Heat load calculation
References
European Standard EN 12831:2003
Heating systems in buildings – Method for calculation of the
design heat load
ASHRAE Handbook Fundamentals 2005 Chapter 29, page 29.1129.14
European Standard EN 12831:2003
Ways of the calculation:
1. Calculation procedure for a heated space
• calculate the total design heat loss of the heated space by adding
the design transmission heat loss and the design ventilation heat
loss;
• calculate the heating-up capacity of the heated space, i.e.
additional power required to compensate for the effects of
intermittent heating;
• obtain the total design heat load of the heated space by adding
the total design heat loss and the heating-up capacity
1
2. Calculation procedure for a building entity or a building
For sizing of the heat supply, e.g. a heat exchanger or a heat generator,
the total design heat load of the building entity or the building shall be
calculated. The calculation procedure is based on the results of the
heated space by heated space calculation.
3. Calculation Procedure for the Simplified Method
The calculation procedure for the simplified method follows the
procedure given above. However, simplifications are made when
determining the different heat losses.
2
Total design heat loss for a heated space – basic cases
The total design heat loss for a heated space (i), Φi, is calculated as
follows:
Φi = ΦT,i + ΦV,i [W]
where:
ΦT,i – design transmission heat loss for heated space (i) in Watts (W);
ΦV,i – design ventilation heat loss for heated space (i) in Watts (W).
Design transmission heat loss
ΦT,i = (HT,ie + HT,iue + HT,ig + HT,ij) (θint,i - θe ) [W]
where:
HT,ie – transmission heat loss coefficient from heated space (i) to the
exterior (e) through the building envelope in Watts per Kelvin
(W/K);
HT,iue – transmission heat loss coefficient from heated space (i) to the
exterior (e) through the unheated space (u) in Watts per Kelvin
(W/K);
HT,ig – steady state ground transmission heat loss coefficient from
heated space (i) to the ground (g) in Watts per Kelvin (W/K);
HT,ij – transmission heat loss coefficient from heated space (i) to a
neighbouring heated space (j) heated at a significantly different
temperature, i.e. an adjacent heated space within the building
entity or a heated space of an adjacent building entity, in Watts
per Kelvin (W/K);
3
θint,I – internal design temperature of heated space (i) in degrees
Celsius (°C);
θe – external design temperature in degrees Celsius (°C)
Examples:
Heat losses directly to the exterior - heat loss coefficient HT,ie
The design transmission heat loss coefficient from heated space (i) to
the exterior (e), HT,ie, is due to all building elements and linear thermal
bridges separating the heated space from the external environment,
such as walls, floor, ceiling, doors, windows.
H T,ie = ∑ Ak ⋅ U k ⋅ ek + ∑ Ψl ⋅ ll ⋅ el [W/K]
k
l
Heat losses through the ground - heat loss coefficient HT,IG


H T,ig = fg1 ⋅ f g2 ⋅  ∑ Ak ⋅ U equiv,k  ⋅ Gw


k

4
Uequiv is given in diagrams
a – Concrete floor, no insulation
b – characteristic parameter, B´,
B' =
Ag
0 ,5 ⋅ P
5
Design ventilation heat loss
The design ventilation heat loss, ΦV,i, for a heated space (i) is
calculated as follows:
(
Φ V,i = H V,i ⋅ θint,i − θ e
) [W]
where:
HV,i – design ventilation heat loss coefficient in Watts per Kelvin
(W/K);
θint,i – internal design temperature of heated space (i) in degrees
Celsius (°C);
θe – external design temperature in degrees Celsius (°C).
H V,i = V&i ⋅ ρ ⋅ cp
[W/K]
6
Simplified Calculation Method
EN 12831 9.1 Design heat loss for a heated space
The calculation method in the standard is based on the following
hypotheses:
– The temperature distribution is assumed to be uniform;
– The heat losses are calculated in steady state conditions
assuming constant properties.
