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1.2
Applications
1.3
Conduction of Heat in a Rod
1.4
Boundary Conditions
Problems
1. Suppose the initial temperature of the rod was
u
(
x,
0) =
2
x
0
≤
x
≤
1
/
2
2(1
−
x
)1
/
2
≤
x
≤
1
and the boundary conditions were
u
(0
,t
)=
u
(1
)=0
,
what would be the behavior of the rod’s temperature for later time?
2. Suppose the rod has a constant internal heat source, so that the equation describing the
heat conduction is
u
t
=
ku
xx
+
Q,
0
<x<
1
.
Suppose we Fx the temperature at the boundaries
u
(0
u
(1
)=1
.
What is the steady state temperature of the rod? (Hint: set
u
t
=0
.
)
3. Derive the heat equation for a rod with thermal conductivity
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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