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

AI Thread Summary
The discussion focuses on determining the heat transfer rate by convection from a circular fin with uniform cross-section, where both ends are attached to surfaces. The user has derived an equation that varies with position along the fin but is uncertain about its validity. They seek a general equation that can represent the overall heat transfer rate from the fin's surface. The conversation highlights the need for clarity on whether convection heat transfer can be effectively modeled along the fin. Additional insights or findings on this topic are requested to help progress the discussion.
kp3legend
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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.
 
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