# 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)

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)

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