This article presents an optimal shape design methodology for heat convection problems. In this study, the shape of the convective medium is parameterized by means of non-uniform rational B-spline (NURBS) surfaces, and their control points represent the design variables. The convective domain is discretized by choosing the parameters of NURBS surfaces as generalized curvilinear coordinates, and the conservation equations are 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 shape profile of a natural convective cavity with the objective of reducing the maximum wall temperature.

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