How to insulate a pipe?
Published in Journal of Optimization Theory and Applications, 2025
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 and 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 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.
title: “Shape optimization for a heat exchanger with a thin layer” collection: preceedings permalink: /publication/2024-jaca date: 2024-03-01 venue: ‘Monografías matemáticas “García de Galdeano”’ paperurl: ‘https://fcaubet001.perso.univ-pau.fr/Publications/2023%20-%20Shape%20optimization%20for%20heat%20exchangers%20with%20a%20thin%20layer.pdf’ citation: ‘Caubet, F., Conca, C., Dambrine, M., & Zelada, R. (2022). Shape optimization for a heat exchanger with a thin layer. In Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications (Vol. 43, pp. 51-61).’
Recommended citation: F. Caubet, C. Conca, M. Dambrine, and R. Zelada. How to Insulate a Pipe? J. Optim. Theory Appl., 207(3):46, 2025.
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