Investigation of the heat transfer coefficient for a red clay brick

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
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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
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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.