A three-dimensional shape design problem in determining the boundary geometry to yield isotherms

A three-dimensional shape design problem is studied in this work. The objective is to estimate the optimal boundary geometry of a conductive body for producing boundary isotherms and the technology can be utilized in designing the shape of heating probe for thermostatic bath. The combination of CFD-ACE + package and Levenberg-Marquardt method (LMM) are used to build the optimization algorithm for the present shape design problem. The general as well as axially symmetric type of boundary geometries are both considered in this work and the validity of the design algorithm is verified through numerical experiments. Results show that the desired boundary temperatures can be assigned arbitrarily and the corresponding optimal boundary surfaces can be estimated with reasonable iteration numbers when constraint of domain volume is not considered. When the constraint of domain volume is considered, the optimal boundary surfaces can be obtained with very few iteration numbers.