TP-05: Fabric Heat Loss | HEM Reference

Overview

Fabric heat loss quantifies the rate of heat transfer through the thermal envelope of a dwelling — walls, roofs, floors, windows, and doors. Each building element contributes a heat loss coefficient in W/K, which represents the steady-state heat flow per degree of temperature difference between inside and outside.

The calculation follows BS EN ISO 52016-1:2017 for the element-level methodology and BS EN ISO 13789:2017 for surface heat transfer coefficients. Ground floor heat loss uses the periodic method from BS EN ISO 13370:2017.

Inputs

Parameter	Symbol	Unit	Description
Element area	$A$	m²	Gross area of the building element
Pitch	—	degrees	Tilt from horizontal (0° = ceiling, 90° = wall, 180° = floor)
Thermal resistance of construction	$R_{c}$	m²K/W	Total resistance of the material layers
U-value	$U$	W/(m²K)	Overall thermal transmittance (pre-calculated for ground floors)
Areal heat capacity	$κ_{m}$	J/(m²K)	Thermal mass per unit area
Mass distribution class	—	—	One of: I, E, IE, D, M
Solar transmittance	$g$	—	Total solar energy transmittance of glazing
Frame factor	$F_{f}$	—	Ratio of frame area to total window area
Linear thermal transmittance	$ψ$	W/(mK)	Thermal bridge coefficient
Thermal bridge length	$L$	m	Length of the linear thermal bridge

Calculation

Surface Resistances

Each building element has an external and internal surface resistance that accounts for convective and radiative heat transfer at the surfaces.

External Surface Resistance

The external surface resistance is a constant:

$R_{se} = \frac{1}{h _{ce} + h _{r e}}$

where:

$h_{ce} = 20.0 W/(m²K)$ — external convective heat transfer coefficient
$h_{r e} = 4.14 W/(m²K)$ — external radiative heat transfer coefficient

giving $R_{se} = 0.0414 m²K/W$ .

Internal Surface Resistance

The internal surface resistance depends on the direction of heat flow, which is determined by the element's pitch:

$R_{s i} = \frac{1}{h _{c i} + h _{r i}}$

where $h_{r i} = 5.13 W/(m²K)$ (from BS EN ISO 13789:2017, Table 8) and the internal convective coefficient $h_{c i}$ varies with heat flow direction:

Pitch range	Heat flow direction	$h_{c i}$ (W/(m²K))	$R_{s i}$ (m²K/W)
< 60°	Upwards	5.0	0.0987
60°–120°	Horizontal	2.5	0.1310
> 120°	Downwards	0.7	0.1716

Element Fabric Heat Loss

The fabric heat loss for each element type is calculated as follows.

Opaque Elements (Walls, Roofs)

$H_{e l} = A \times U$

where the U-value is derived from the construction resistance and surface resistances:

$U = \frac{1}{R _{c} + R _{se} + R _{s i}}$

Transparent Elements (Windows, Doors)

For glazed elements, an additional resistance for window treatments (curtains) is included per SAP10.2:

$U = \frac{1}{R _{c} + R _{se} + R _{s i} + r _{c u r t ain s}}$

where $r_{c u r t ain s} = 0.04 m²K/W$ .

The fabric heat loss is then:

$H_{e l} = A \times U$

Ground Floor Elements

Ground floor U-values are pre-calculated using the periodic heat transfer method from BS EN ISO 13370:2017, which accounts for floor type, perimeter, edge insulation, and wall-floor junction thermal bridging:

$H_{e l} = A \times U_{g r o u n d}$

The ground floor model uses a 3+2 node representation with separate ground and floor thermal resistances ( $r_{g r}$ and $r_{f l oor}$ ), giving inter-node conductances:

$h_{pl i, 0} = \frac{2}{r _{g r}}, h_{pl i, 1} = \frac{1}{\frac{r _{f l oor}}{4} + \frac{r _{g r}}{2}}, h_{pl i, 2} = \frac{2}{r _{f l oor}}, h_{pl i, 3} = \frac{4}{r _{f l oor}}$

Adjacent Zone Elements

Adjacent conditioned space (ZTC): $H_{e l} = 0$ — no heat loss to another conditioned zone.
Adjacent unconditioned space (ZTU): $H_{e l} = A \times U$ — standard calculation; the additional thermal resistance of the unconditioned space is incorporated in the external conditions (see TP-03).

