Radial Heat Conduction through a Cylindrical Pipe

AI Thread Summary
The discussion focuses on calculating the heat transfer rate through a cylindrical PVC pipe using Fourier's Law of Conduction. The user has derived the formula for heat transfer rate (Q) but is unsure about the units for Q and how to proceed with the calculation. Participants clarify that the units can be deduced by analyzing the algebraic variables in the expression. Additionally, they note that more information is needed to determine the decrease in inner temperature after one minute. The conversation emphasizes understanding unit cancellation to clarify the calculation process.
Thisbe Schwer
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Homework Statement


A 1.75m long PVC pipe with a thermal conductivity of 0.19 W/mK has an internal diameter of 3mm and an external diameter of 5.5mm. Inner temperature is 298K and outer temperature is 273K. Calculate the heat transfer rate through the pipe and thus the decrease in the inner temperature after one minute.

Homework Equations


Fourier's Law of Conduction: Q = -kA(dT/dr)
Surface area of cylinder: A = 2πrL

The Attempt at a Solution


I've got the formula Q = [k2πL(Ti - To)] / [In(r2/r1)] and substituted in the values:
Q = [0.19W/mK * 2π * 1.75m * 25K] / [In(1.8333)]
Q = 16.625/0.6061...
Q = 27.428 (3dp)
But I'm a complete newbie to this kind of calculation, and I'm not sure what the unit for Q is? So I'm kind of stuck at this part of the question and not sure where to go from here.
Sorry for the silly question, but any help would really be appreciated![/B]
 
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Thisbe Schwer said:
not sure what the unit for Q is
You can deduce it by treating the units in your expression (K, m, W) as algebraic variables and cancelling as appropriate.
Thisbe Schwer said:
thus the decrease in the inner temperature after one minute.
You need more information to compute this, such as what is in the pipe.
 
So would the units for Q be W/m?
 
Thisbe Schwer said:
So would the units for Q be W/m?
You had
Thisbe Schwer said:
0.19W/mK * 2π * 1.75m * 25K
Leaving out everything except the units:
(W/mK) * m * K. What does that reduce to?
 
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