Energy System Heat Transferred by transmission.pptx

The formula and how to solve and calculate the heat transfer calculation in the basic residential building. The building is a small project with archiCAD.

1. Energy Systems Assignment 2 Basic Residential Heat Transferred By Transmission

2. Energy System 1 24/04/2024

3. Energy System 1 24/04/2024 1. Hallway 15,5m2 2. Living + dining room 37,5m2 3. Bedroom 12m2 4. Bedroom 12m2 5. Bedroom 12m2 6. Kitchen 7,5m2 7. Toilet 4m2 8. Bathroom 9m2 9. Storage room 10,5m2 Total Area 120m2

4. Energy System 1 24/04/2024

5. RADIATOR PLAN 1. Hallway 15,5m2 2. Living + Dining Room 37,5m2 3. Bedroom 12m2 4. Bedroom 12m2 5. Bedroom 12m2 6. Kitchen 7,5m2 7. Guess Bathroom 4m2 8. Bathroom 9m2 9. Storage Room 10,5m2 Total Area 120m2 HALLWAY LIVING ROOM DINING ROOM KITCHEN BEDROOM 3 BEDROOM 2 BEDROOM 1 BATHROOM BATHROOM STORAGE ROOM UTILITY ROOM

6. Q 𝒕𝒓𝒂𝒏𝒔 = ∑ 𝒏 𝒋=𝟏 𝑼𝒋 ∙𝑨𝒋 ∙(𝒕 internal −𝒕 external) Q 𝒕𝒓𝒂𝒏𝒔 : Heat transferred by transmission, U : The heat transfer coefficient by transmission, [ 𝑤/ 𝑚2∙𝐾 ] A : Area, [𝑚2] 𝒕 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙: Internal temperature, [℃] 𝒕 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙: External temperature, [℃] 𝒕 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙− 𝒕 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙, temperature difference, [K] For example, {20℃-(-11℃)} = {(20+273.15) K - (-11+273.15) K} = 31K Q 𝒗𝒆𝒏𝒕𝒊𝒍𝒂𝒕𝒊𝒐𝒏 = 𝑳∙𝝆∙𝑪𝒑∙(𝒕 internal −𝒕 external ) Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 : Heat transferred by ventilation , [W] L : the air flow rate through the conditioned space, 𝑚3 / 𝑠 From homework 1, L in depressive areas is 0.045 𝑚3/𝑠 ,and L in compressive areas is 0.117 𝑚3/𝑠 𝜌 : Density of the air , 𝜌 = 1.2 𝑘𝑔/𝑚3 C 𝑝 : The heat capacity of the air , 𝐶𝑝 = 1006 𝐽/𝑘𝑔∙𝐾 Since J = W∙s, the unit is same as 𝑊∙𝑠/𝑘𝑔∙𝐾 In these above two equations, 𝒕 internal −𝒕 external has the biggest impact on the equations. Measurements used in the following calculations: Brick wall : 0.20 m Wall Isolator : 0.07 m Roof concrete : 0.20 m Roof Isolator : 0.07 m Floor : 0.10 m Floor Isolator : 0.07 m Secondary gazing low-emission glass window Thermal conductivity of concrete: 0.11 𝑊/𝑚∙𝐾 Thermal conductivity of solid brick: 0.80 𝑊/𝑚∙𝐾 Typical insulation material: 0.04𝑊/𝑚∙𝐾 For windows and doors, 𝑈𝑗= 1.8 𝑤/𝑚2∙𝐾

7. Room1 (Bedroom 1) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((3+0.27+4+0.27)-(1.7+2.5)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x (3.34 x 2.5) x 31℃ = 298.97175 [W] ≒ 298.97 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (3+0.27)(4+0.27) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 13.9629 x 31℃ = 192.1853556 [W] ≒ 192.19 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (3+0.27)(4+0.27) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 13.9629 x 5℃ = 34.90 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (1.7 x 2.5)∙ {20℃-(-11℃)} = 171.27 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚1 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 298.97 [W] + 192.19 [W] + 34.90 [W] + 171.27 [W] + 4378.51 [W] = 3514.988 [W]

