How Can I Calculate the Outside Temperature of a Heated Pipe?

[bill nye scienceguy!]

I want to calculate the temperature on the outside of a pipe which has a heated fluid flowing through it. If I know the temperature of the fluid and the ambient temperature, as well as all the material properties such as thermal conductivity and convective heat transfer coefficient, is there a way I can do this?

All the examples I've been looking at assume you know the temperature on the outside of the pipe and are being used to calculate intermediate temperatures, i.e., at a pipe/insulation interface.

 

[Dadface]

For an unlagged pipe there will be a non uniform temperature gradient along its length in other words the temperature falls towards the pipe outlet.Perhaps you could use dQ/dt equals kAdT/dl for when thermal equilibrium is reached.

 

[henxan]

This question is very interesting. I have been wondering about this, or a very simiilar scenario.

Ive been thinking of the general enthusiasm concerning ground heat. So I wanted to understand how much energy transfer one can expect in the ideal case.

Looking at the case with a axial symmetry I was only able to find one formula, developed by Ingersoll:

q = L (T_1 - T_2) * k

Where L is the length of line which is kept at T_2, situated in the ground, with heat T_1.. k is thermal conductivity.

This would mean that if a ground heat line is 100m, kept at 1*C, and T_1 is 11*C of a marble "infinite" reservoir with k=2w/mK, the q would be 2000Watts..

But this doesn't make any sense. So I also would like to see any further explanation.