Boundary condition for PDE heat eqaution

[Taylor_1989]

Homework Statement

I am having an issue, not with the maths but with the boundary conditions for this question.

A bar 10 cm long with insulated sides, is initially at $100 ^\circ$. Starting at $t=0$
Find the temperature distribution in the bar at time t.

The heat flow equation is

$$\frac{\partial ^2u}{\partial x^2}=\frac{1}{k}\frac{\partial u}{\partial t}$$

where $u(x,t)$ is the tempreture, Because the sides of the bar are insulated, the heat flows only in the, the same happens for a slab of finite thickness but infinitely large.

The initial condition is $u(x,0)=100$ and the boundary condition for $t>0$ is $u (0 ,t ) = u (10 ,t ) = 0.$

Have read this incorectly but if the sides are insulated then surely the boundary condtions are,

$U_{x}(0,t)=U_{x}(L,t)=0$

as the heat is moving along the x direction?

 

[LCKurtz]

Have read this incorectly but if the sides are insulated then surely the boundary condtions are,

$U_{x}(0,t)=U_{x}(L,t)=0$

as the heat is moving along the x direction?

No. The sides that are insulated are the curved sides, not the ends. That is what makes it a one dimensional flow equation with the heat flowing through the ends. So those partials with respect to $x$ are not zero.