Natural environment: sun, wind and climate
Every place has a climate: its usual temperature, rain, wind and sunshine. A building is designed to work with the climate.
- Sun: high in summer, low in winter. An eave or louvre blocks the high sun and lets the low sun in.
- Wind: carries fresh air. Windows on opposite sides use it for ventilation.
- Ground and trees: shade and cool the surroundings.
Indoor environment: what we feel
Four things decide comfort indoors.
- Temperature and humidity: most people feel good at about 22 to 26 °C.
- Light: daylight from windows saves electricity; glare is bad.
- Air quality: people breathe out carbon dioxide, so fresh air must come in. Ventilation is measured in air changes per hour (ACH) = airflow (m³/h) ÷ room volume (m³).
- Sound: thick walls and shut windows cut noise.
Fluid mechanics: how air moves
Air is a fluid. It moves for two reasons.
- Wind pressure: air flows from a high-pressure side to a low-pressure side, so it goes in at the windward window and out at the other.
- Buoyancy (stack effect): warm air is less dense and rises. It leaves through high openings and pulls cool air in through low ones. The taller the building, the stronger the effect.
In ducts, flow rate Q = A × v (area × speed). If the duct narrows, the air speeds up.
Thermal mechanics: how heat moves
Heat always flows from the hotter to the colder place in three ways.
- Conduction: through solids like walls.
- Convection: carried by moving air or water.
- Radiation: as rays, like the sun on your face.
Heat flow through a wall: Q = U × A × ΔT in watts. U is the U-value in W/(m²·K): small U means a good insulator. A is area in m². ΔT is the temperature difference between inside and outside in K (same size as °C). To warm air: Q = m × c × ΔT, with c ≈ 1000 J/(kg·K) for air and density about 1.2 kg/m³.
Key formulas and definitions
- Heat flow through a wall: Q = U × A × ΔT (watts)
- Wall layers in series: R_total = R1 + R2 + …, U = 1 ÷ R_total
- Air changes per hour: ACH = airflow (m³/h) ÷ room volume (m³)
- Duct flow rate: Q = A × v (m³/s)
- Heat to warm air: Q = m × c × ΔT, with m = density × volume
Worked examples
1. A wall of area 10 m² has U = 1.2 W/(m²·K). Inside is 25 °C, outside 5 °C. Find the heat flow.
ΔT = 25 − 5 = 20 K. Q = 1.2 × 10 × 20 = 240 W.
2. How much energy does that wall lose in one day?
240 W × 24 h = 5760 Wh = 5.76 kWh.
3. The same wall gets insulation and U falls to 0.3 W/(m²·K). New heat flow?
Q = 0.3 × 10 × 20 = 60 W. It is a quarter of before.
4. A room is 4 m × 5 m × 3 m. A fan moves 120 m³ of air per hour. Find ACH.
Volume = 60 m³. ACH = 120 ÷ 60 = 2 air changes per hour.
5. A duct of area 0.2 m² carries air at 2 m/s. Find the flow rate. If the duct narrows to 0.1 m², what is the speed?
Q = 0.2 × 2 = 0.4 m³/s. Same Q at 0.1 m²: v = 0.4 ÷ 0.1 = 4 m/s.
6. A wall has brick R = 0.4 and insulation R = 1.6 (m²·K/W). Find U.
R_total = 0.4 + 1.6 = 2.0. U = 1 ÷ 2.0 = 0.5 W/(m²·K).
7. How much heat warms the 60 m³ of air in the room above by 10 K? (density 1.2 kg/m³, c = 1000 J/(kg·K))
m = 1.2 × 60 = 72 kg. Q = 72 × 1000 × 10 = 720 000 J = 720 kJ.
Common mistakes
- Using °C difference wrongly: ΔT is outside minus inside (or the reverse) as a positive number; the sign only shows direction.
- Thinking cold "enters" a room. Heat leaves; cold is only the absence of heat.
- Adding U-values of layers. Add the R-values, then take 1 ÷ R_total.
- Thinking closed rooms are best. Without ventilation, stale air and moisture build up.