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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?

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# Homework Help: Boundary condition for PDE heat eqaution

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