spherical layers
A
and
B
that are at perfect contact. The radius of
the interface is
r
o
. Assuming transient onedimensional conduction in the radial direction, the boundary
conditions at the interface can be expressed as
t Trt
AB
(,
)
)
00
=
r
and
−
k
Trt
x
k
x
A
A
B
B
∂
)
)
245
Heat conduction through the bottom section of a steel pan that is used to boil water on top of an
electric range is considered (Fig. P245). Assuming constant thermal conductivity and onedimensional
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Conductivity, Convection, Mass, Heat, Radiation

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