Shape Optimization of Two-Dimensional Thermal Conducting Solid Using Boundary Integral Equation Formulation

Abstract

A method for shape design sensitivity analysis of two-dimensional thermal conducting solid is presented using the material derivative concept and the adjoint variable method. A general thermal boundary condition with heat convection is considered in addition to prescribed temperature and heat flux. The method for deriving the sensitivity formula is based on standard direct boundary integral equation formulation. The sensitivity of a general functional depending on temperature and heat flux is considered. The method is then applied to obtain the sensitivity analysis is demonstrated by a hollow cylinder problem with exact solution. A weight minimization problem of a thermal diffuser is considered as a practical application. The sensitivity by the presented method is compared with that by finite differences and an optimal shape is found by use of an optimization routine.