Piping Heat Loss: Solving for Internal Temperature

[cpscdave]

So I'm trying to figure out where a heat tracing program is getting some numbers.

What I'm trying to figure out is how the program calculates the internal temperature of the tracing lines.

What I know is the k value of the insulation 0.0215 watts per metre*degree
I know the temperature that the program says the cable will be at, and how much heat the cables are providing in watts/ft

using the pipe heat loss formula $$Q = 2*\pi*k*(t_o - t_i)/ln(r_o/r_i)$$ and solving for $$t_o$$ I got an answer that was wrong. I had converted watts/ft into watts/meter by multiplying by 3.2 (as there are 3.2 feet per meter)
As the numbers didn't work out I ran the same formula instead converting k into watt per foot. This is where things got odd, I found that again I got the wrong answer but the ratio of how much the answers were off were different. Same formula same number but different units should produce the same relative error.

Figuring it had to be a unit conversion error, I found that if I instead multiplied watts/ft by 3.2*3.2 (and similar conversion for changing k to be w/ft) not only did the 2 answer agree but I got the correct $$t_i$$

So my question is: While it makes sense to me that the foot to meter conversion should be squared as we are looking at an area not a linear distance, the formula doesn't seem to support those units. So is the squared conversion correct? or has this just been an odd coincidence :)

 

[cpscdave]

Talking with some of the process engineers I gather that Q is actually m^2 which explains everything :)