Quiz 2 Prep: Steady state heat flow
The left end of bar of length 2 is held at the constant temperature $T=3$ while the right side is insulated.
- Write down the boundary value problem as an ODE and pair of boundary conditions that describes this situation mathematically.
- Solve your boundary value problem and show that it agrees with our physical understanding.
Comments
I'm having a really hard time setting this one up....
same, and the only class recording available is from august 24th. Even googling hasn't really helped.
Not totally confident but I think we have:
$u(0)=3,$ $u'(2)=0$ and $u''=0.$
So $$u''=0 \rightarrow u'=a \rightarrow u=ax+b.$$
Using boundary conditions:
$$u(0)=3=a(0)+b \rightarrow b=3$$
and
$$u'(2)=0=a.$$
Thus
$$u(x)=3.$$
I chose $u'(2)=0$ because the right side of the bar is insulated. Which implies there is no change in temperature across that boundary. So I interpret this situation to mean that after the bar reaches steady-state, the temp is constant across the bar.
This is what I got... Using 317 of the textbook.
But as Stephen said, it should be $u'(2)=0$