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In the recent years, adjoint optimization has gained popularity in the automotive industry with its growing applications. Since its inclusion in the mainstream commercial CFD solvers and its continuously added capabilities over the years, its productive usage became readily available to many engineers who were previously limited to interfacing the customized adjoint source code with CFD solvers. The purpose of this work is to demonstrate using an adjoint solver a method to optimize duct shape that meets multiple design objectives simultaneously. To overcome one of the biggest challenges in the duct design, i.e. the severe packaging constraints, the method here uses geometrically constrained adjoint to ensure that the optimum shape always fits into the user-defined packaging space. In this work, adjoint solver and surface sensitivity calculations are used to develop the optimization method.