Finite Difference Method - 1D Conduction 1

[CHCl3]

Heat conduction on a insulated rod with the ends at constant temperatures of T0=100 and T10=500 degC. L=0.5m delX=0.05

Governing Equation: d/dx(k dT/dx)=0
Analytical Solution: T=800x + 100

k(d2T/dx2)=0

Central Difference:
d2T/x2=((T,i-1)-2(T,i)+(T,i+1))/delX^2

So for i=1 on k(d2T/dx2)=0
(k/delX^2)(T0-2T1+T2)=0 ???


That means if I set up the matrices

(k/delX^2) [-2 1...] [T1;T2...] = [T0 0...T10]

However I don't get the correct answer. If I drop the (k/delX^2), I get the correct the answer. Why is that?

[-2 1...] [T1;T2...] = [T0 0...T10]

 

[corus]

K and delx shouldn't be in your equation as these are constant and the RHS of the equation is zero. Strictly speaking, however, k should also be differentiated, unless you're assuming it to be constant and not dependent upon temperature.