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Engineering ToolBox > Heat Loss from Buildings
The overall heat loss from a building can be calculated as
H = Ht + Hv + Hi (1)
where
H = overall heat loss (W)
Ht = heat loss due to transmission through walls, windows, doors, floors and more (W)
Hv = heat loss caused by ventilation (W)
Hi = heat loss caused by infiltration (W)
The heat loss through walls, windows, doors, ceilings, floors etc. can be calculated as
Ht = A U (ti - to) (2)
where
Ht = transmission heat loss (W)
A = area of exposed surface (m2)
U = overall heat transmission coefficient (W/m2K)
ti = inside air temperature (oC)
to= outside air temperature (oC)
Heat loss through roofs should be added 15% extra because of radiation to space. (2) can be modified to:
H = 1.15 A U (ti - to) (2b)
For walls and floors against earth (2) should be modified with the earth temperature:
H = A U (ti - te) (2c)
where
te= earth temperature (oC)
The overall of heat transmission coefficient - U - can be calculated as
U = 1 / (1 / fi + x1 / k1 + x2 / k2+ x3 / k3 +..+ 1 / fo) (3)
where
fi = surface conductance for inside wall (W/m2K)
x = thickness of material (m)
k = thermal conductivity material (W/mK)
fo= surface conductance for outside wall (W/m2K)
The conductance of a building elements can be expressed as:
C = k / x (4)
where
C = conductance, heat flow through unit area in unit time (W/m2K)
The thermal resistivity of the building element can be expressed as:
R = x / k = 1 / C (5)
where
R = thermal resistivity (m2K/W)
Using (4) and (5), (3) may be modified to
1 / U = Ri + R1 + R2 + R3 + .. + Ro (6)
For walls and floors against earth (6) should be modified to
1 / U = Re + SR (6b)
The heat loss due to ventilation without heat recovery can be expressed as:
Hv = cp ρ qv (ti - to) (7)
where
Hv = ventilation heat loss (W)
cp = specific heat capacity of air (J/kg/K)
ρ = density of air (kg/m3)
qv = air volume flow (m3/s)
ti = inside air temperature (oC)
to = outside air temperature (oC)
The heat loss due to ventilation with heat recovery can be expressed as:
Hv = (1 - β / 100) cp ρ qv (ti - to) (7)
where
β = heat recovery efficiency (%)
An heat recovery efficiency of approximately 50% is common for a normal cross flow heat exchanger. For a rotating heat exchanger the efficiency my exceed 80%.
Due to leakages in the building construction, opening and closing of windows, etc. the air in the building shifts. As a rule of thumb the number of air shifts is often set to 0.5 per hour. The value is hard to predict and depend of several variables - wind speed, difference between outside and inside temperatures, the quality of the building construction etc.
The heat loss caused by infiltration can be calculated as
Hi = cp ρ n V (ti - to) (8)
where
Hi = heat loss infiltration (W)
cp = specific heat capacity of air (J/kg/K)
ρ = density of air (kg/m3)
n = number of air shifts, how many times the air is replaced in the room per second (1/s) (0.5 1/hr = 1.4 10-4 1/s as a rule of thumb)
V = volume of room (m3)
ti = inside air temperature (oC)
to = outside air temperature (oC)