Minimum Volume of the Longitudinal Fin with Rectangular and Triangular Profiles by a Modified Newton–Raphson Method

Abstract

The minimum volume of the nonlinear longitudinal fin with rectangular and triangular profiles by using the modified Newton–Raphson method is presented in this paper. The dimension of the fin profile is regarded as the optimization variable. Furthermore, a mechanism called “volume updating” is added into the modified Newton–Raphson algorithm to obtain the minimum volume of the fin. Two examples are illustrated to demonstrate the proposed method. The obtained results showed that the proposed method can be used efficiently and accurately in finding the minimum volume of the nonlinear longitudinal fin problem with rectangular and triangle profiles.