Total Zone Fabric Heat Loss

The total fabric heat loss for a zone is the sum of all element contributions:

$H_{T, f ab r i c} = \sum_{i = 1}^{n} H_{e l, i} [W/K]$

Thermal Bridges

Thermal bridges — junctions between building elements where the insulation layer is interrupted — are modelled separately and added to the zone heat balance.

Linear Thermal Bridges

$H_{ψ} = ψ \times L$

where $ψ$ is the linear thermal transmittance W/(mK) and $L$ is the length of the junction m.

Point Thermal Bridges

$H_{χ} = χ [W/K]$

Total Thermal Bridge Heat Loss

$H_{t b} = \sum_{j = 1}^{m} H_{ψ, j} + \sum_{k = 1}^{p} H_{χ, k} [W/K]$

The thermal bridge heat loss coefficient $H_{t b}$ enters the zone air node equation directly, contributing heat loss proportional to the difference between internal and external temperature.

Node Models

The dynamic thermal behaviour of each element is modelled using a discretised node structure per BS EN ISO 52016-1:2017.

5-Node Model (Opaque Elements)

Opaque elements use five thermal nodes distributed through the construction. The inter-node conductances are derived from the construction resistance:

$h_{pl i, 0} = \frac{6}{R _{c}}, h_{pl i, 1} = \frac{3}{R _{c}}, h_{pl i, 2} = \frac{3}{R _{c}}, h_{pl i, 3} = \frac{6}{R _{c}}$

The thermal mass $κ_{m}$ is distributed across the five nodes according to the mass distribution class:

Class	Description	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$	$k_{5}$
I	Internal	0	0	0	0	$κ_{m}$
E	External	$κ_{m}$	0	0	0	0
IE	Internal + External	$κ_{m} /2$	0	0	0	$κ_{m} /2$
D	Distributed	$κ_{m} /8$	$κ_{m} /4$	$κ_{m} /4$	$κ_{m} /4$	$κ_{m} /8$
M	Middle	0	0	$κ_{m}$	0	0

2-Node Model (Transparent Elements)

Transparent elements use only external and internal surface nodes with zero heat capacity and a single conductance:

$h_{pl i, 0} = \frac{1}{R _{c}}$

Outputs

Quantity	Symbol	Unit	Description
Element fabric heat loss	$H_{e l}$	W/K	Heat loss coefficient per element
Total fabric heat loss	$H_{T, f ab r i c}$	W/K	Sum of all element heat loss coefficients
Element heat capacity	$C_{e l}$	kJ/K	$A \times κ_{m} /1000$
Total heat capacity	$C_{T}$	kJ/K	Sum of all element heat capacities
Thermal bridge heat loss	$H_{t b}$	W/K	Sum of all thermal bridge coefficients

Assumptions

External surface resistance is constant at $R_{se} = 0.0414$ m²K/W regardless of exposure or wind speed. Wind effects on convective heat transfer are not modelled at element level.
Internal radiative heat transfer coefficient $h_{r i} = 5.13$ W/(m²K) is constant (BS EN ISO 13789:2017, Table 8).
Window curtain resistance is fixed at $r_{c u r t ain s} = 0.04$ m²K/W per SAP10.2.
Adjacent conditioned zones contribute zero fabric heat loss.
Thermal bridges are modelled as additional heat loss at the zone air node, not distributed across element surfaces.
The air and furniture internal heat capacity is fixed at $C_{in t} = 10, 000$ J/(m²K) per unit floor area.

Cross-references

TP-03: External Conditions — external temperature used in heat loss calculations; ZTU thermal resistance
TP-04: Space Heating Demand — fabric heat loss feeds into the zone heat balance matrix
TP-07: Thermal Mass — node model heat capacity and dynamic thermal response
TP-08: Solar Gains and Shading — solar gains on element external surfaces; glazing g-value and frame factor