# Heat Current in a Sphere

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1. Sep 22, 2016

### TheDemx27

1. The problem statement, all variables and given/known data
A spherical shell has inner and outer radii r_a and r_b, respectively, and the temperatures at the inner and outer surfaces are T_a and T_b. The thermal conductivity of he shell material is k. Derive an equation for the total heat current thought the shell in the steady state. Then calculate the temperature as a function of r, the distance from the center of the shell.

2. Relevant equations
H=-kA(T_b-T_a)/(r_b-r_a)

3. The attempt at a solution
I know that I'm supposed to use calculus somehow, I write the area A as a function of r, A(r)=4pi*r^2. I don't know what to do from there

2. Sep 22, 2016

### TheDemx27

Oh I think I got it. It is just a separable differential equation, right?

3. Sep 22, 2016

### Bystander

Hint: "Maxwell."

4. Sep 22, 2016

### TheDemx27

That does nothing for me. I was only ever taught the derived forms of maxwell's equations...

Treating it as a separable differential equation H=-kA*(dT/dr) I got
H=k*4pi*(T_b-T_a)/(1/r_b-1/r_a)

Last edited: Sep 22, 2016
5. Sep 22, 2016

### Bystander

6. Sep 22, 2016

### Staff: Mentor

This result is right on target, and is the way I would have solved the problem too. Nice job.

7. Sep 22, 2016

### TheDemx27

Thanks for checking me.