Shape design for heat conduction problems using curvilinear grid generation, conjugate gradient, and redistribution methods

This study is concerned with the application of an approach combining the curvilinear grid generation and conjugate gradient (CG) methods for shape design of heat conduction problems. Shape design for a conductive medium that contains a heating object and features an isothermal outer surface is investigated. Several practical cases with multiply-connected domains associated with various imbedded heating objects and thermal boundary conditions are studied to demonstrate the performance of the approach. Optimal shape profiles that meet different heat transfer requirements are obtained. Meanwhile, a redistribution method is proposed to numerically regularize the ill-ordered grids, which are commonly found during the iterative optimization process. By using the redistribution method, the locations of the nodal points at the outer surface may be adjusted automatically once the ill-ordered grid patterns are detected, so that the convergence of the optimization process can be facilitated.