Shape optimization with Ventcel transmission conditions: application to the design of a heat exchanger
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This paper aims to optimize the shape of a fluid-to-fluid heat exchanger in order to maximize heat exchange under constraints of energy dissipation and volume. The novelty consists in taking into account the thin layer separating the two fluids by using Ventcel-type second-order transmission conditions. The physical model is then a weakly coupled problem between the steady-state Navier-Stokes equations for the dynamics of the two fluids dynamics and the convection-diffusion equation for the heat. We provide a shape sensitivity analysis and characterize the shape derivatives involved. Finally, we demonstrate the feasibility and effectiveness of the proposed method through 3D numerical simulations.
Recommended citation: Fabien Caubet, Carlos Conca, Marc Dambrine, Rodrigo Zelada. Shape optimization with Ventcel transmission conditions: application to the design of a heat exchanger. 2025. (hal-05033794)
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