Radial Heat Conduction through a Cylindrical Pipe

[Thisbe Schwer]

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]

 

[haruspex]

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.

thus the decrease in the inner temperature after one minute.

You need more information to compute this, such as what is in the pipe.

 

[Thisbe Schwer]

So would the units for Q be W/m?

 

[haruspex]

So would the units for Q be W/m?

You had

0.19W/mK * 2π * 1.75m * 25K

Leaving out everything except the units:
(W/mK) * m * K. What does that reduce to?