Homework Help: Temperature distribution with heat generation

1. Nov 9, 2015

noName2

hey i really need help with solving this question.

1. The problem statement, all variables and given/known data

the problem is in one dimention 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)
plz help :(

2. Relevant equations
foriers' law of conduction & Qin-Qout+Qgen=Qacc

3. The attempt at a solution

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

2. Nov 9, 2015

Staff: Mentor

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

Chet

3. Nov 9, 2015

noName2

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

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

4. Nov 10, 2015

noName2

anyone?

5. Nov 10, 2015

Staff: Mentor

The flux has to be continuous at the interface.

Chet

6. Nov 10, 2015

noName2

i know that..

7. Nov 10, 2015

Staff: Mentor

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

Last edited: Nov 10, 2015
8. Nov 10, 2015

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!

9. Nov 10, 2015

Staff: Mentor

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

Chet

10. Nov 10, 2015

Staff: Mentor

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

Last edited: Nov 10, 2015