# For what values of B is there an equilibrium temperature distribution.

Hey guys, I am trying to solve this problem. As far as I understand in order to get an equilibrium solution we need to set partial U w.r.t t =0 and solve. In this case I would obtain u'' w.r.t x = -1. Integrating this twice would potentially give me the solution in the form of: -x^2/2+Ax+B...Am I on the right path? Because I do not see how I would find beta here...

Also, can anyone recommend a good book on the subject, the one I am using for this course is absolutely horrendous.

Thanks for any input, Leo.

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You are on the right track. Note that $u' = -x + A$, so the condition at $x=0$ makes $A=1$, so $u'=1-x$. From the condition at $x=L$ then, $\beta = 1-L$.
How do you solve for the other const B though in the $u(x)$ function? – Ren Aug 27 at 2:29