Transient Heat Conduction with a Nuclear Heat Source

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Consider a spherical nuclear fuel element consisting of a sphere of fissionable material of radius , surrounded by a spherical shell of alloy cladding with outer radius
, initially at temperature
, that is suddenly immersed at
in a cooling bath of temperature
. The heat equation describing this system is:
Contributed by: Clay Gruesbeck (January 2017)
Open content licensed under CC BY-NC-SA
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Details
A similar steady-state problem is solved in [1].
Reference
[1] R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, rev. 2nd ed., New York: John Wiley & Sons, Inc., 2007.
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