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Steady state conduction in a hollow sphere

  1. Jun 2, 2013 #1
    Hello,

    I'm having trouble with a conduction problem, I have access to the answer but not the solution. I did it on my own and my value is half of what the answer is. Now, my calculus is a little rusty, but I don't know where I am going wrong. So the dimensions and temperatures of the sphere are:

    ri=0.01 m
    ro=0.02 m
    Ti=70 oC
    To=100 oC
    k=0.58 W/m K

    Attempt:

    q/A = -k dT/dr

    q/A dr = -k dT

    Where A = 4[itex]\pi[/itex]r2 then

    q ∫ dr/r2 evaluated from ri to ro = -4 [itex]\pi[/itex] k ∫ dT from Ti to To yields...

    -q (ro-1 - ri-1) = -4 [itex]\pi[/itex] k (To - Ti)

    Substituting in the values, I get q = 4 [itex]\pi[/itex] [(0.58)(100-70)](0.02-0.01) = 2.18 W

    The actual answer is double that and negative, -4.37 W. Any idea what I'm doing wrong?

    Thanks in advance!
     
  2. jcsd
  3. Jun 2, 2013 #2
    Your algebraic solution is correct, but you substituted into it incorrectly. The problem is with the ro and ri. You should have (1/ri-1/ro) in the denominator.
     
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