# Heating consumption of buildings

## Scope

Presents day degree method, which is used to define heating consumption of buildings. R↻

Analytica model of Bioher calculations is available here.

## Definition

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Fig 1. Total heating consumption of buildings (kWh/m2 year)

### Heating consumption

Heating consumption (Q) of buildings can be defined with knowledge of surface area of building, inside and outside temperature in certain time period, and heat permeability factors. Easiest way to use heating consumption is to define it as floor area weighted calculation.

Assumptions:

```Af = Ar
Aw = n(Af)
Awindow = 15/100 * Aw (By Finnish regulation windows covered area can be maximum of 50 % the
buildings frontage, typical value used is 15 % of the buildings frontage)
```

Buildings overall heat transfer coefficient per floor area is calculated as:

```UTotal,f = (Af * Uf + Aw * Uw + Ar * Ur  + Awindow * Uwindow + Adoor * Udoor)/Af
=Uf + [n * (100-15)/100 - x * Adoors] * Uw + Ur + (15/100) * Uwindow + x * 2m2/Af * Udoor
```

where Af is area of floor, Ar is area of roof, Aw is area of walls, Awindow is area of windows, Adoor is area of doors, x is number of doors, n is number of floors in the building and Uf is the overall heat transfer coefficient of floor, Uw the overall heat transfer coefficient of walls, Uwindow is the overall heat transfer coefficient of window, Udoor is the overall heat transfer coefficient of door and Ur is the overall heat transfer coefficient of roof. Unit of areas are m2, unit of the overall heat transfer coefficients are kW/(m2 K).

Building overall heat transfer coefficients are regulated in Finnish building regulations, which are presented in Table 1.

Table 1. Building overall heat transfer coefficients in Finnish buildings.

 Part of building 1978-1985 1985-2002 2003-2006 2007-2010 2010-? , Mass less than Mass over Warm area Half warm area Warm area Half warm area Warm area Half warm area Warm area Half warm area , 100 kg / m2 100 kg / m2 > 17 °C > 5 °C > 17 °C > 5 °C > 17 °C > 5 °C > 17 °C > 5 °C , [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] [W / m2 K] Walls 0,29 0,35 0,28 0,45 0,25 0,45 0,24 0,38 0,17 0,26 Roof 0,23 0,29 0,22 0,45 0,16 0,45 0,15 0,28 0,09 0,14 Floor 0,23 0,29 0,22 0,45 0,16 0,45 0,15 0,28 0,09 0,26 Part which is against ground 0,4 0,4 0,36 0,45 0,25 0,45 0,24 0,34 0,16 0,24 Window 2,1 3,1 1,4 2,1 1,4 1,8 1 1,4 Door 0,7 2,9 1,4 2,1 1,4 1,8 1 1,4

Total need of thermal energy in buildings is

```Q = Qh + Qw or
Q = sum(Qh) + Qw if monthly variation is considered
```

Analytica code:

```sum(Heating_consumption1)+Heating_of_tap_water
```

#### Total heating insulation fractions

Total heating insulation fractions was calculated with knowledge of heating insulation fractions (Table 2), number of doors were assumed to be 3 and number of floors was assumed to be 1.

Table 2. Insulation fractions for floor, roof, and wall (kW/m2 K)

 Heating insulation fractions (kW/m2 K) Ufloor 0.17 Uroof 0.09 Uwall 0.17 Uwindow 1.4 Udoor 1.4

Finlex See also: Motiva: current standard and Low-energy (pientalo ja matala energia talo)

Analytica code:

```var a:=Heating_insulation_1[Heat_perm_factors='Ufloor'];
var b:=Heating_insulation_1[Heat_perm_factors='Uwall'];
var c:=Heating_insulation_1[Heat_perm_factors='Uroof'];
var d:=Heating_insulation_1[Heat_perm_factors='Uwindow'];
var e:=Heating_insulation_1[Heat_perm_factors='Udoor'];
var n:=Number_of_floors;
var x:=Number_of_doors;
(a+n*((100-15)/100)*b+c+(15/100)*d+x*(2/100)*e)
```

Heating consumption per floor area of the buildings is calculated as:

```Qh = UTotal,f * (Tin-Tout)dt
```

where Qh is heating consumption of the buildings (kW/m2/year), Uf is floor weighted overall heat transfer coefficient per floor area of building (kW/m2 K) and Tin is inside temperature (usually used 17oC=290,15 K) and Tout outside temperature (K) in time dt.

