Annular fin

Adding an annular fin to an object increases the amount of surface area in contact with the surrounding fluid, which increases the convective heat transfer between the object and surrounding fluid.

Because surface area increases as length from the object increases, an annular fin transfers more heat than a similar pin fin at any given length.

To derive the governing equation of an annular fin, certain assumptions must be made.

The fin must have constant thermal conductivity and other material properties, there must be no internal heat generation, there must be only one-dimensional conduction, and the fin must be at steady state.

Applying the energy conservation principle to a differential element between radii r and r + Δr yields where the first two terms are heat transferred through conduction, while the third is heat lost due to convection with the surrounding fluid.