The external wall of a timber framed house has the following specification: External Plaster: thickness 15 mm Block outer leaf: thickness 100 mm Timber stud inner leaf: thickness 125 mm Ultrathin board insulation: thickness 100 mm Plasterboard: thickness 12.5 mm Thermal data of outer leaf : - Resistance of the external plaster (R): 0.048 m² C/W - Resistivity of the external plaster (r): 2.170 Wm² C - Conductivity of block (k): 1.320 Wm² C Thermal data of inner leaf : - Conductivity of urethane board (k): 0.023 Wm² C - Conductivity of plasterboard (k): 0.160 Wm² C - Resistance of the internal surface (R): 0.104 m² C/W - Resistance of the cavity (R): 0.170 m² C/W Ignore the timber studs of inner leaf. a) Calculate the U-value of the wall. b) Calculate the annual cost of the heat loss through the external wall of the timber framed house outlined above, using the following data: Total external wall area: 125 m² Average internal temperature: 18 °C Average external temperature: 6 °C U-value: as calculated at (a) above Heating period: 12 hours per day for 40 weeks per annum Calorific value of oil: 37530 kj per litre Cost of heating oil: 65 cent per litre 1000 Watts = 1 kj per second. c) With the aid of notes and freehand sketches, a design detail which will prevent moisture reaching the insulation material from inside the building.

Leaving Cert Construction Studies Heat & U-Value Calculations: The external wall of a timber fr

The external wall of a timber framed house has the following specification: External Plaster: thickness 15 mm Block outer leaf: thickness 100 mm Timber stud inner leaf: thickness 125 mm Ultrathin board insulation: thickness 100 mm Plasterboard: thickness 12.5 mm Thermal data of outer leaf : - Resistance of the external plaster (R): 0.048 m² C/W - Resistivity of the external plaster (r): 2.170 Wm² C - Conductivity of block (k): 1.320 Wm² C Thermal data of inner leaf : - Conductivity of urethane board (k): 0.023 Wm² C - Conductivity of plasterboard (k): 0.160 Wm² C - Resistance of the internal surface (R): 0.104 m² C/W - Resistance of the cavity (R): 0.170 m² C/W Ignore the timber studs of inner leaf - Leaving Cert Construction Studies - Question 5 - 2006

Question 5

The external wall of a timber framed house has the following specification: External Plaster: thickness 15 mm Block outer leaf: thickness 100 mm Timber stud i... show full transcript

Worked Solution & Example Answer:The external wall of a timber framed house has the following specification: External Plaster: thickness 15 mm Block outer leaf: thickness 100 mm Timber stud inner leaf: thickness 125 mm Ultrathin board insulation: thickness 100 mm Plasterboard: thickness 12.5 mm Thermal data of outer leaf : - Resistance of the external plaster (R): 0.048 m² C/W - Resistivity of the external plaster (r): 2.170 Wm² C - Conductivity of block (k): 1.320 Wm² C Thermal data of inner leaf : - Conductivity of urethane board (k): 0.023 Wm² C - Conductivity of plasterboard (k): 0.160 Wm² C - Resistance of the internal surface (R): 0.104 m² C/W - Resistance of the cavity (R): 0.170 m² C/W Ignore the timber studs of inner leaf - Leaving Cert Construction Studies - Question 5 - 2006

Step 1

Calculate the U-value of the wall.

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Answer

The U-value is calculated using the total thermal resistance (R) of the wall.

First, we will find the resistance of each layer:

External Plaster:
- R = 0.048 m² C/W
Block Outer Leaf:
- R = rac{t}{k} = rac{0.1}{1.320} = 0.07576 m² C/W
Cavity:
- R = 0.170 m² C/W
Timber Stud Inner Leaf:
- R = rac{t}{k} = rac{0.125}{0.023} = 5.43478 m² C/W
Ureth Bd:
- R = rac{t}{k} = rac{0.1}{0.160} = 0.625 m² C/W
Internal Plaster:
- R = rac{0.0125}{0.160} = 0.078125 m² C/W

Now let's calculate the total resistance R:

$ext{Total } R = 0.048 + 0.07576 + 0.170 + 5.43478 + 0.625 + 0.078125 = 6.431665 m² C/W$

Now, calculate the U-value: $U = \frac{1}{R} = \frac{1}{6.431665} \approx 0.155 \text{ W/m² °C}$

Step 2

Calculate the annual cost of heat loss.

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Answer

The heat loss through the wall can be calculated using:

$\text{Heat Loss} = U \times A \times \text{Temp Diff}$

Where:

U = 0.155 W/m² °C
A = 125 m²
Temp Diff = (18 - 6) °C = 12 °C

So, $\text{Heat Loss} = 0.155 \times 125 \times 12 = 231.25 \text{ Watts}$

Convert Watts to kW: $\text{Heat Loss} = 0.23125 kW$

Calculate the annual heat loss in kWh: $\text{Annual Heat Loss} = 0.23125 \times 3360 \text{ hours} = 777.3 kWh$

Cost of heating oil = 65 cents per litre, and calorific value = 37530 kJ/litre.

Convert kWh to kJ: $777.3\text{ kWh} = 777300 \times 3600 = 2,800,380,000\text{ kJ}$

Now calculate the litres of oil needed: $\text{Litres} = \frac{2,800,380,000}{37530} \approx 74656.1 \text{ litres}$

Now calculate the total cost: $\text{Total Cost} = 74656.1 \times 0.65 = 48,271.48 \text{ euros}$ (should simplify as needed).

Step 3

Design detail to prevent moisture reaching insulation.

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Answer

To prevent moisture from reaching the insulation material, the following design features are recommended:

Vapor Barrier: Install a vapor barrier on the warm side of the insulation to prevent humidity from penetrating the insulation material.
Proper Insulation: Ensure the insulation is continuous and thoroughly installed to avoid thermal bridges that may lead to moisture accumulation.
Ventilation: Properly ventilate areas to allow moisture to escape, reducing the chances of condensation.
Material Selection: Use moisture-resistant materials for both internal and external finishes to further insulate against humidity infiltration.

Sketch Guidance: Draw a section view of the wall indicating the placement of the vapor barrier, insulation, and the layers involved in the construction to clearly show how moisture is managed.

Calculate the U-value of the wall.

Calculate the annual cost of heat loss.

Design detail to prevent moisture reaching insulation.

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