# Homework Help: Heat conduction

1. Mar 6, 2005

### Wiz

Hi,
I have to find the rate of heat flow through a cross-section of the rod in steady state as shown in the figure.Thermal conductivity of the rod is K.
I have used a $(dollar) sign for theta. The formula i know is ΔQ/Δt = [KA($2 - $1)] /x where ΔQ/Δt is the heat current,where A is area of cross section and x is the thickness. since the area of cross section varies.i think integration will be used..... can ANYBODY GUIDE ME THROUGH..?? [NOTE - THE FIGURE READ THAT$2 > $2 , which is a mistake and the correction is$2 > \$1.]
Thanks,

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2. Mar 6, 2005

### davidY

1. assume that the steady state
2. get a thin slice of tube
3. since steady state: heat enter=heat exit
4. this means H is constant over all x
5. our equation:
H=-kA(dT/dx)​
H=-k*pi*r^2*(dT/dx)​
7. well, pi is constant over all x
8. well, r is not constant over all x
9. good luck integrating...

3. Mar 7, 2005

### Wiz

??

how do i relate x and r......
there are 3 variables and we need only 2 for integration.
hope u understand,
wiz

(btw - all the steps u wrote were know to me already0