Adjoint-based shape optimization of fin geometry for heat transfer enhancement in solidification problem

In the present study, an adjoint-based shape-optimization method is formulated for heat transfer enhancement in liquid-solid phase change problems, in which heat conduction is dominant. In the present shape-optimization scheme, extended heat transfer surfaces with constant wall temperature are allowed to deform based on variational information of a cost functional, which is obtained from the physical temperature and adjoint enthalpy fields. In the computation of the developed scheme with an enthalpy-based formulation, a meshless local Petrov-Galerkin (MLPG) method is implemented for dealing with the complex boundary shape. For high-resolution analyses, a bubble-mesh method for boundary-fitted node arrangement in a well-controlled manner is employed, combined with a high-efficiency searching algorithm for choosing the neighboring bubbles interacted with each other. In the shape evolution process for different initial fin shapes, it is demonstrated that, within a certain range of the initial state, the present shape-optimization scheme leads to tree-like fin shapes that achieve the temperature field with global similarity.