Non-uniform thermal conductivity

  • Thread starter matt222
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  • #1
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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 plz
 

Answers and Replies

  • #2
gneill
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If
[tex]\frac{d f(x)}{d x} = 0[/tex]
then what does this say about f(x)?
 
  • #3
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f(x) is constant
 
  • #4
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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
 
  • #5
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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
 
  • #6
gneill
Mentor
20,925
2,866
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
 
  • #7
132
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thats it , many thanks got it
 

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