The procedure can be used for buildings
− A ceiling height not exceeding 5 m
− The air temperature and operative temperature are assumed to be
of the same value
7
Total design heat loss
Φ = (ΦT + ΦV ) ⋅ f∆ϑ ,i
ΦT – design transmission heat loss through walls, floor, ceiling,
windows, doors, etc.
Φv – design ventilation heat loss infiltration or ventilation of heated
space,
f∆θ – temperature correction factor taking into account the additional
heat loss of rooms heated at a higher temperature then the
adjacent heated rooms -> national standards or Annex D.7.3
higher temperature: f∆θ =1.6
8
Design transmission heat loss
ΦT = ∑ f k ⋅ Ak ⋅ U k (ti − to ), W
k
fk – temperature correction factor for a building element, which
depends on the heat flow and thermal bridges insulation
Annex D.7.2
Ak – area of building element, m2,
Uk – overall heat transfer coefficient, thermal transmittance
ti – design internal temperature, °C, Annex A, Table A.2
to – design external temperature, °C
Design ventilation heat loss
ΦV = 0,34 ⋅ V&inf ⋅ (ti − t o ), W
V&inf – minimum air flow rate of a heated space required for hygienic
reasons, m3/h,
with the air exchange rate n50 (1/h):
V&inf = n50 ⋅ Vi ⋅ ei ⋅ ε i ,
m3 / h
Where
Vi – volume of heated space, calculated on the basis of internal
dimensions, m3
n50 – air exchange rate, resulting from pressure difference of 50 Pa between
inside and outside, h-1
ei – shielding coefficient, (-)
ε – height correction factor, (-)
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Air exchange rate – n50 – EN 12831:2003 D 5.2
Default values for the air exchange rate, n50 for the whole building resulting
from pressure difference of 50 Pa between inside and outside:
Construction
n50 (h-1)
Degree of air-tightness of the building envelope (quality of the
window seal)
high (high quality
medium (double
low (single glaze
sealed windows and
glaze windows,
windows, no sealant)
doors)
normal seal)
single family
dwellings
other dwellings or
buildings
<4
4-10
> 10
<2
2-5
>5
The whole building air exchange rates may be expressed for other pressure
differences than 50 Pa, but these results should be adapted to suit the equation
above.
Shielding coefficient – e – EN 12831:2003 D 5.3
Default values for the shielding coefficient, e, are:
Shielding Class
No shielding (building in
windy areas, high rise
buildings in city centres)
Moderate shielding (buildings
in the country with trees or
other buildings around them,
suburbs)
Heavy shielding (average
height buildings in city
centres, buildings in forests)
Heated space
without exposed
openings
e
Heated space with
one exposed
opening
Heated space with
more than one
exposed opening
0
0.03
0.05
0
0.02
0.03
0
0.01
0.02
Height correction factor - ε – EN 12831:2003 D 5.4
Default values for the height correction factor, ε, are:
Height of heated space above ground-level
(centre of room height to ground level)
0 – 10 m
> 10 – 30 m
> 30 m
ε
1.0
1.2
1.5
10
Steps of the calculation:
Step 1
Determination of basic data:
External design temperature
Step 2
Definition of each space of the building
Heated space or not
Unheated space
Step 3
Determination of
• Dimensional characteristics
• Thermal characteristics
of all building elements
External dimensions:
11
U-values:
Requirements in Hungary
Building element
U-value [W/m2K]
Heavy
Light
elements elements
External wall
0,45
0,35
Deck roof
0,25
0,20
Loft-ceiling
0,30
0,25
Floor above an unheated cellar
0,50
0,50
Window side (wood/PVC frame)
1,60
0,60
Window side (aluminium frame)
2,00
2,00
12
Step 4
Determination of indoor design conditions in all heated
and unheated spaces
CR 1752, or EN 12831 Class A, B or C
Step 5
Calculation of design transmission heat loss
Step 6
Calculation of design ventilation heat loss
Step 7
Calculation of total design heat loss
13
Example 1
Calculation of design transmission and ventilation heat loss of a living
room in a single family house. The building project will be built in
Budapest.
