## Abstract

There is a need for the development of materials for thermal isolation. Heat energy is used in different ways, e.g., for house

warming or production of electricity from solar power plants. However, to use the heat energy efficiently isolating materials

are needed. There are different materials available to isolate houses and heat storage containers. However, those materials are

expensive and some are over engineered. The best available material for thermal isolation would be air that has the thermal

W

coefficient λ air = 0.02446 mK

. Thus, materials that trap a large amount of air are good isolators. On the other hand, some

isolating materials are harmful for the environment, e.g., glass wool, asbestos. An alternative are red clay bricks because

red clay is a natural product that is present everywhere on the planet. But the thermal coefficient of red clay bricks is high

W

λ clay = 0.6 mK

. To reduce the thermal coefficient cavities can be added in the brick. The cavities trap air and reduce the

thermal coefficient of the brick.

We simulate the heat transfer trough a hollow brick. The holes in the brick are cavities. In order to determine the heat

transfer coefficient we solve the heat flux trough the hollow brick. For that a model of the brick is formulated as sequence

of a solid and a fluid part. In the solid part only heat conduction is present and in the fluid heat transfer is present in form of

conduction, convection and radiation. The flow field in the fluid part is modelled with the velocity-vorticity formulation of the

incompressible Navier-Stokes. It is assumed that the Rayleigh number is below 10 6 , hence, natural convective laminar fluid

flow is present in the cavities. The cavities are also heated by heat radiation of the surrounding walls.

The numerical realisation is done with the Boundary-Domain Integral Method (BDIM). To handle suitable geometries

the complexity of the BDIM is reduced from quadratic to logarithmic O(M log M ) or almost linear O(M ) by applying the

H 2 -methodology. M is the number of unknown domain nodes. Numerical studies will be presented.

warming or production of electricity from solar power plants. However, to use the heat energy efficiently isolating materials

are needed. There are different materials available to isolate houses and heat storage containers. However, those materials are

expensive and some are over engineered. The best available material for thermal isolation would be air that has the thermal

W

coefficient λ air = 0.02446 mK

. Thus, materials that trap a large amount of air are good isolators. On the other hand, some

isolating materials are harmful for the environment, e.g., glass wool, asbestos. An alternative are red clay bricks because

red clay is a natural product that is present everywhere on the planet. But the thermal coefficient of red clay bricks is high

W

λ clay = 0.6 mK

. To reduce the thermal coefficient cavities can be added in the brick. The cavities trap air and reduce the

thermal coefficient of the brick.

We simulate the heat transfer trough a hollow brick. The holes in the brick are cavities. In order to determine the heat

transfer coefficient we solve the heat flux trough the hollow brick. For that a model of the brick is formulated as sequence

of a solid and a fluid part. In the solid part only heat conduction is present and in the fluid heat transfer is present in form of

conduction, convection and radiation. The flow field in the fluid part is modelled with the velocity-vorticity formulation of the

incompressible Navier-Stokes. It is assumed that the Rayleigh number is below 10 6 , hence, natural convective laminar fluid

flow is present in the cavities. The cavities are also heated by heat radiation of the surrounding walls.

The numerical realisation is done with the Boundary-Domain Integral Method (BDIM). To handle suitable geometries

the complexity of the BDIM is reduced from quadratic to logarithmic O(M log M ) or almost linear O(M ) by applying the

H 2 -methodology. M is the number of unknown domain nodes. Numerical studies will be presented.

Original language | English |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Proceedings in Applied Mathematics and Mechanics |

Volume | 23 |

Issue number | 2 |

DOIs | |

Publication status | Published - 12 Aug 2023 |

Event | 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2023 - Dresden, Dresden, Germany Duration: 30 May 2023 → 2 Jun 2023 |