Basics and Some Theory of AnTherm
Linear and Point Thermal Transmittance
Often thermal bridges will be described in terms of linear and point thermal
transmittances characteristic to building components analysed.
linear thermal transmittance, Ψ
[W/mK]
Psi 
heat flow rate in the steady state divided by length and by
the temperature difference between the environments on either side of a
thermal bridge (definition in ISO 10211)
NOTE The linear thermal transmittance is used as a correction term for
the linear influence of a thermal bridge.The linear thermal
transmittance is given by:
where:
Ψ 

is the linear thermal transmittance Psi of the linear thermal bridge
separating the two environments being considered; 
L^{2D} 

is the thermal coupling coefficient obtained from a
2D calculation of the component separating the two environments being
considered; 
U_{j} 

is the thermal transmittance of the 1D component j
separating the two environments being considered; 
b_{j} 

is the length within the 2D geometrical model over which the
value U_{j} applies 
J 

is the number of 1D components. 
Note: When determining the linear thermal transmittance, it is necessary to
state which dimensions (e.g. internal or external) are being used because
for several types of thermal bridges the value of the linear thermal
transmittance depends on this choice. 
point thermal transmittance,
χ
[W/K]
chi 
heat flow rate in the steady state divided by the
temperature difference between the environments on either side of a thermal
bridge (definition in ISO 10211)
NOTE The point thermal transmittance is used as a correction term for the
influence of a point thermal bridge.The point thermal
transmittance is given by:
where:
χ 

is the point thermal transmittance Chi of the point thermal bridge
separating the two environments being considered; 
L^{3D} 

is the thermal coupling coefficient obtained from a
3D calculation of the 3D component separating the two environments
being considered; 
U_{j} 

is the thermal transmittance of the 1D component j
separating the two environments being considered; 
A_{j} 

is the area over which the value U_{j}
applies; 
Ψ_{j} 

are respective linear thermal transmittances (see
above); 
l_{j} 

is the length over which the value Ψ_{j}
applies; 
J 

is the number of 2D components. 
I 

is the number of 1D components. 
Note: When determining Ψ and
χ values, it is necessary to state
which dimensions (e.g. internal or external) are being used because for
several types of thermal bridges the Ψ
and
χ values depend on this choice..
Rewriting the above equation by replacing the linear thermal transmittance
by its definition, provides following alternative means of calculating the
point thermal transmittance:

An alternative expression for the total coupling coefficient L_{i,j}
which uses the linear and point thermal transmittances, Ψ
and
χ , is then given by
where:
U_{k(i,j)} 

is the thermal transmittance of part k of the room or
building; 
A_{k} 

is the area over which the value U_{k(i,j)}
applies; 
Ψ_{m(i,j)} 

is the linear thermal transmittance Psi of part m of the room
or building; 
l_{m} 

is the length over which the value Ψ_{m(i,j)}
applies; 
χ_{n(i,j)} 

is the point thermal transmittance
Chi of
part n of the room or building; 
K 

is the number of thermal
transmittances. 
M 

is the number of linear thermal transmittances; 
N 

is the number of point thermal transmittances; 
Note: In above formula ΣA_{k}
is equal to the total surface area of the envelope. Note: L_{i,j}
is equivalent to the heat transfer coefficient, H often used in other
standards. See also: Conductance ,
On calculation of Ψvalues for building
constructions in connection with ground,
Theoretical background 