An inverse shape design problem in determining the optimal snowflake-shaped fins

摘要

A three-dimensional shape design problem is considered to determine the optimal snowflake-shaped fins (SSF), based on the minimization of maximum domain temperature of fin. The Levenberg-Marquardt method (LMM) and software package CFD-ACE+ are used as the design tools. The SSF can be obtained by modifying the helm-shaped fins (HSF), the fine surfaces of HSF can be increased by splitting central part of the extended bodies from the center line outward and perforations can therefore be formed. The validity of CFD-ACE+ is first performed to verify the accuracy of the numerical solutions, and two categories of test cases are examined in the present study. The estimated optimal SSF are then compared with the HSF. Results indicate that the optimal SSF can achieve lower maximum fin temperature than HSF since (i) for single IHS problems, the decrease percentages of dimensionless maximum thermal resistance (DMTR) of SSF vary from 0.182% to 11.553% for various fin heights when compared with the values of HSF, and (ii) For multiple IHS problems, the decrease percentages of DMTR can be as large as 14.358% and 17.631% for two and four IHSs, respectively, as convective heat transfer coefficient a = 0.1.