## Videos

### Video 1

Introduction to the thermal-electrical analogy. PDF slides

### Video 2

Some examples on how to use the thermal-electrical analogy to model a variety of transfer phenomena. PDF slides

## Formulas

The heat flux per square meter of a wall is proportional to the temperature difference across the wall , and to its transmittance [W/(m.K)] :

The unit of this heat flux is [W/m]. The total heat flowing across a wall of area , in [W], is then:

We can also define a global heat loss coefficient such as [W/K]

The thermal resistance of a component of thickness and heat conductivity is:

A wall made of several material layers behaves like a series circuit of resistances: their values add up.

A building envelope made of several separated parts (opaque wall, windows, roof…) can be modelled as a parallel circuit of resistances: heat flows through each surface (m) simultaneously with more or less intensity. The heat loss coefficients of each surface add up:

**Warning:**Surface transfer coefficients must be summed in unit [W], not in [W/m]

Variable | Unit | ||
---|---|---|---|

Thermal resistance | (m.K)/W | can be summed in series | |

Thermal transmittance | W/(m.K) | ||

Heat loss coefficient | W/K | can be summed in parallel |

Cette méthode peut être appliquée pour représenter les transferts à l’échelle de tout un bâtiment, y compris en incluant des transferts par renouvellement d’air (voir vidéo 2).

## Exercise

Calculate the heat loss coefficient of an insulated room.

The walls of a room are made of:

- 44 m of concrete wall ( cm, W/(m.K)) with an insulation layer ( cm, W/(m.K))
- 8 m of double glazing ( W/(m.K))
- The indoor heat transfer coefficient is (m.K)/W, the outdoor one is (m.K)/W

The room is ventilated with an air renewal rate of 9 m/h.

Calculate the heating power that should be prescribed to maintain an indoor temperature of 19°C, if the outdoor temperature is 2°C.

The total heat loss of the room is the sum of three parts: heat flux through the concrete+insulation wall, heat flux through the windows and air renewal.

**1. Insulated concrete wall**

The thermal resistance is the sum of each layer’s resistance, and the surface resistances:

(m.K)/W

The heat loss is the reciprocal of this total resistance, times the area of the wall:

W/K

**2. Windows**

The transmittance that describes the glazing probably doesn’t include the heat transfer coefficients and . They should be included in the equation of the total glazing heat loss coefficient:

W/K

**3. Air renewal**

If the air renewal rate is given in the unit (m/h), the heat loss associated to it can be calculated easily:

W/K

**Summary**

The total heating power lost by the room is the sum of these three types of heat loss, times the indoor-outdoor temperature difference:

W