A new minimum volume straight cooling fin taking into account the "length of arc"

The problem of determining the shape of a straight cooling fin of minimum volume without the "length of arc" assumption is addressed. Proceeding from the conventional assumptions of one-dimensionality of the temperature distribution and its linearity for the minimum volume fin we found the profile of the optimum fin to be a circular arc and computed its geometric parameters. The volume of the optimum circular fin found in this paper is 6.21-8 times smaller than the volume of the corresponding Schmidt’s parabolic optimum fin. The optimum circular fin tends to be shorter and to have a larger base height than Schmidt’s fin.