# Heat Loss from Buildings

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

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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)

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}+(6b)R_{e}

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}=(J/kg/K)specific heat air

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)

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