Unit 4: Science and Materials in Construction and the Built Environment
Calculation of heat loss
Various methods are available for calculating the rate at which heat flows
out of a building, and the quantity of heat lost in a given time. It is
relatively difficult to calculate heat losses for unsteady or cyclic conditions
where temperatures fluctuate with time. However, certain simplified
calculations can be used for predicting heating requirements and the
amount of fuel required. The results obtained by these calculations are
found to give adequate agreement with the conditions that actually exist.
With steady state conditions the temperatures inside and outside the
building do not change with time and the various flows of heat from the
building occur at constant rates. Assuming steady state conditions the
heat losses from a building can be classed as either a ‘fabric loss’ or a
‘ventilation loss’ and then calculated by the methods described below.
7.1
Fabric Heat Loss
Fabric heat loss from a building is caused by the transmission of heat
through the materials of walls, roofs and floors. Assuming steady
conditions, the heat loss for each element can be calculated by the
following formula.
Where
Pf = rate of fabric heat loss = heat energy lost/time (J/s or W)
U = U-value of the element considered (W/m2K)
A = area of that element (m2)
t = difference between the inside and outside temperatures
This heat loss per second is a form of power (energy divided by time) and
therefore measured in watts (which are joules per second). The notation P
is used here to represent this rate of heat energy.
Chapter 7
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Unit 4: Science and Materials in Construction and the Built Environment
7.2
Heat loss due to Ventilation
The natural ventilation of buildings, such as open windows, leads to the
complete volume of air in a room changing a certain number of times in
one hour. Typical air change values are given in table 3.1
The fresh air entering the room will need to be heated to the internal
temperature of the room/building. This is calculated with the formula:
Where
C = heat energy (J)
cv = volumetric specific heat capacity (J/m3K)
N = the number of complete changes per hour
V = volume of room (m3)
t = difference between the inside and outside temperatures
The volumetric specific heat for air is approximately 1300J/m3K and is
considered a constant in this formula which will give an answer in joules
required per hour.
This then has to be converted in watts in order to find the rate of heat
loss, which is achieved by dividing the number of joules by the number of
seconds in one hour, 3600 seconds (60 sec × 60 min):
Where
Pv = rate of ventilation heat loss = C/time (J/s or W)
To calculate daily heat losses (fabric and ventilation), appropriate
temperatures would be the internal environment temperature and the
outside environmental temperature, both averaged over 24 hours. For the
calculation of maximum heat losses, such as when choosing the size of
heating equipment, it is necessary to assume a lowest external design
temperature, in case of Malta 4oC.
Chapter 7
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Unit 4: Science and Materials in Construction and the Built Environment
Practical Example 1
A window measuring 2 m by 1.25 m has a average U-value, including the
frame, of 6.2 W/m2K. Calculate the rate of fabric heat loss through this
window when the inside comfort temperature is 20oC and the outside air
temperature is 4oC.
Answer
Fabric heat loss
Where
Pf = ? (J/s or W)
U = 6.2 W/m2K
A = 2 × 1.25 = 2.5 m2
t = (20 – 4) = 16 oC
So
So fabric loss = 248 W
Practical Example 2
A simple building is 4 m long by 3 m wide by 2.5 m high. In the walls
there are two windows, each 1 m by 0.6 m, the first one is a single glazed
metal frame window and the second one is a double glazed wooden frame
window filled with argon with gap of 12 mm between panes. There is one
large solid wooden door 1.75 m by 0.8 m. For U-values of windows and
doors see Chapter 6. Other U-values in W/m2K are: walls 2.5, roof 3.0,
floor 1.5. The inside environmental or comfort temperature is maintained
at 18oC while the outside air temperature is 10oC. The volumetric specific
heat capacity of air is taken to be 1300 J/mK. There are 1.5 air changes
per hour. Calculate the total rate of heat loss for the building under the
above conditions.
Chapter 7
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Unit 4: Science and Materials in Construction and the Built Environment
Step 1
Sketch the building with its dimensions and then calculate the
areas of each section and the temperature difference.
Outside temperature
= 10oC
3m
4m
Inside temperature
= 18oC
2.5 m
1.5 air changes
per hour
One door
Two windows
1.75 m × 0.8 m
1m × 0.6 m each
Step 2
Tabulate the information and calculate the rate of fabric heat
.
losses using
Element
U-value
(W/m2K)
single glazed metal
5.7
frame window
double glazed wooden
frame window filled with
2.7
argon 12mm gap
solid wooden door
3.0
Walls
2.5
Roof
3.0
Floor
1.5
Total rate of fabric heat loss
Step 3
Area
(m2)
Temperature
difference (oC)
Rate of heat
loss Pf (W)
0.6
8
27.36
0.6
8
12.96
1.4
32.4
12
12
8
8
8
8
33.6
648
288
144
1153.92 W
Calculate the ventilation heat loss (Pv)
Using
Chapter 7
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Unit 4: Science and Materials in Construction and the Built Environment
Where
Pv = ? (J/s or W)
cv = 1300 J/m3K
N = 1.5 h-1
V = 4 × 3 × 2.5 = 30 m3
t = 18 – 10 = 8 oC
So
So rate of ventilation heat loss = 130 W
Step 4
Total rate of heat loss = fabric heat loss + ventilation heat loss
= 1153.92 + 130
= 1283.92 W
Chapter 7
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Unit 4: Science and Materials in Construction and the Built Environment
Exercise 7.1
1) The external wall of a room measures 4.5 m by 2.6 m and has an
average U-value 1.8 W/m2K. The internal air temperature is 19oC,
the mean radiant temperature is 22oC, and the external air
temperature is 38oC.
a) Calculate the environmental temperature inside the room.
b) Use the environmental temperature to calculate the rate of heat
loss through the wall.
2) A house has a floor area of 85 m2 and a ceiling height of 2.5 m. The
average inside air temperature is kept at 23oC, the outside air
temperature is 6oC, and the average infiltration rate is 1.5 air
changes per hour. The volumetric specific heat capacity of the air is
1300J/m3K.
a) Calculate the rate of ventilation heat loss.
b) Calculate the cost of the heat energy lost during 24 hours if the
above conditions are maintained and replacement heat costs 16c
per megajoule.
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Unit 4: Science and Materials in Construction and the Built Environment
3) Use the example found in Chapter 3 to answer the following
questions.
a) Calculate the ventilation heat loss of the room if the outside
temperature is measured as 33oC. (Note: quote the inside
environmental
temperature
found
as
an
inside
comfort
temperature)
b) Calculate the fabric heat loss if one considers the maximum Uvalues permitted in each installation for the Maltese building
sites and the window has a metallic frame with and double
glazed pane filled with argon, emissivity of 0.1, and 6 mm gap
and a thermal break of 8 mm. The room is found on the top
floor.
c) Calculate the total rate of heat loss for this room.
4) An ice skating complex has internal dimensions of 100 m × 55 m ×
25 m high. 80% of the wall area is triple glazed with metallic frame
argon fill, emissivity of 0.05, and an 18 mm gap between panes
with a thermal break of 16 mm. The doors have a total area of 20
m2. The U-values in W/mK are: walls 1.6, doors 2.5, roof 1.5 and
floor 0.4. The inside air temperature is maintained constantly
throughout the year at 3oC while the outside temperature on a
sunny day is 35oC. There are 6 air changes per hour and the
volumetric specific heat capacity of air is 1300 J/m3K. Calculate the
total rate of heat loss for this type of building.
Chapter 7
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