Optimization of Fin with Rectangular and Triangular Shapes by Levenberg – Marquardt Method

The article proposes using the Levenberg – Marquardt (L – M) method to optimize the fin with the longitudinal profile. The objective in optimizing the fin shape: The fin volume achieved the minimum value, with the optimization variables being the fin's width and length. The research performed two problems about optimal design the fin with the straight profile for triangular and rectangular shapes, obtained a tiny relative error compared to the results of the published studies. Specifically, the problem with the triangular-shaped fin, the relative error of the minimum volume compared to the two published is 0.022% & 0.092%; and the problem with the rectangular-shaped fin, the relative error is 0.68% & approximately 0%, respectively.