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Timeline for Heat equation: boundary conditions?

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Aug 15, 2014 at 11:47 comment added maze-cooperation Why zero? The heat flows through the bar must match the heat flow through the rod as in your original post. The temperature profile in the rod is obviously linear, so the heat flow though the rod is $\propto T_0-T_\inf$. Then use the symmetry of the problem around $x=0$, the result is a Robin type of boundary condition for the bar: $2\partial_x T + T_0 = const$ With this it should be easy to find a solution of the form $T(x) = ax^2+bx+c$.
Aug 14, 2014 at 15:20 comment added Fire This is what I was trying, but I can't seem to get anything other than $\kappa S \left(\frac{d T}{dx}_{x=0^+}-\frac{d T}{d x}_{x=0^-} \right)=0$. I am obviously making an incorrect assumption or handling the equations incorrectly.
Aug 13, 2014 at 16:37 history answered guillefix CC BY-SA 3.0