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Chapter 2
Heat Conduction Equation
2127
A spherical liquid oxygen container is subjected to specified temperature on the inner surface and
convection on the outer surface.
The mathematical formulation, the variation of temperature, and the rate
of evaporation of oxygen are to be determined for steady onedimensional heat transfer.
Assumptions
1
Heat conduction is steady and onedimensional since there is no change with time and there
is thermal symmetry about the midpoint.
2
Thermal conductivity is constant.
3
There is no heat generation.
Properties
The thermal conductivity of the tank is given to be
k
= 18 W/m
⋅
°C. Also,
h
fg
= 213 kJ/kg for
oxygen.
Analysis
(
a
) Noting that heat transfer is onedimensional in the radial
r
direction, the mathematical
formulation of this problem can be expressed as
0
2
=
⎟
⎠
⎞
⎜
⎝
⎛
dr
dT
r
dr
d
and
Tr
T
()
11
183
==
−°
C
−=
−
∞
k
dT r
dr
hTr
T
[( )
]
2
2
(
b
)
Integrating the differential equation once with respect to
r
gives
r
dT
dr
C
2
1
=
r
1
r
2
h
T
∞
r
183°C
O
2
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat

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