Optimal Shape Design for Heat Conduction Problems Using NURBS

This article presents an optimal shape design methodology for heat conduction problems. In this study, the shape of the conductive medium is parameterized by means of non-uniform rational B-spline (NURBS) surfaces, and their control points represent the design variables. The conductive domain is discretized by choosing the parameters of NURBS surfaces as generalized curvilinear coordinates, and the heat conduction equation is solved using the finite difference method. The simplified conjugate-gradient method (SCGM) is used as the optimization method to obtain the optimal shape and adjust the design variables intelligently. The methodology is demonstrated by optimizing the profile of a straight fin with the objective of enhancing heat transfer rate and reducing the fin mass.