Heating consumption of buildings
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Scope
Presents day degree method, which is used to define heating consumption of buildings. R↻
Analytica model of Bioher calculations is available here.
Definition
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:
A_{f} = A_{r} A_{w} = n(A_{f}) A_{window} = 15/100 * A_{w} (By Finnish regulation windows covered area can be maximum of 50 % the buildings frontage, typical value used is 15 % of the buildings frontage) A_{door} = x * 2m^{2}
Buildings overall heat transfer coefficient per floor area is calculated as:
U_{Total,f} = (A_{f} * U_{f} + A_{w} * U_{w} + A_{r} * U_{r} + A_{window} * U_{window} + A_{door} * U_{door})/A_{f} =U_{f} + [n * (10015)/100  x * A_{doors}] * U_{w} + U_{r} + (15/100) * U_{window} + x * 2m^{2}/A_{f} * U_{door}
where A_{f} is area of floor, A_{r} is area of roof, A_{w} is area of walls, A_{window} is area of windows, A_{door} is area of doors, x is number of doors, n is number of floors in the building and U_{f} is the overall heat transfer coefficient of floor, U_{w} the overall heat transfer coefficient of walls, U_{window} is the overall heat transfer coefficient of window, U_{door} is the overall heat transfer coefficient of door and U_{r} is the overall heat transfer coefficient of roof. Unit of areas are m^{2}, unit of the overall heat transfer coefficients are kW/(m^{2} 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  19781985  19852002  20032006  20072010  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 = Q_{h} + Q_{w} or Q = sum(Q_{h}) + Q_{w} 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^{[1]} See also: Motiva^{[2]}: current standard and Lowenergy (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*((10015)/100)*b+c+(15/100)*d+x*(2/100)*e)
Heating consumption per floor area of the buildings is calculated as:
Q_{h} = U_{Total,f} * (T_{in}T_{out})dt
where Q_{h} is heating consumption of the buildings (kW/m^{2}/year), U_{f} is floor weighted overall heat transfer coefficient per floor area of building (kW/m^{2} K) and T_{in} is inside temperature (usually used 17^{o}C=290,15 K) and T_{out} outside temperature (K) in time dt.
Heating consumption with monthly variation
Seasonal variation of heating consumption (Q_{h}) can be evaluated also with monthly mean temperature differences.
Heating consumption with monthly variation (kWh/ m^{2} year) is calculated with days in month, mean outside temperature (Table 4) and mean inside temperature.
Analytica code:
var a:= Temperature_inMean_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 19002000 ^{[3]}
Heating of warm tap water in buildings
Buildings also need thermal energy for warm tap water. This can be calculated by a following function
Q_{w} = c_{p,w} p_{w} q_{m,w} * (T_{warm}  T_{cold} )t
where Q_{w} is thermal energy which is needed to heat tap water (kW/m^{2}/year), c_{p,w} is specific thermal capacity of water (4.1962 kJ/kgK), p_{w} is density of water (1000 kg/m^{3}), q_{m,w} is volume of needed warm tap water, which can be estimated to be 40 % of total used tap water (in Finland 100224 (dm^{3}/inhabitant)/day or 3,5  4,9 (dm^{3}/m^{2})/day<), T_{warm} is temperature, where the tap water is heated (60 ^{o}C = 333,15 K), T_{cold} is temperature of the cold water (4 ^{o}C = 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 28^{o}C).
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. ^{[4]} ^{[5]}) 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
Unit
kW/m^{2}/year R↻
Result
Total heating consumption of buildings with monthly variation and used warm tap water in Bioher is 110.9 kWh/m^{2} year.
 Total heating insulation fraction is 0.6984999999999999 W/m^{2} K.
 Heating consumption with monthly variation (kWh/m^{2} 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 dm^{3}/ year.
 In Bioher heating of tap water as thermal energy, which is used to heat tap water in a building was 28.51 kWh/m^{2} year.
References
 ↑ http://www.finlex.fi/fi/viranomaiset/normi/700001/
 ↑ http://www.motiva.fi/fi/kuluttajat/pientalonlammitysjarjestelmat/vertailupalvelu/tyyppitalot.html]
 ↑ http://www.fmi.fi/saa/tilastot_4.html#5
 ↑ Olli Seppänen, 2001, rakennusten lämmitys
 ↑ Helsingin vesi[www.helsinginvesi.fi]
Rakennuksen energiankulutuksen ja lämmitystehontarpeen laskenta[2]
Rakennusten lämmitys. Olli Seppänen. 2001, 2 päivitetty painos. Suomen LVIliitto ry. Gummerus kirjapaino Oy, Jyväskylä 2001. ISBN 9519881107.
See also
Monthly mean temperature in years 19002000 at Helsinki Jyväskylä and Sodankylä [3].