### Heating consumption with monthly variation

Seasonal variation of heating consumption (Qh) can be evaluated also with monthly mean temperature differences.

Heating consumption with monthly variation (kWh/ m2 year) is calculated with days in month, mean outside temperature (Table 4) and mean inside temperature.

Analytica code:

```var a:= Temperature_in-Mean_out_temperature;
var b:= Total_heating_insula;
var c = Days_in_a_month;
sum(a*b/1000*c*24)
```

Table 4. Temperature of months (Celsius) (huom miinusmerkkiset ei näy wikissä!!)

 Month Temperature (C) Jan -7.8 Feb -8.8 Mar -3.8 Apr 1.9 May 8.7 Jun 14.1 Jul 16.5 Aug 14.4 Sep 9 Oct 3.9 Nov -0.9 Dec -5.7

Mean monthly temperature in Jyväskylä between years 1900-2000 

### Heating of warm tap water in buildings

Buildings also need thermal energy for warm tap water. This can be calculated by a following function

```Qw = cp,w pw qm,w * (Twarm - Tcold )t
```

where Qw is thermal energy which is needed to heat tap water (kW/m2/year), cp,w is specific thermal capacity of water (4.1962 kJ/kgK), pw is density of water (1000 kg/m3), qm,w is volume of needed warm tap water, which can be estimated to be 40 % of total used tap water (in Finland 100-224 (dm3/inhabitant)/day or 3,5 - 4,9 (dm3/m2)/day<), Twarm is temperature, where the tap water is heated (60 oC = 333,15 K), Tcold is temperature of the cold water (4 oC = 277,15 K) and t is time (1 year = 360 days). This can be also estimated by looking buildings thermal energy consumption in summer months, when there can be estimated to be only warm tap water use, because of outdoor temperature. Note that specific thermal capacity and density of water changes when the temperature changes. In calculations is used extrapolated value for the specific thermal capacity value (in 28oC).

Volume of needed warm tap water was calculated with the knowledge of number of days in season (summer = 180, winter = 180), used tap water in buildings (In Finland the guide value for tap water use is 130 dm^3/day/inhabitant. In Helsinki metropolitan area tap water usage is 155 dm^3/day/inhabitant. In 1999 tap water use was max. 224 dm^3/day/inhabitant in Finland.  ) and fraction of used warm tap water for seasons (summer = 0.4, winter = 0.25).

Analytica code:

Volume of needed tap water:

```var a:= Population_in_bioher;
var b:= Fraction_of_warm_tap;
var c:= Number_of_days_in_a_;
var d:= Used_tap_water_in_a_;
sum(a*b*c*d)
```

Heating of warm tap water:

```(Density_of_water*Thermal_capacity_of_*Volume_of_needed_war*Water_temperature)/Total_floor_area
```

kW/m2/year R↻

## Result

Total heating consumption of buildings with monthly variation and used warm tap water in Bioher is 110.9 kWh/m2 year.

• Total heating insulation fraction is 0.6984999999999999 W/m2 K.
• Heating consumption with monthly variation (kWh/m2 year) results are in Table 1.

Table 1. Heating consumption per m^2 - monthly T variation

 Month Heating consumption kWh/m^2 Jan 12.8881632 Feb 12.1103136 Mar 10.8094272 Apr 7.594092 May 4.3133772 Jun 1.458468 Jul 0.259842 Aug 1.3511784 Sep 4.02336 Oct 6.8078604 Nov 9.002268 Dec 11.7968268 Total 82.4151768

• In Bioher volume of needed warm tap water was 218800 dm3/ year.
• In Bioher heating of tap water as thermal energy, which is used to heat tap water in a building was 28.51 kWh/m2 year.