Basics and Some Theory of AnTherm
Conductance
An exact description of the thermal behaviour of a building assembly would by
nature be nonlinear, and thus very complicated to evaluate. Fortunately, for
most construction situations of interest, it is possible to drastically reduce
the complexity of the physical model without sacrificing any appreciable
accuracy.
A linear description of thermal transmission involving an entire building can
be introduced by
 assuming that the temperature of each environment (space) associated
with the building is unique, i.e. independent of position, and
 forfeiting an exact treatment of radiation exchange within the
spaces in favour of an approximation of this factor through adjusted surface
transfer coefficients.
thermal conductance,
L^{3D}
[W/K] 
In light of this simplified physical model, it can be
stated that the amount of heat which flows from one space to another, Q,
is proportional to the temperature difference between the two environments
under consideration (i and j). The factor of proportionality
is a conductance , L_{ij}, and linearly defined by
Q = L_{ij} • ( T_{i} − T_{j })

conductance matrix 
The analogy of an electrical circuit can be extended to
model a building structure more generally as a set of environments thermally
connected through a resistance, i.e. the heatconducting material elements.
A complete description of the thermal relationships in a particular
structure is given by a conductance matrix of values for all thermal
connections, i • j, between the spaces of the model.
The conductance matrix defines the heat transfer characteristics of a
given model based solely on the geometry and materials (thermal properties)
of the resistance, that is, independently of temperature conditions in
adjacent spaces. This matrix is symmetrical.

thermal transmittance,
Uvalue,
L^{1D}
[W/m^{2}K] 
The arearelated term "thermal transmittance" (Uvalue
in Wm^{2}K^{1}) commonly used in standards to date
essentially describes the same conductance as the reciprocal of the sum of
resistances of a planar component, that is, resistances in "series":
1/U = R = R_{si} + ΣR_{j} + 1/α_{se} = 1/α_{si} + ΣR_{j} + 1/α_{se}
whereby α_{si} and α_{se} are the
surface transfer coefficients of the interior and exterior environments, and
ΣR_{j} represents the sum of material resistances of j constituent
component layers. The resistance of an individual homogeneous (isotropic)
layer is directly proportional to layer thickness, d, and indirectly
proportional to the material conductivity, λ:
R_{j} = d/λ However, this simple formula applies only to
the planar regions of a building assembly in which strictly onedimensional
heat flow can be reasonably assumed.

lengthrelated conductance,
L^{2D}
[W/mK] 
A further type of special situation is given where
twodimensional heat flow patterns are to be expected. Such a region is a
stretch of the building assembly which can be evaluated with respect to a
twodimensional section  under the assumption that no heat flow occurs
normal to the section plane. In this case, a lengthrelated conductance,
L^{2D} [Wm^{1}K^{1}], must be calculated for
the applicable region.
The most general case, of course, is that of
threedimensional heat flow. For the regions of a construction in which no
directional assumptions can be made about local heat flow patterns, only the
evaluation of the (3D) conductance, L^{3D} [WK^{1}],
provides a reliable indicator of the thermal behaviour.

total conductance 
Due to the linearity of conductances, an entire building
can be modelled as a sum of parts, with each part evaluated according to the
applicable geometric conditions. Of course, the summation of conductances is
only applicable if the temperature difference is the same through all model
parts (e.g. one interior and one exterior temperature valid for the whole
building). The model is subdivided by introducing theoretical cutoff
planes, which must be located such that any potential heat flow through
these planes can be considered negligible.
The total thermal conductance of a building thus modelled can be
written as
whereby l_{j} is the length over which the twodimensional
conductance, L^{2D}, is valid for part j, and A_{k}
is the area of validity for U_{k}.
This reliable and flexible approach to analysing the thermal performance
of buildings is referred to in the Standards as the direct
method. It requires the implementation of a suitable computer program
for attaining two and threedimensional conductance results with the
necessary precision
The program AnTherm makes use of the linear nature of the heat
conduction model by first determining a generally applicable calculation
model: a characteristic set of temperatureindependent base solutions
(see also "Method of Analysis"). 
See also: Linear and Point Transmittance,
The building envelope as thermal heat
bridge, Theoretical
background
