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.
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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