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# Thermal: Heat Balance

Thermal balance occurs when the sum of all the different types of heat flow into and out of a building is zero. That is, the building is losing as much heat as it gains so it can be said to be in equilibrium. Thus:

$\large Q_c + Q_v + Q_s + Q_i + Q_e = 0$

The five values on the left hand side of the equation refer to the five different sources of heat gain or heat loss within a building, and are defined as follows:

Figure 1 - Sources of heat gain and loss within a building. Section through Simpson-Lee House, by Glenn Murcutt. Drawn by craines.

### Qc - Conduction Gains

Conduction gains occur when heat from the outside flows through the external building envelope. This occurs almost exclusively by conduction, however some convection may occur within some cavity constructions.

The external envelope is deemed to include the walls, windows, doors, roofs and floor.

In a building element, instantaneous heat flow will depend upon the characteristics of the materials that make up that element, as well as overall surface area and the temperature difference between inside and outside. The total heat flow at any particular time is therefore given by:

$\large Q_c = U A \delta T$

where:
Qc = the total instantaneous heat flow in Watts (W),
DT = the instantaneous temp. difference between inside & outside,
A = the surface area of the building element, and
U = the U-Value of the building element.

### Qv - Ventilation Gains

Ventilation gains occur when outside air enters the building. This can be by natural leakage through the building fabric (infiltration) or by the intentional opening of doors and windows (ventilation).

$\large Q_v = 0.33 N V \delta T$

where:
Qv = total ventilation gain in Watts (W),
N = the number of air changes per hour within the zone,
V = the total internal volume of the zone, and
DT = the temperature difference between inside and outside.

The value 0.33 results from the fact that moist air has a volumetric heat capacity of 1200J/mÃ‚Â³K and the flow rate is given as a factor of air changes per hour. Hence, as Watts = J/s, 1200/3600 = 0.33.

### Qs - Solar Gains

Solar gains refer to additional heat flows generated within the building by the sun. This can be directly through the windows or indirectly through opaque elements. In the case of opaque elements, the sun acts to heat up exposed surfaces, thereby increasing the amount of heat flowing through the building fabric.

##### Direct Gains

Direct solar gains through transparent elements are given by:

$\large Q_s = G A sgf$

where:
Qs = total direct solar gain in Watts (W),'
G = the total solar radiation incident on the specified window (W/mÃ‚Â²), A = the surface area of the window in mÃ‚Â², and sgf = the solar gain factor.

The solar gain factor is a function of the type of window and represents the amount of direct radiation that actually makes it through the element and into the zone. This is simply a fraction between 0 and 1.

##### Indirect Gains

Indirect solar gains through opaque elements are slightly more complex. This is because the incident solar radiation acts first to increase the external surface temperature of the element. The resulting surface temperature is termed the sol-air temperature.

As this increases the DT value of the conduction gain component, more heat will flow from outside to in.

In order to isolate indirect gains, it is convenient to deal with the increased temperature due to solar radiation separately from the outside air temperature. Thus, only the sol-air excess temperature is used.

$\large Q_s = U A (G abs R_{so})$

where:
Qs = total direct solar gain in Watts (W),
U = the U-Value of the specified element,
G = the total solar radiation incident on the specified window (W/mÃ‚Â²),
A = the surface area of the opaque elementin mÃ‚Â²,
abs = the surface absorption of the element, and
Rso = the outside air-film resistance.

Surface absorption is a function of colour and material, referring to the amount of solar radiation actually absorbed by the surface. This is simply a fraction between 0 and 1. The outside air-film resistance is described in the U-Value section below.

### Qi - Internal Gains

Internal gains result from heat sources within the building. These range from people to electric lights, typewriters, computers and almost every electrical appliance. An average person adds around 70W of heat energy to a zone, just by being there. A computer may add up to 150 Watts of heat energy, mainly from the monitor. These values are simply summed and added to the total heat gain. Internal gains are most often given in W/mÃ‚Â² floor area, based on the type of activity within each zone.

### Qe - Evaporative Loss

Evaporative losses occur when water changes phase from a liquid into moisture vapour within the air. If the evaporation rate (ev) in kg/h is known, the total evaporative heat loss will be:

$\large Q_e = 666.66 ev$

where:
QE = total evaporative loss in Watts (W), and
ev = the evaporation rate in kg/h.

The value 666.66 is derived from the latent heat of evaporation of water (2400,000 J/kg) and the fact that the evaporation rate is given in hours (3600 seconds). Hence, 2400,000/3600 = 666.66

Heating and Cooling Requirements, CBD-105
http://www.nrc.ca/irc/cbd/cbd105e.html
Thermal: Analysis Methods
Thermal: Heat Flow