# Stuck on Boundary Conditions

1. Nov 20, 2006

### Tomsk

I have done most of a question except for the most important part, putting in the boundary conditions, I can't really interpret them.

The question is:

I managed to solve this, with -c^2 as a separation constant, and I got:

$$T(x,t) = X(x)F(t) = (A_{1} \cos{\frac{cx}{\sqrt{\kappa}}} + A_{2} \sin{\frac{cx}{\sqrt{\kappa}}})e^{-c^2 t}$$

But then the question says,

And I can't figure out how to get this. I got T(0,t) = 100, therefore A1 e^(-c^2 t) = 100, but that doesn't tell me much. I know I need to sum over c or n at some point, but am I right in thinking you can't sum over c yet because it's a real arbitrary constant, rather than an integer n? That would probably give you the 1 though from n=0. But the problem is with the insulated end x=L, surely if it's insulated it won't lose heat, so the temperature would just go up?

Last edited: Nov 20, 2006
2. Nov 21, 2006

### SGT

The maximum temperature at any point is 100 degrees. The temperature at the insulated end will only reach this limit at t = infinity. So you have T(L,inf) = 100.

3. Nov 21, 2006

### Tomsk

Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.

4. Nov 21, 2006

### Tomsk

Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.

5. Nov 21, 2006

### Tomsk

Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.