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 (m²)

U = overall heat transmission coefficient (W/m²K)

t_i = inside air temperature (^oC)

t_o= outside air temperature (^oC)

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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 (^oC)

Overall Heat Transmission Coefficient

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

U = 1 / (1 / C_i + x₁ / k₁ + x₂ / k₂ + x₃ / k₃ + .. + 1 / C_o)                                            (3)

where

C_i = surface conductance for inside wall (W/m²K)

x = thickness of material (m)

k = thermal conductivity of material (W/mK)

C_o= surface conductance for outside wall (W/m²K)

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/m²K)

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 (m²K/W)

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

1 / U = R_i + R₁ + R₂ + R₃ + .. + R_o                                                     (6)

where

R_i = thermal resistivity surface inside wall (m²K/W)

R_1.. = thermal resistivity in the separate wall/construction layers (m²K/W)

R_o =  thermal resistivity surface outside wall (m²K/W)

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

1 / U = R_i + R₁ + R₂ + R₃ + .. + R_o + R_e                                                (6b)

where

R_e = thermal resistivity of earth (m²K/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/m³)

q_v = air volume flow (m³/s)

t_i = inside air temperature (^oC)

t_o = outside air temperature (^oC)

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/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)

t_i = inside air temperature (^oC)

t_o = outside air temperature (^oC)