Building Envelope Heat Transfer & Thermal Performance Analysis

Building Envelope Heat Transfer & Thermal Performance Analysis

Building envelope thermal performance determines heating and cooling loads, occupant comfort, and energy efficiency. This guide covers heat transfer mechanisms, U-value calculations, thermal bridging, fenestration performance, infiltration, and moisture control for residential and commercial building design.

Heat Transfer Mechanisms

Steady-State Conduction Through Walls

Fourier’s Law (one-dimensional conduction):

$$q = -k \cdot A \cdot \frac{dT}{dx}$$

Where:

• $q$ = heat transfer rate (Btu/hr)
• $k$ = thermal conductivity (Btu·in/hr·ft²·°F or Btu/hr·ft·°F)
• $A$ = area (ft²)
• $dT/dx$ = temperature gradient (°F/ft)

For composite wall (series resistance):

$$q = \frac{A \cdot \Delta T}{R_{total}} = U \cdot A \cdot \Delta T$$

Where:

• $R_{total}$ = total thermal resistance (ft²·°F·hr/Btu)
• $U$ = overall heat transfer coefficient (Btu/hr·ft²·°F)
• $\Delta T$ = temperature difference (°F)

Total resistance:

$$R_{total} = R_{out} + R_{1} + R_{2} + … + R_{n} + R_{in}$$

Where:

• $R_{out}$ = exterior surface film resistance
• $R_{1}, R_{2}, …$ = material layer resistances
• $R_{in}$ = interior surface film resistance

Surface film coefficients (still air):

Material resistance:

$$R = \frac{L}{k}$$

Where:

• $L$ = thickness (ft or in)
• $k$ = thermal conductivity (Btu/hr·ft·°F or Btu·in/hr·ft²·°F)

U-Value Calculation

Overall heat transfer coefficient:

$$U = \frac{1}{R_{total}}$$

Example: Insulated wall assembly:

graph LR
    A[Outdoor Air<br/>T_out] -->|R_out<br/>0.17| B[Brick Veneer<br/>4 in]
    B -->|R_air<br/>Air space| C[Sheathing<br/>1/2 in]
    C -->|R_insulation<br/>Cavity insulation| D[Drywall<br/>1/2 in]
    D -->|R_in<br/>0.68| E[Indoor Air<br/>T_in]

Resistance calculation:

U-value: $U = 1/22.92 = 0.044$ Btu/hr·ft²·°F

Thermal Bridging

Thermal bridge: Conductive path through insulation (studs, structural members)

Effect: Local U-value increase, condensation risk, reduced overall R-value

Parallel Path Method

For walls with framing:

$$U_{effective} = (U_{cavity} \times f_{cavity}) + (U_{framing} \times f_{framing})$$

Where:

• $f_{cavity}$ = fraction of wall area with cavity insulation
• $f_{framing}$ = fraction of wall area with framing (studs)

Typical framing fractions:

• 2×4 studs @ 16" o.c.: 15-20% framing
• 2×6 studs @ 24" o.c.: 10-15% framing
• Steel studs @ 16" o.c.: 25% framing (worse thermal bridging)

Example:

• Cavity R-value: R-19 (fiberglass between studs)
• Framing R-value: R-5 (wood studs through cavity)
• Framing fraction: 15%

$$U_{eff} = (1/19 \times 0.85) + (1/5 \times 0.15) = 0.045 + 0.030 = 0.075$$

$$R_{eff} = 1/0.075 = 13.3$$

Thermal bridging reduces R-19 wall to effective R-13.3 (30% reduction)

Mitigation Strategies

1. Continuous exterior insulation: Eliminates thermal bridges

   • Rigid foam over sheathing (1-2 in typical)
   • Adds R-5 to R-10 without bridging

2. Advanced framing: Reduce framing fraction

   • 24" o.c. spacing instead of 16"
   • Single top plate, eliminate headers on non-bearing walls
   • Reduces framing to 10-12%

3. Structural insulated panels (SIPs): Minimal thermal bridging

   • Effective R-value ≈ 95% of nominal

4. Thermal break in steel framing: Critical for metal buildings

   • Z-girts with thermal spacers
   • Exterior insulation over studs

Fenestration Performance

Window and Glazing U-Values

Window performance metrics:

