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# Heat Loss from Buildings

## Overall heat transfer loss from buildings - transmission, ventilation and infiltration.

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)

### 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

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)

#### Overall Heat Transmission Coefficient

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

U = 1 / (1 / Ci + x1 / k1 + x2 / k2 + x3 / k3 + .. + 1 / Co)                                            (3)

where

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

x = thickness of material (m)

k = thermal conductivity of material (W/mK)

Co= 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 = Ri + R1 + R2 + R3 + .. + Ro                                                     (6)

where

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

R1.. = thermal resistivity in the separate wall/construction layers (m2K/W)

Rothermal resistivity surface outside wall (m2K/W)

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

1 / U = Ri + R1 + R2 + R3 + .. + Ro + Re                                                (6b)

where

Re = thermal resistivity of earth (m2K/W)

### 2. Heat loss by ventilation

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)

cpspecific heat 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)                                                (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

Hi = cp ρ n V (ti - to)                                                            (9)

where

Hi = heat loss infiltration (W)

cpspecific 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)

ti = inside air temperature (oC)

to = outside air temperature (oC)

## Related Topics

• Heating - Heating systems - capacity and design of boilers, pipelines, heat exchangers, expansion systems and more.

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