(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img444.imageshack.us/img444/7641/20240456gw8.png [Broken]

2. Relevant equations

http://img14.imageshack.us/img14/5879/63445047rj2.png [Broken]

Note that the rightside of the rod is insulated.

3. The attempt at a solution

I get this model:

[tex] \frac{ \partial{u} }{ \partial{t} } = \kappa \frac{ \partial{ ^2 u} }{ \partial{x^2} } +s [/tex]

[tex]u(0,t)=u_0[/tex]

[tex]\frac{ \partial{u}} { \partial{x} } = 0[/tex]

In steady state this gives: [tex]u(x) = \frac{- s}{ \kappa} \frac{1}{2}x^2 + \frac{s}{ \kappa } L x + u_0 [/tex]

But if I calcute than the asked u' at x=0:

I get:

[tex]\frac{du}{dx} = \frac{s}{ \kappa} L [/tex]

Is this correct?

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# Heat equation applied to a rod

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