A new minimum volume straight cooling fin taking into account the “length of arc”. (English) Zbl 1137.49314
The authors consider the problem of determining the shape of a straight cooling fin of minimum volume without the usual “length of arc” assumption. They keep the conventional assumption of one-dimensionality of the temperature distribution and its linearity for the minimum volume fin. The main result is that the profile of the minimum volume fin is a circular arc. The geometric parameters of the profile are computed. Comparisons with Schmidt’s parabolic optimum fin are also carried on.
Reviewer: Luigi de Pascale (Pisa)
MSC:
49Q10 | Optimization of shapes other than minimal surfaces |
49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
74P99 | Optimization problems in solid mechanics |