High performance thermal insulation materials for buildings - Nanotechnology in Eco-efficient Construction - page 187

insulators are generally defi ned as an insulator with a thermal conductivity
below 0.02 W/(mK). Similarly to the distinction in traditional thermal insula-
tors, current high performance thermal insulators are distinguished by how
they achieve rarefaction of the gas, i.e., by a nanoporous solid structure, or
by application of a partial vacuum, whereas the best results are achieved with
a combination of both. The exploitation of the divergent physical theory of
heat transfer in nanoporous materials is the reason why nanotechnology has
produced a breakthrough in thermal insulators the last decade, as summa-
rized in Fig. 9.1.

9.2 Heat transfer in thermal insulators

9.2.1 Macroscopic heat transfer

The macroscopic heat transfer in a material is described by Fourier's law
relating the energy fl ux ø to the temperature gradient by its thermal con-
ductivity k as

ø =− ∇ kT [9.1]

The effective heat transfer ø for a porous insulator is a combination of four
heat transfer mechanisms and can be approximated by their sum

( )

øø =++++ ø ø ø ø [9.2]

cd s , rd cd g , cv k

where φ cd,s denotes heat conduction of the solid skeleton, φ rd heat transfer

by longwave radiation, φ cd,g heat conduction of encapsulated gas molecules

and φ k describing

possible reciprocity between the different processes is generally neglected.
Traditional thermal isolators use the inherently low conductivity k cd,g of a
gas at standard temperature and pressure to achieve a low overall heat
transfer. Convection in the gaseous material is avoided by reducing the pore
sizes, and the impact of solid conduction

φ cv heat transfer by gas convection. The coupling term

￿ ￿ ￿ ￿ ￿ ￿

φ cd,s is reduced by means of a high

porosity.

9.2.2 Rarefi ed gas regimes in current HPTIs
The traditional Fourier law is no longer valid if the materials characteristic
time scale

θ or length scale Λ has the same order of size as the natural time

or length scale l of the physical problem, meaning that the physical
process of heat transfer occurs at the same scale as the scale at which the
basic solid properties of the materials are defi ned. Recent progress in the
development of high performance insulators is based on this principle for
the gaseous component

scale τ

φ cd,g of the overall heat transfer. Here, the natural
time or length scale denotes the distance traveled or time between two