Heat Loss from Buildings

The overall heat loss from a building can be calculated as

H = H _t + H _v + H _i (1)

where

H = overall heat loss (W)

H _t = heat loss due to transmission through walls, windows, doors, floors and more (W)

H _v = heat loss caused by ventilation (W)

H _i = heat loss caused by infiltration (W)

1. Heat loss through walls, windows, doors, ceilings, floors, etc.>

The heat loss, or norm-heating load, through walls, windows, doors, ceilings, floors etc. can be calculated as

H _t = A U (t _i - t _o ) (2)

where

H _t = transmission heat loss (W)

A = area of exposed surface (m ² )

U = overall heat transmission coefficient (W/m ² K)

t _i = inside air temperature ( ^o C)

t _o = outside air temperature ( ^o C)

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Heat loss through roofs should be added 15% extra because of radiation to space. (2) can be modified to:

H = 1.15 A U (t _i - t _o ) (2b)

For walls and floors against earth (2) should be modified with the earth temperature:

H = A U (t _i - t _e ) (2c)

where

t _e = earth temperature ( ^o C)

Overall Heat Transmission Coefficient

The overall of heat transmission coefficient - U - can be calculated as

U = 1 / (1 / C _i + x ₁ / k ₁ + x ₂ / k ₂ + x ₃ / k ₃ + .. + 1 / C _o ) (3)

where

C _i = surface conductance for inside wall (W/m ² K)

x = thickness of material (m)

k = thermal conductivity of material (W/mK)

C _o = surface conductance for outside wall (W/m ² K)

The conductance of a building element can be expressed as:

C = k / x (4)

where

C = conductance, heat flow through unit area in unit time (W/m ² K)

Thermal resistivity of a building element is the inverse of the conductance and can be expressed as:

R = x / k = 1 / C (5)

where

R = thermal resistivity (m ² K/W)

With (4) and (5), (3) can be modified to

1 / U = R _i + R ₁ + R ₂ + R ₃ + .. + R _o (6)

where

R _i = thermal resistivity surface inside wall (m ² K/W)

R _1.. = thermal resistivity in the separate wall/construction layers (m ² K/W)

R _o = thermal resistivity surface outside wall (m ² K/W)

For walls and floors against earth (6) - can be modified to

1 / U = R _i + R ₁ + R ₂ + R ₃ + .. + R _o + R _e (6b)

where

R _e = thermal resistivity of earth (m ² K/W)

2. Heat loss by ventilation

The heat loss due to ventilation without heat recovery can be expressed as:

H _v = c _p ρ q _v (t _i - t _o ) (7)

where

H _v = ventilation heat loss (W)

c _p = specific heat air (J/kg K)

ρ = density of air (kg/m ³ )

q _v = air volume flow (m ³ /s)

t _i = inside air temperature ( ^o C)

t _o = outside air temperature ( ^o C)

The heat loss due to ventilation with heat recovery can be expressed as:

H _v = (1 - β/100) c _p ρ q _v (t _i - t _o ) (8)

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 may exceed 80% .

3. Heat loss by infiltration

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

H _i = c _p ρ n V (t _i - t _o ) (9)

where

H _i = heat loss infiltration (W)

c _p = specific heat air (J/kg/K)

ρ = density of air (kg/m ³ )

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 (m ³ )

t _i = inside air temperature ( ^o C)

t _o = outside air temperature ( ^o C)