8. Room 2 (Bathroom) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((3+0.27+3)-(0,75+1,70)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x 23.875 x 31℃ = 341.93775 [W] ≒ 341.93 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (3+0.27)(3) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 9.81 x 31℃ = 135.02484 [W] ≒ 135.02 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (3+0.27)(3) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 9.81 x 5℃ = 24.52 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (0.75 x 1.7)∙ {20℃-(-11℃)} = 51.38 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.045 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 1684.04 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚 2 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 341.93 [W] + 135.02 [W] + 24.52 [W] + 51.38 [W] + 1684.04 [W] = 2236.89 [W]

9. Room 3 (Bedroom 2) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((4+0.27+3)-(1.8+1.7)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x (3.77 x 2.5) x 31℃ = 134.98485 [W] ≒ 134.98 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (4+0.27)(3) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 12.81 x 31℃ = 176.31684 [W] ≒ 176.31 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (4+0.27)(3) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 12.81 x 5℃ = 32.02 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (1.8 x 1.7) x {20℃-(-11℃)} = 123.31 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚3 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 134.98 [W] + 176.31 [W] + 32.02 [W] + 123.31 [W] + 4378.51 [W] = 4845.13 [W]

10. Room 4 (Bedroom 3) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((3+0.27+4+0.27)-(1.5+1.7)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x (4.34 x 2.5) x 31℃ = 155.3937 [W] ≒ 155.39 [/W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (3+0.27)(4+0.27) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 13.9629 x 31℃ = 192.1853556 [W] ≒ 192.19 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (3+0.27)(4+0.27) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 13.9629 x 5℃ = 34.90 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (1.5 x 1.7)∙ {20℃-(-11℃)} = 102.76 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚 4 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 155.39 [W] + 192.19 [W] + 34.90 [W] + 102.76 [W] + 4378.51 [W] = 4863.75 [W]

11. Room 5 (Guess Bathroom) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((1.25+0.27+3.2)-(0,80+1,70)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x 13.875 x 31℃ = 198.71775 [W] ≒ 198.71 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (1.25+0.27)(3.2) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 4.864 x 31℃ = 66.9480 [W] ≒ 66.94[W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (1.25+0.27)(3.2) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 4.864 x 5℃ = 12.16 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (0.80 x 1.7)∙ {20℃-(-11℃)} = 54.80 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.045 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 1684.04 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚 5 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 198.71 [W] + 66.94 [W] + 12.16 [W] + 54.80 [W] + 1684.04 [W] = 2016.65 [W]

12. Room 6 (Hallway) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((15.5+0.27)-(1.0+2.4)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x (12.37 x 2.5) x 31℃ = 1107.269625 [W] ≒ 1107.26 [/W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (15.5+0.27) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 15.77 x 31℃ = 217.05828 [W] ≒ 217.05 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x 15.77 x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 15.77 x 5℃ = 39.42 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, door = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (1.0 x 2.4)∙ {20℃-(-11℃)} = 96.72 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚6 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑑𝑜𝑜𝑟 + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 1107.26 [W] + 217.05 [W] + 39.42 [W] + 96.72 [W] + 4378.51 [W] = 5838.96 [W]

13. Room 7 & 8 Living Room & Dining Room) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((5+0.27+7.5+0.27)-(4.9+3.5)(2.5)) x {20℃+11℃)} = 0.462 𝑤/𝑚2∙℃ x (4.64 x 2.5) x 31℃ = 166.1352 [W] ≒ 166.13 [/W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (5+0.27)(7.5+0.27) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 40.9479 x 31℃ = 563.6068956 [W] ≒ 563.61 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (5+0.27)(7.5+0.27) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 40.9479 x 5℃ = 102.37 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, door = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (2.5 x 2.4)(1.8 x 1.7) ∙ {20℃-(-11℃)} = 739.90 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚6 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑑𝑜𝑜𝑟 + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 166.13 [W] + 563.61 [W] + 102.37 [W] + 739.90 [W] + 4378.51 [W] = 5950.52 [W]

