Optimization of the insulation domain for heat transfer in building walls

Karashbayeva Z. Gasparin S. Berger J.
April 2025 Springer Science and Business Media Deutschland GmbH

Journal of the Brazilian Society of Mechanical Sciences and Engineering
2025 #47 Issue 4

The objective of this paper is to minimize the energy consumption of a building wall by finding the optimal locations of the insulation elementary blocks. The direct problem considers a 2D steady state heat transfer equation. A density (in the mathematical sense) function is introduced to represent the thermal properties of the wall, i.e., insulation blocks and load bearing materials. On the outside boundary surface, the convection and incident short-wave radiation flux vary with space. The objective function is defined as the total heat flux on the inside part of the wall. It is optimized respecting the constraint of proportion insulation/load bearing material given by standard wall configurations. The optimal locations of the insulation material blocks are retrieved using an exchange algorithm. It ensures to find a local minimum solution with a reduced computational effort. Finally, a case study located in Paris investigates the thermal design optimization. Results show the efficiency of the numerical strategy. On the top of that, the aim of the study is reached by obtaining an improved energy efficient wall with optimized insulation locations.

Building energy efficiency , Parameter estimation problem , Thermal design problem , Topology optimization , Two-dimensional heat transfer

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Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE), UMR 7356 CNRS, La Rochelle Université, La Rochelle, 17000, France
Astana IT University, Astana, 010000, Kazakhstan
CEREMA, French Ministry of Ecological Transition, BPE Research Team, Nantes, F-44000, France

Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE)
Astana IT University
CEREMA

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