Building Physics & the Building Envelope

How heat, air and moisture move through buildings. Learn conduction, convection and radiation in buildings, thermal resistance and U-values of layered walls and roofs, thermal mass and time lag, solar heat gain through glazing (SHGC, WWR, shading), sol-air temperature, infiltration, condensation and dew point, insulation materials, cool roofs, and envelope performance under ECBC — with Python for U-values, the effect of insulation and envelope heat gain.

The envelope — walls, roof, floors, windows — separates indoors from outdoors. Its thermal performance determines how much cooling or heating a building needs and how comfortable it is.

In hot Indian climates, the roof and west-facing glass are the biggest heat sources; insulation, shading and reflective surfaces can cut cooling loads dramatically.

An analogy

A building envelope is like clothing: insulation is a woollen layer slowing heat flow, a reflective roof is like a white shirt in the sun, windows are like holes in the fabric, and shading devices are a hat.

Heat transfer in buildings

Heat enters or leaves by conduction through walls and roofs, convection with air leakage and ventilation, and radiation (sunlight through windows, long-wave exchange with the sky). Internal gains from people, lights and equipment add more. Resistances add in series; U-value is the inverse of total resistance.

Windows and shading

Glazing is usually the weakest part of the envelope:

Thermal mass and roofs

Heavy materials (brick, concrete, stone) store heat and delay its passage (time lag of 6–10 h for thick walls), useful in hot-dry climates with cool nights. Roofs receive the most solar radiation: insulation, cool roofs (high solar reflectance, e.g. white coatings), green roofs and roof shading reduce top-floor heat gain dramatically.

Air and moisture

Infiltration through cracks adds heat and humidity; airtightness is tested with blower-door tests (ACH50). Interstitial condensation occurs where temperature falls below dew point inside a wall — vapour barriers go on the warm, humid side. Thermal bridges (slab edges, columns, window frames) short-circuit insulation. Dynamic simulation (EnergyPlus, DesignBuilder) captures transient effects and verifies ECBC compliance.

Formulas

Worked example: Layer resistance

Given: 75 mm XPS, k 0.03

Find: R.

Answer: 2.5 m²K/W

Worked example: Solar gain

Given: 20 m² west glass, SHGC 0.6, I 500 W/m²

Find: Q.

Answer: 6.0 kW

Worked example: Conduction gain

Given: Roof 200 m², U 3.3, ΔT_sa 25 K

Find: Q.

Answer: 16.5 kW

U-value of a brick wall with and without insulation

# Building physics: U-value of a wall and heat gain through the envelope
layers = [("outside surface", None, None, 0.04), ("plaster 15 mm", 0.015, 0.72, None),
          ("brick 230 mm", 0.230, 0.81, None), ("plaster 12 mm", 0.012, 0.72, None), ("inside surface", None, None, 0.13)]
R_total = 0.0
for name, t, k, R in layers:
    r = R if R is not None else t / k
    R_total += r
    print(f"{name:16s} R = {r:.3f} m2K/W")
U = 1 / R_total
print(f"R total {R_total:.3f} -> U = {U:.2f} W/m2K")
# Add 50 mm EPS insulation (k 0.035)
U_ins = 1 / (R_total + 0.05 / 0.035)
print(f"with 50 mm EPS: U = {U_ins:.2f} W/m2K ({(1-U_ins/U)*100:.0f}% less heat flow)")
# Heat gain through 100 m2 of wall, sol-air temperature difference 15 K
print(f"heat gain: {U*100*15/1000:.2f} kW -> {U_ins*100*15/1000:.2f} kW insulated")
# outside surface  R = 0.040 m2K/W
# plaster 15 mm    R = 0.021 m2K/W
# brick 230 mm     R = 0.284 m2K/W
# plaster 12 mm    R = 0.017 m2K/W
# inside surface   R = 0.130 m2K/W
# R total 0.491 -> U = 2.03 W/m2K
# with 50 mm EPS: U = 0.52 W/m2K (74% less heat flow)
# heat gain: 3.05 kW -> 0.78 kW insulated

A traditional 230 mm brick wall has U ≈ 2.0 W/m²K — ECBC requires ≤ 0.40 for walls in many climate zones. Just 50 mm of EPS cuts heat flow by 74%, because its resistance (1.43 m²K/W) dwarfs the brick's. The same logic applies even more strongly to roofs, which receive the most sun.

Common mistakes

Applications

Key takeaways

Going further