1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Heat Current in a Sphere

  1. Sep 22, 2016 #1

    TheDemx27

    User Avatar
    Gold Member

    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. jcsd
  3. Sep 22, 2016 #2

    TheDemx27

    User Avatar
    Gold Member

    Oh I think I got it. It is just a separable differential equation, right?
     
  4. Sep 22, 2016 #3

    Bystander

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Hint: "Maxwell."
     
  5. Sep 22, 2016 #4

    TheDemx27

    User Avatar
    Gold Member

    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
  6. Sep 22, 2016 #5

    Bystander

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

  7. Sep 22, 2016 #6
    This result is right on target, and is the way I would have solved the problem too. Nice job.
     
  8. Sep 22, 2016 #7

    TheDemx27

    User Avatar
    Gold Member

    Thanks for checking me.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Heat Current in a Sphere
Loading...