Non-uniform thermal conductivity

[matt222]

Homework Statement

solve d/dx(kdT/dx)=0
where k is linear function of temperature
k=k(0)(1+BT)

Homework Equations

this is the solution

T+BT^2/2=Ax+C

The Attempt at a Solution

i opened the equation so that it becomes equal to

dk/dx*dT/dx+kd^2T/dx^2=0

i subtitute the value of K in the equation and tried to integrate it but i relize that i am not doing it in a correct way, can you giude me please

 

[gneill]

If
$$\frac{d f(x)}{d x} = 0$$
then what does this say about f(x)?

 

[matt222]

f(x) is constant

 

[matt222]

the problem now we have another variable which is K which is a linear function of T , i need to integrate this but i need a giude i did it but i have a term of k(0) which is not accepted as the final answer said

 

[matt222]

it is ok if i need to integrate df(x)/dx=0, so f(x)=A

same with d^2f(x)/dx=0

f(x)=Ax+B

but the problem here with the another term which is K as a linear of temperature

 

[gneill]

So you have:

d/dx(kdT/dx)=0

which implies that:

kdT/dx) = const

Substituting for k:

k0(1+BT) dT/dx = const

(1+BT) dT = (const/k0)*dx

(1+BT) dT = A*dx letting A = const/k0

 

[matt222]

thats it , many thanks got it