The aim of this paper is to determine the shape of a xed-bed reactor which maximizes the conversion rate under the constraints of process model equations (i.e. continuity, Navier-Stokes, and mass balance equations), energy dissipation, iso-volume, and manufacturing. Incompressible uid, laminar ow regime and steady-state conditions in the reactor are the main assumptions taken into account. The optimization method developed is based on the adjoint system method and OpenFOAM framework is used as CFD solver to compute the state vector and its adjoint variables introduced by the optimization approach. The algorithm developed is then tested on two dierent cases, a reactor where a rst order homogeneous reaction takes place and another one involving a surface reaction. The optimization results show a signicant improvement of the conversion rate by 2.7% in the rst case, and by 16% in the second one. Finally, initial and optimal shapes are manufactured using a 3D printing technique.

The main goal of the current study is to propose a model for determining the cutting forces taking into account the complex kinematics of the hobbing process. This model is based on one hand on the CAD geometrical simulations of undeformed chip generated by hobbing process and on the other hand on a mechanistic model. In this mechanistic approach, the specific force coefficients have been obtained from a 2D numerical model. As a result of this investigation, the evolution of cutting forces was used to analyze the effect of the cutting parameters on the machinability of the machined material.

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