Heat gain calculations-after passive improvements

1.Roof

T s= T o+ ( I ×a)f o

= 36 +( 1000×0.65

56 )

= 36 + 11.61 = 47.61° C

Area = 13.4m×10.2m = 136.68m2

Qc= A×U × ∆T = 136.68 × 0.62 × (47.61-32) = 136.68 × 0.62 × 15.61 = 1322.82 watts

2.Wall

(a) North-West wall (Exposed)

T s= T o+ ( I ×a)f o

= 36 +( 400×0.518.9 )

= 36 + 10.58 = 46.58° C

Area = (5m×3m) – (2.4m×2m¿−¿(1.5m×2.5m)¿−¿(0.03m×15m) = 6m2

Qc= A×U ×∆T = 6× 3.24× (46.58-32) = 6×3.24×14.58°C = 283.8watts

(b) North-East wall (Sheltered)

Area = 4.4m×3m = 13.2m2

Qc= A×U ×∆T = 13.2× 3.24× (36-32)

= 13.2×3.24×4°C = 171watts

(c) South-East wall (Exposed)

T s= T o+ ( I ×a)f o

= 36 +( 350×0.518.9 )

= 36 + 9.26 = 45.26° C

Area = (3.4m×3m) – (2.2m×1.5m¿ = 6.9m2

Qc= A×U × ∆T = 6.9 × 3.24 × (45.26-32) = 6.9 × 3.24 × 13.26 = 296.44 watts

(d) South-West wall (Exposed)

T s= T o+ ( I ×a)f o

= 36 +( 620×0.518.9 )

= 36 + 16.4 = 52.4° C

Area = (9.2m×3m)–(3.8m×2.6m¿ – (1.8m×0.7m)– (1.4m×1.8m) – (0.03m×15m) = 13.49m2

Qc= A×U × ∆T = 13.49 × 3.24 × (52.4-32) = 13.49 × 3.24 × 20.4 = 891.6 watts

3.Window

(a) North-West window (Exposed)

Area = 2.4m×2m = 4.8m2

Qc= A×U ×∆T = 4.8× 5.67× (36-32) = 4.8×5.67×4°C

= 108.86watts

(b) South-East window (Exposed)

Area = 2.2m×1.5m = 3.3m2

Qc= A×U ×∆T = 3.3× 4.48× (36-32) = 3.3×4.48×4°C = 59.14watts

(c) South-West window 1 (Exposed)

Area = 1.8m×0.7m = 1.26m2

Qc= A×U ×∆T = 1.26× 1.25× (36-32) = 1.26×1.25×4°C = 6.3watts

(d) South-West window 2 (Exposed)

Area = 1.8m×1.4m = 2.52m2

Qc= A×U ×∆T = 2.52× 1.25× (36-32) = 2.52×1.25×4°C = 12.6watts

4.Door

(a) North-West Door (Exposed)

T s= T o+ ( I ×a)f o

= 36 +( 400×0.1618.9 )

= 36 + 3.4 = 39.4° C

Area = 2.5m×1.5m = 3.75m2

Qc= A×U × ∆T = 3.75 × 1.8 × (39.4-32) = 3.75 × 1.8 × 7.4 = 49.95 watts

(b) South-West Door (Exposed)

Area = 3.8m×2.6m = 9.88m2

Qc= A×U ×∆T = 9.88×4.48× (36-32) = 9.88×4.48×4°C = 177.05watts

Total Qc= 1322.82 watts + 283.8watts + 171 watts + 296.44 watts + 891.6 watts + 108.86 watts + 59.14 watts + 6.3 watts + 12.6 watts + 49.95 watts + 177.05= 3379.56 watts

(a) North-West Window

Qs= A ×I ×θ = (2.4 ×2) ×400 × 0.8 = 4.8 ×400 × 0.8 =1536 watts

(b) South-East Window

Qs= A ×I ×θ = (2.2 ×1.5) ×350 × 0.8 = 3.3 ×350 × 0.8 =924 watts

Total Qs= 1536 + 924 = 2460 watts

V = N ×roomvol .

3600

= 2×(1.34×5×3)3600

= 2×20.13600

= 0.11 m3/s

Qv= 1300 ×v×∆T = 1300 ×0.11× (36−32 ) = 1300 ×0.11×4 = 572 watts

5 occupants Qi= lighting + people + fan = [3 ×80%(40)¿ + (5 ×150¿ + 70 = 96 + 750 + 70 = 916 watts

Total Heat Gain = Qc +Qs +Qv+ Qi= 3379.56 watts + 2460watts + 572 watts + 916 watts= 7327.56 watts= 9.83 hp