Heat Conduction with Insulated Ends

[k.kuhlmann]

Homework Statement

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

Homework Equations

I think this involves the Fourier Series but I'm not sure.

The Attempt at a Solution

I'm not sure how to start it. I haven't seen a problem like this where it is heated from the middle.

 

[Mapes]

Hi k.kuhlmann, welcome to PF!

One way to approach this problem is to use the heat equation for steady state

$$\frac{d^2T}{dx^2}=0$$

and solve it (integrate it twice, for example) at either the left or right side of the rod (they're reflectively symmetric, of course) with the temperature boundary conditions that you're given. Does this make sense?