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Let the ends of a copper rod 100cm long be maintained at 0C. Suppose that the center of the bar is heated to 100C by an external heat source and that this situation is maintained until a steady state results. Find this steady-state temperature distribution.


i know that two separate boundary-value problems on the rod from 0 to 50 cm and on the rod from 50 to 100cm. For the rod from 0 to 50 cm, T1 = 0, T2 = 100, and L = 50 therefore

v(x) = (T2 − T1)/L *x + T1 = 2x, 0 < x < 50. @

For the rod from 50 to 100 cm, @

T1 = 100, T2 = 0, and L = 50 therefore@

v(x) = (T2 − T1)/L*(x − 50)+ T1 = 200 − 2x, 50 < x < 100.@

and then how can solve it? there isn't initial condition f(x)

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  • $\begingroup$ You don't need an initial condition to find the steady state. $\endgroup$ – ultrainstinct Dec 16 '17 at 9:53
  • $\begingroup$ why?? i dont understand that $\endgroup$ – kim Dec 16 '17 at 12:28
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    $\begingroup$ Please format your post with MathJax! People will be more likely to respond. $\endgroup$ – DaveNine Dec 16 '17 at 19:26
  • $\begingroup$ @kim Because the steady state is what happens really far into the future, it's independent of what the rod initially looked like. $\endgroup$ – ultrainstinct Dec 16 '17 at 20:38

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