I was reading the below document on heat exchangers and noticed that when people define their overall heat transfer coefficient, they use the outer diameter of the inner pipe.
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node131.html
An illustration is shown below (taken from the above link)
The equation in question is shown below:
So here's what I know:
- D refers to the outer diameter of the inner pipe (r2*2)
- L refers to the length of your pipe
- $h_o$ is the overall heat transfer coeffcient
- $deltaT_{lm}$ refers to the log-mean temperature difference
- We need the log mean temperature difference because we are dealing with cylindrical coordinates (similar to normal temperature difference for Cartesian coordinates). Derivation is in the article
- We are defining an overall heat transfer coefficient as we see fit and people just happen to use the outer surface area of the inner pipe for the area when defining the overall heat transfer coefficient
Here's what I don't know:
- Why would people choose to use the outer area of the inner pipe instead of the inner area of the inner pipe? Heat travels from hot to cold (talking about net travel here. I am aware that random molecular collisions are what transfer heat excluding radiation), so wouldn't it make sense to use the inner pipe inner area for ho since the inner area is the first spatial limiting factor for heat transfer? This is where the hot fluid is on the inside and the cold is on the outside.