Steady state conduction in a hollow sphere

1. Jun 2, 2013

rcummings89

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$\pi$r2 then

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

-q (ro-1 - ri-1) = -4 $\pi$ k (To - Ti)

Substituting in the values, I get q = 4 $\pi$ [(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?