For an assignment, I was given:
Calculate the heat loss per linear ft from $2$ $in$ nominal pipe. ($2.375$ $in$ outside diameter covered with $1$ $in$ of an insulating material having an average thermal conductivity of $0.0375$ $Btu/hrft^oF$. Assume that the inner and outer surface temperatures of the insulation are $380^oF$ and $80^oF$ respectively.
The correct answer is $116$ $Btu/lb^oF$
I used the formula from conduction through pipes:
$${ Q = \frac{\triangle t}{R_{total}} = \frac{\triangle t}{ \frac{ln \frac{r_2}{r_1} }{2 \times \pi \times k \times L} } = \frac{\triangle t}{ \frac{ln \frac{d_2}{d_1} }{2 \times \pi \times k \times L} } }$$
Where:
$${ \triangle t = 380-80= 300^oF }$$ $${ d_2 = 3.375 }$$ $${ d_1 = 2 }$$ $${ k = 0.0375 }$$
And I get close, but not correct. I calculated it to be: $135.090464$ $Btu$
What am I doing wrong?