Calculations of the losses
We are going to determine the losses of a house of 15.40×8.40 = 129.36 m2 of floor surface intra-muros,
of (15.80+8,80)×2 = 49.20m of perimeter,
of 2.60m of ceiling height, that is to say 127,92m2 of lateral surface,
in an area where the average of the extremas of low temperature is of -7°C, with an inside temperature of 20°C.
The surface of the openings is
6×2.15×1.40+2.15×1.20+2.15×0.80+1.25×1.00+0.95×0.60 = 24.15 m2.
Hence, wall surface :
127.92-24.15 = 103.77m2.
The insulation coefficient is given by the curves of the CSTB for a wall with bay windows for 10cm of outside insulation and 0.07 for the residual thermal bridges, which gives a coefficient of 0.42.
For an inside insulation, with the same thickness of polystyrene, the thermal bridges are worth 0.52, that is to say cumulatively a coefficient of 0.87, more than the double!
The polystyrene being fixed by glue pins or on plastic rails, there is about 1.5 cm of stuffy aire which increases the insulation thickness, hence the coefficient 0.04/0.115=0.35 given by the CSTB. In our case, all the thermal bridges are eliminated, the losses through the threshold will be calculated separately, we can take this last coefficient for a calculation basis.
Losses through the walls are thus
103.77×27×0.35 = 980.63 Watt
Losses by the openings, with a current coefficient of 1.50, are :
24.15×27×1.5 = 978.07 Watts
We can notice incidentally that the losses through the openings are almost equal to the losses through the walls
Calculations of the losses through the thresholds :
Length of the thresholds
6×1.5+1.3+1+0.7 = 12 m
Width of the thershold vis-à-vis the tile and the wall
0.17+0.13 = 0.30 m
Average thickness of the thresholds : 0.06 m
Hevay concrete conductibility coefficient : 1.4 Watt/m;°C
Styrodur coefficient : 0.04 Watt/m.°C
Thermal resistance by m2: Rth = 0.06/1,4+0.03/0.04 = 0.79 °C.m2/W
Conductance: g = 1/Rth = 1.26 Watt/m2.°C
Surface: 12×0.30 = 3,60 m2
Tile temperature : 25 °C, gap = Text-Tint = 25+7 = 32 °C
Losses through the thresholds
3.60×32×1.26 = 145.15 Watts
To underline the importance of a thermal bridge, we will suppose that the thresholds are cast with the tile like it is habitually done.
The conductivity is then the one of the concrete hence the losses
3.60×32×1.4/0.06 = 2688 Watts
That is to say, 20 times more ! We will see at the end of the calculations that this represents 2/3 of the losses of the house for only 12 meters of thresholds!
Losses through the foundations :
Average perimeter of the foundations : (15.60+8.60)×2 = 48.40 m
Floor surface of the fondations : 48.40×0.20 = 9.68 m2
Conductibility coefficient of a wall of 0,20 m of height : 2 Watts/m2.°C, that is to say for 0,80 of foundation : 2/4 = 0.5
Floor temperature at 0,80 m deep : 4°C,
Tile temperature : 25 °C, thus a gap of 21°C
Losses through the sole of the foundations :
9.68×21×0.5 = 101.64 Watt
Losses through lateral surface of the foundations
By -7 outside and +4 at 80 cm deep, this makes an average outside temperature of 4+(-7-+4)/2 = 4-5.5 = -1.5°C;
With +25 in the tile and +4 at 80 cm deep, this make an average inside temperature of 4+(25-4)2 = 14.5°C;
The lateral surface to take into account is the passage surface, that is to say the thickness of the wall thus 0,20cm, thus 49.20×0.2 = 9.84 m2;
The lateral losses of the foundations are thus of :
9.84×0.04/0.1×(14.5-(-1.5)) = 62.98 W.
Losses through the ceiling insulated by two layers of crossed glass wool :Ceiling temperature : 23°C, gap 23+7 = 30°C
Losses through the ceiling :
129.36×30×0.04/0.40 = 388.08 Watt
Losses through the floor : the floor is insulated with two crossed layers of 6 cm of polystyrene plus a layer of styrodure of 5 cm under the heating screed, this make about 17 cm, to which must be added 80 cm of soil rather dry
The thermal resistance is then: Rth = 0.17/0.04 + 0.6/0.8 = 5
hence the losses through the floor
129.36×21×1/5 = 543.31 Watts
Losses through the double flux ventilation :
The renewal must be about 25 m3 of aire per hour and per person, for an occupation of the house by four persons, this makes 100 m3 per hour.
The VMC has an effectiveness of 60%, the specific heat of the air is 0.3 kcal/m3.
The losses are thus of :
0.3×30×0.4×100×1.16 = 417.60 Watts
The total losses for a house with -7°C outside and +20°C inside are :
980.63+978.07+145.15+101.64+62.98+388.08+543.31+417.60 = 3617.46 Watt say 3600 Watts
The volume of the house is : 129.36×2.60 = 336.34 m3
The volumic coefficient of the losses is : G = 3617.46/(27×336.34) = 0.398 Watt/m3.°C, that is to say 0.40Watt/m3.°C
With regards to the traditional houses, nowadays built with inside insulation, we are three times better.
There is a free and renewable ad infinitum energy : it is the one that we do not consume.
The surface of the outside faces of the house is: 127.92+2×129.36 = 386.64 m2
The average surfacic conductivity coefficient is then : K = 3617.46/(27×386.64) = 0.347 Watts/m2.°C