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.