Is there a general equation for convection of a fin's side surface

[kp3legend]

I'm wondering with the circular fin, with uniform cross section area with given length and diameter. both ends are attached to surfaces. is there a general equation to find the heat rate by convection of the fin side surface. I tried to relate all the conditions and ended up with a equation that varies with position x along the fin. But I don't know if its a right way or not. Can heat transfer by convection along the fins be presented by a function which will gives the overall heat transfer rate.
thank you for your time.
i know this is wordy but i really need you help so i can move on with the next stuffs.

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?