# Fourier Law + Heat Transfer

1. Jun 9, 2007

### skimmer

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

We have a wall of 30cm thickness, an inner surface temp of 500Kelvins and outer surfce temperature of 60Kelvins.

2. Relevant equations

thermal conductivity = k(a) = 60 + 0.0006a^2, where a = temperature.
fouriers law = q = -kA(da/dx)

3. The attempt at a solution

What is the expression for da/dx and how would the rate of heat transfer be derived? I know there an inegration in there somewhere!!

I'm completely stuck with this one so haven't even attempted to find a solution.

2. Jun 9, 2007

### marcusl

You don't state the question!

I'm guessing you need to find a(x) and q. You'd say that the heat entering any infinitesimal slab leaves the other so q=constant. Then integrating gives you a(x) = -q*x/(k*A) + const, so the temperature has a uniform gradient inside.

Apply boundary conditions (you know a(0) and a(30)) to find q and const.

3. Jun 10, 2007

### skimmer

The question is, What is the expression for da/dx and how would the rate of heat transfer be derived?

'Then integrating gives you a(x) = -q*x/(k*A) + const'. Don't mean to sound thick, but what have you integrated here? Fouriers Law?

I have it in my notes that da/dx = -(a1 - a2) / b, where a1 = 500, a2 = 60 and b = 0.03m. I can see the q=constant part, however, in the formula a(x) = -q*x/(k*A) + const, is the k term to be substituted as follows:
a(x) = -q*x/((60 + 0.0006a^2)*A) + const?

I'm sure you have the answer above, I'm just trying to get my head around it all !! Thaks for the help.