14. Room 9 (Kitchen) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((2.5+0.27+3.2+0.27)-(2.7+3.4)(2.5)) x {20℃+11℃)} = 0.462 𝑤/𝑚2∙℃ x 0.875 x 31℃ = 12.488784 [W] ≒ 12.49 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (2.5+0.27)(3.2+0.27) x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 9.6119 x 31℃ = 132.2981916 [W] ≒ 132.30 [W] \ Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (2.5+0.27)(3.2+0.27) x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 9.6119 x 5℃ = 24.03 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, door = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (1.0 x 1.7) (1.0 x 2.4) ∙ {20℃-(-11℃)} = 164.42 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.045 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 1684.04 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚 2 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑑𝑜𝑜𝑟 + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 12.49 [W] + 132.30 [W] + 24.03 [W] + 164.42 [W] + 1684.04 [W] = 2017.28 [W]

15. Room 10 (Utility Room) External Wall: U = 1 / (1/24 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.462 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.462 𝑤/𝑚2∙℃ x ((2.5+0.27+3.2)-(0.50+1.70)(2.5)) x {20℃-(-11℃)} = 0.462 𝑤/𝑚2∙℃ x (3.77 x 2.5) x 31℃ = 134.98485 [W] ≒ 134.99 [W] Ceiling: U = 1 / (1/8 + 0.2/0.8 + 0.07/0.04+1/8) ≒ 0.444 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, ceiling = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.444 𝑤/𝑚2∙℃ x (2.5+0.27) 3.2 x {20℃-(-11℃)} = 0.444 𝑤/𝑚2∙℃ x 8.864 x 31℃ = 122.004096 [W] ≒ 122.00 [W] Floor: U = 1 / (1/8 + 0.1/0.8 + 0.07/0.04) ≒ 0.5 𝑤/𝑚2∙℃ Q 𝑡𝑟𝑎𝑛𝑠, external 𝑤𝑎𝑙𝑙 = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 0.5 𝑤/𝑚2∙℃ x (2.5+0.27) 3.2 x {20℃-15℃)} = 0.5 𝑤/𝑚2∙℃ x 8.864 x 5℃ = 22.16 [W] Windows / Doors: Q 𝑡𝑟𝑎𝑛𝑠, window = 𝑼𝒋 x 𝑨𝒋 x (𝒕 internal −𝒕 external) = 1.3 𝑤/𝑚2∙𝐾 x (0.5 x 1.7)∙ {20℃-(-11℃)} = 34.25 [W] Ventilation: Q 𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 𝐿∙𝜌∙𝐶𝑝∙ (𝒕 internal −𝒕 external) = 0.117 𝑚3/𝑠 ∙ 1.2 𝑘𝑔/𝑚3 ∙ 1006 𝑊∙𝑠/𝑘𝑔∙𝐾 ∙ {20℃-(-11℃)} ≒ 4378.51 [W] Q 𝑡𝑟𝑎𝑛𝑠,𝑠𝑢𝑚,𝑟𝑜𝑜𝑚1 = 𝑄𝑡𝑟𝑎𝑛𝑠,𝑤𝑎𝑙𝑙 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑐𝑒𝑖𝑙𝑖𝑛𝑔 + 𝑄𝑡𝑟𝑎𝑛𝑠,𝑓𝑙𝑜𝑜𝑟 + 𝑄𝑡𝑟𝑎𝑛𝑠, window + 𝑄𝑣𝑒𝑛𝑡𝑖𝑙𝑎𝑡𝑖𝑜𝑛 = 134.99 [W] + 122.00 [W] + 22.16 [W] + 34.25 [W] + 4378.51 [W] = 4691.91 [W]

16. Chosen Radiators Function Watts [W] Radiators Bedroom 1 3514.988 [W] Kos H type 33 : 1500x600 : 3713 [W] Bathroom 2236.89 [W] MAU 22 09 : 2560 [W] Bedroom 2 4845.13 [W] Kos H type 33 : 1500x900 : 4902 [W] Bedroom 3 4863.75 [W] Kos H type 33 : 1500x900 : 4902 [W] Guess Bathroom 2016.65 [W] IMI 18 12 : 2274 [W] Living Room & Dining Room 5950.52 [W] Kos H type 33 : 1950x900 : 6372 [W] Utility Room 4691.91 [W] Kos H type 33 : 1950x600 : 4826 [W]