- #1
rcummings89
- 19
- 0
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!
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!