Ground-plan of the building:
14
Step 1
Determination of external design temperature
National standard:
–13 °C
(Other source: ASHRAE Handbook Fundamentals 2001 Ch. 27.36:
Heating Dry Bulb Temperature: –13.2 … – 10.2 °C)
Step 2
Definition of each space of the building. This is a heated space. Above
the heated space there is a loft, below there is a basement.
Step 3
Determination of dimensional characteristics thermal characteristics of
building elements
Element
Surface, m2
U-value, W/m2,K
W1 Window
6.6
1.6
W2 Window
2.25
1.6
D1 Door
2.0
1.6
OW1 Wall
6.38 · 3.1 – 6.6 – 2.0 = 11.2
0.45
OW2 Wall
5.38 · 3.1 – 2.25 = 14.4
0.45
PD1 Partition door
2.0
3.0
PW1 Partition wall
6.21 · 3.1 – 2.0 = 17.25
3.75
PW2 Partition wall
5.21 · 3.1 = 16.15
3.75
Ceiling
5.38 · 6.38 = 34.3
0.3
Floor
5.38 · 6.38 = 34.3
0.5
15
Step 4
Determination of indoor design conditions in all heated and unheated
spaces
EN 12831 Annex A, Table A.2 Internal design temperature
Heated spaces
1 – Living room:
20 °C
2 – Room:
20 °C
3 – Kitchen:
20 °C
(Table A.2. Residential)
Unheated spaces
Loft:
–8 °C
Basement:
+5 °C (closed space)
Step 5
Calculation of design transmission heat loss
No
Element
Area
1
W1
6.6
U-Value Tempr.Diff Heat flow
1.6
20-(-13) =
348 W
= 33
2
D1
2.0
1.6
33
106 W
3
OW1
11.2
0.45
33
166 W
4
W2
2.25
1.6
33
119 W
5
OW2
14.4
0.45
33
214 W
6
Ceiling
34.3
0.3
20-(-8)=
288 W
=28
7
Floor
34.3
0.5
20-5=15
257 W
Total
ΦT
1498 W
16
Step 6
Calculation of design ventilation heat loss
Infiltration air flow rate:
V&inf = 2 ⋅ Vi ⋅ n50 ⋅ ei ⋅ ε i
Vi = 5 · 6 · 2.8 = 84 m3
n50 = 4 (medium air-tightness, other dwellings than single family
houses)
ei = 0.03 (heated spaces with more than one exposed opening)
εi = 1.0 (0 – 10 m)
V&inf = 2 ⋅ 84 ⋅ 4 ⋅ 0.03 ⋅ 1.0 = 20.16 m3 / h
ΦV = 0.34 ⋅ V&inf ⋅ (ti − to ) = 0.34 ⋅ 20.16 ⋅ (20 − (−13)) = 226 W
Step 7
Calculation of total design heat loss
Φ = (Φ T + ΦV ) ⋅ f ∆θ
f∆θ = 1.0 (EN 12831:2003 D.7.3, Internal design temperature: normal)
Φ = ΦT + ΦV = 1498 W + 226 W = 1724 W
17
ASHRAE Handbook Fundamentals 2005 Chapter 29, p. 29.1129.14
Summary of Heating Load Calculation Equations
Load Source
Equation
Exterior surfaces above grade
q = U·A·∆t
Where ∆t = ti – to
Partitions to unconditioned buffer space
q = U·A·∆t
Where ∆t = tempr. difference across partition
Walls below grade
Where
q = Uavg.bw ·A·(tin – tgr)
Uavg.bw – below-grade wall average U-factor
tin
– below-grade space air temperature
tgr
– design ground surface temperature
Floors on grade
Where
q = Fp·p·∆t
Fp
– heat loss coefficient per foot of perimeter
p
– perimeter of floor
Floors below grade
Where
Uavg.bf – below-grade floor average U-factor
Ventilation/infiltration
Where
q = Uavg.bf ·A·(tin – tgr)
qvi = Cs·Q·∆t
Cs
– air sensible heat factor
Q
– air volume flow rate
Total sensible load
qs = Σq
18