How to Insulate a Pipe?

Fabien Caubet (), Carlos Conca (), Marc Dambrine () and Rodrigo Zelada ()
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Fabien Caubet: Université de Pau et des Pays de l’Adour E2S UPPA, CNRS, LMAP, UMR 5142
Carlos Conca: University of Chile
Marc Dambrine: Université de Pau et des Pays de l’Adour E2S UPPA, CNRS, LMAP, UMR 5142
Rodrigo Zelada: Université de Pau et des Pays de l’Adour E2S UPPA, CNRS, LMAP, UMR 5142

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 6, 41 pages

Abstract: Abstract This paper focuses on the problem of finding the optimal distribution of a thermal insulator around a pipe. We consider the framework of one fluid inside a pipe of thin width which is surrounded by a thermal insulator. We use an asymptotic model to avoid dealing with the thin layer, leading to non-standard transmission conditions which involve discontinuities at the interface and second order tangential derivatives. We thus consider the shape optimization problem that aims to minimize the heat flux outside an insulator with a given volume. Then we characterize the shape derivative of the objective functional and perform 3D numerical simulations using the level set evolution method.

Keywords: Shape optimization; Asymptotic model; Ventcel conditions; Transmission conditions; Navier-Stokes equations; Thermal insulation; 49Q10; 35Q79; 80M50; 76D55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02782-6

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