Temperature distribution with heat generation

[noName2]

hey i really need help with solving this question.

1. Homework Statement

the problem is in one dimension x ( 2 plates with diffrent K joined together)
for x=0 T=500 ( constat temp)
0<x<L - electric wire is generating heat that maintane the constant temp in x=0 ,it has K=40W/mK.
L<x<2L - there is rubber preventing electriciution and heat loss Ki= 0.2 W/Km , where T(2L)=300K(constant).

how do i find the tempreture distribiotion in the 0<x<2L? (q* gen should be unknown but expressed in the finle answer)
please help :(

Homework Equations

foriers' law of conduction & Qin-Qout+Qgen=Qacc

The Attempt at a Solution

i can find the distribution using the heat balance integral.. but I am not sure about the temperature at x=L..

 

[Chestermiller]

hey i really need help with solving this question.

1. Homework Statement

the problem is in one dimension x ( 2 plates with diffrent K joined together)
for x=0 T=500 ( constat temp)
0<x<L - electric wire is generating heat that maintane the constant temp in x=0 ,it has K=40W/mK.
L<x<2L - there is rubber preventing electriciution and heat loss Ki= 0.2 W/Km , where T(2L)=300K(constant).

how do i find the tempreture distribiotion in the 0<x<2L? (q* gen should be unknown but expressed in the finle answer)
please help :(

Homework Equations

foriers' law of conduction & Qin-Qout+Qgen=Qacc

The Attempt at a Solution

i can find the distribution using the heat balance integral.. but I am not sure about the temperature at x=L..

Let's see what you've done so far?

Chet

 

[noName2]

well , i found the general form of the distribution of the electric wire area(0<x<L) but I am missing a constant because I am not sure what's the temprature in the middle.
i was asked to find the distribution from 0<x<2L ..so i don't know if what i did is right..

here's what i did (image ) :http://www.imageurlhost.com/di/NME6/-.png

 

[noName2]

anyone?

 

[Chestermiller]

The flux has to be continuous at the interface.

Chet

 

[noName2]

i know that..

 

[Chestermiller]

If the electrical wire is generating just enough heat to maintain the boundary at x = 0 constant at 500 K, to me that means that the boundary at x = 0 is essentially insulated (i.e., no external heat flux required). What does that mean with regard to the constant C2 in your equation?

Chet

 

[noName2]

i know that constant i wrote in my answer that it is equal to T0. problem is the c1. i have no idea how to calculate it becase the other side of it has a diffrent k and has no heat generation.even if i compere heat flux. what shall i do ? I've tried everything!

 

[Chestermiller]

i know that constant i wrote in my answer that it is equal to T0. problem is the c1. i have no idea how to calculate it becase the other side of it has a diffrent k and has no heat generation.even if i compere heat flux. what shall i do ? I've tried everything!

Oh. Sorry. I meant C1 in post #7, not C2.

Chet

 

[Chestermiller]

C1 = 0. With this new added information, do you think you will be able to complete the solution?