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The numerical optimization techniques coupled with a three-dimensional Navier-Stokes solver have been developed to design an automotive cooling fan. The conjugate gradient method is used to look for the search direction and the golden section method is used for the one dimensional search. Concerning the constraints, exterior penalty functions are employed. In the applications of this numerical optimization technique to the design of an automotive cooling fan, using the object functions defined as an increase in the pressure coefficients and a ratio of production rate of turbulent kinetic energy to the pressure head, the final shapes are obtained after sixth and seventh changes of shape function, respectively.