Let's say there is a fin that is 1mm thick, extends 8mm from the surface, and is 10 mm wide. The fin is exposed to a moving fluid. Can we assume the adiabatic tip condition and use the characteristic, "Corrected", length for calculations?
The error due to assuming the tip is adiabatic is approximately given by the area ratio of the tip to the total surface area of the fin. That is, $error = 8 mm^2 / 160 mm^2 $.