# Building heat loss and heat gain formulas

Review

## Heat loss

Heat losses of building are important for calculation of energy bilation of building. Heat loss are heat loss penetration and heat loss through air change. The heat penetration can be direct, when the construction is in the direct contact with exterior (through the external walls, roof, windows, doors) or more complex when the heat goes through the unheated space (from room through the floor to unheated basement and through the uninsulated walls of basement to soil. The heat loss depends on area (m2), design temperature (Celsius), U-values of materials (W/(K·m2).

### Total surface heat loss

HT=LD+LS+HU

LD...heat loss through the building envelope (walls, roof, windows, doors)

LS...heat loss through the soil

HU...specific loss through unheated spaces

### Heat loss through material surface

LD = ∑iAi.U-valuei + ∑k.lkk + ∑jj

A...area of building envelope (m2)

U-value... coefficient of thermal transmittance (W/(K·m2), where the U-value is calculated as follow: U-value = 1/Rtot. Where the R-value (K·m2/W) is the sum of material thermal resistances and exterior surface thermal resistance (Rse=0,04 K·m2/W) and interior surface thermal resistance (Rsi=0,13 K·m2/W). Many internet pages offer online calculators of thermal loss, for example Heat loss calculations.

lk...length of linear thermal bridge k (m)

ψk...linear coefficient of thermal conductivity of thermal bridge k (W/m.K)

χj...dot coefficient of thermal conductivity of thermal bridge j (W/K)

### Heat loss through surrounding soil

Complex calculation of heat permeability through soil is calculated through the complex calculation, where the influence of multirange heat conduction close to circuit of building. The calculation plan can be found in norm EN ISO 13370.

### Heat loss through unheated space

HU = Liu.b

b = Hiu/(Hiu.Hue)

Liu...thermal conductivity between heated and unheated space (W/K)

Hiu...heat loss from unheated to heated space (W/K)

Hue...heat loss from unheated space to exterior (W/K)

b...reduction coefficient characterizing the temperature difference of unheated space from exterior temperature

### Heat loss in connection with air exchange

Every building needs to be heated and ventilated and with these processes comes the heat loss via air exchange. Air rates can be calculated and therefore it is possible to calculate the heat loss as well.

Hv = ρ.c.V

ρ...air density (kg/m3)

c...thermal capacity of air (J/kg.K)

Intensity of air change (h-1) in room, when is in use in winter period, has to fulfill certain limits, where nN is required intensity of air change in room, calculated from minimal requirements of needed fresh air. For residential buildings is the range between nN = 0,3 h-1 and nN = 0,6 h-1.

## Heat Gain

### Internal heat gains

Thermal energy from people and appliances are important in calculation scheme but they should not be overestimated. Usually the used values should come from national guidelines. In method  are used two principles: a) use of face values, and b)determination of the best possible values of internal gains from the number of electrical equipments and their use in time, or/and number of people.

The basic values are (according to PHPP):

2,1 W/m2 (floor area) for family house and stock of dwellings

4,1 W/m2 (floor area) for dormitory and hostel

3,5 W/m2 (floor area) for administration building

2,8 W/m2 (floor area) for school

### Passive solar gain

The energy which enter the building through the windows or glass areas in building envelope. The effective accumulating area AS (m2) of window or glazing area can be determined as follows:

AS = A.FS.FC.FF.g

A...total glass area (m2)

FS...correction coefficient of shading (-), shows the shading of surrounding buildings, trees and horizon

FC...correction coefficient of screening (-), characterized the influences of shading devices such as lamellas and curtains, etc.

FF...correction coefficient of casing (-), the quotient of transparent area and total area of glazing

g...total energetic transmissivity of solar energy (-) which characterizes the type of glazing

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