Determine the stability criterion for an explicit solution of three-dimensional transient conduction in a rectangular geometry.

GIVEN
- Three-dimensional transient conduction in a rectangular geometry
FIND
(a) The stability criterion for an explicit situation


From the solution of Problem 3.49, the control volume energy balance equation is



so the coefficient on T is



Since this coefficient must be greater than zero to ensure stability, we have



Note that this expression is consistent with the extension from one-dimensional to two-dimensional

stability criteria.

Physics & Space Science

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a.
?5.0 V

b.
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c.
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d.
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e.
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B. 8.0 W
C. 12 W
D. 16 W
E. 20 W

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