How Does Fourier's Law Apply to Heat Transfer Through a Wall?

[skimmer]

Homework Statement

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

Homework Equations

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

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.

 

[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.

 

[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.