• U-factor: Overall heat transfer coefficient (lower is better)
• SHGC (Solar Heat Gain Coefficient): Fraction of solar radiation transmitted (0-1)
• VT (Visible Transmittance): Fraction of visible light transmitted (0-1)

Typical residential window U-factors (NFRC rated):

Low-emissivity (low-E) coating: Reduces radiant heat transfer between panes

• $\epsilon$ = 0.84 (clear glass)
• $\epsilon$ = 0.10 (hard-coat low-E)
• $\epsilon$ = 0.04 (soft-coat low-E)

Gas fill: Argon or krypton between panes reduces conduction

• Air: k = 0.015 Btu/hr·ft·°F
• Argon: k = 0.010 Btu/hr·ft·°F (reduces U-factor ~10%)
• Krypton: k = 0.005 Btu/hr·ft·°F (expensive, thin gaps)

Solar Heat Gain

Solar heat gain through windows:

$$Q_{solar} = A_{window} \times SHGC \times I_{solar}$$

Where:

• $A_{window}$ = glazing area (ft²)
• $SHGC$ = solar heat gain coefficient (0-1)
• $I_{solar}$ = incident solar radiation (Btu/hr·ft²)

Peak solar radiation (clear day, perpendicular surface):

• South-facing vertical: 200-250 Btu/hr·ft² (winter)
• West-facing vertical: 180-220 Btu/hr·ft² (summer afternoon)
• Horizontal (roof): 250-300 Btu/hr·ft² (summer)

Shading coefficient (older metric):

$$SC = \frac{SHGC_{actual}}{SHGC_{reference}} \approx 1.15 \times SHGC$$

Where reference is single clear glass (SHGC ≈ 0.87)

Infiltration and Air Leakage

Air Leakage Measurement

Blower door test: Pressurize building to 50 Pa, measure airflow

Metrics:

• ACH50: Air changes per hour at 50 Pa pressure
• CFM50: Cubic feet per minute leakage at 50 Pa

Typical ACH50 values:

• Existing homes (no air sealing): 8-15 ACH50
• Standard new construction: 4-7 ACH50
• Energy Star homes: 3-5 ACH50
• Passive House: < 0.6 ACH50

Conversion to natural infiltration:

$$ACH_{natural} = \frac{ACH_{50}}{N}$$

Where $N$ = 20 typical (depends on climate, shielding, height)

Infiltration heat loss:

$$Q_{inf} = \rho \cdot c_p \cdot V \cdot ACH \cdot \Delta T$$

Simplified:

$$Q_{inf} = 1.08 \times CFM_{inf} \times \Delta T$$

Thermal Mass Effects

Thermal mass: Material capacity to store and release heat

Heat storage capacity:

$$Q_{stored} = m \cdot c_p \cdot \Delta T = \rho \cdot V \cdot c_p \cdot \Delta T$$

Where:

• $\rho$ = density (lb/ft³)
• $c_p$ = specific heat (Btu/lb·°F)
• $V$ = volume (ft³)

Volumetric heat capacity:

$$C_v = \rho \cdot c_p$$

Materials:

Benefit: Thermal mass dampens temperature swings, reduces peak loads

Example: Concrete floor slab (4 in thick, 1,000 ft²)

• Volume: $1,000 \times 4/12 = 333$ ft³
• Mass: $333 \times 140 = 46,667$ lb
• Heat capacity: $46,667 \times 0.20 = 9,333$ Btu/°F

Temperature swing reduction: 10°F swing → 5°F swing with thermal mass

Moisture Control and Condensation

Vapor Diffusion

Fick’s Law (vapor diffusion):

$$\dot{m}_v = -M \cdot A \cdot \frac{dP_v}{dx}$$

Where:

• $\dot{m}_v$ = vapor mass flow rate (lb/hr)
• $M$ = permeance (perm = grains/hr·ft²·in Hg)
• $dP_v/dx$ = vapor pressure gradient

Permeability: $M = \mu/L$ (material property / thickness)

Vapor retarder classifications:

• Class I (impermeable): < 0.1 perm (polyethylene sheet, foil)
• Class II (semi-impermeable): 0.1-1.0 perm (kraft paper, some paints)
• Class III (semi-permeable): 1-10 perm (latex paint)

Condensation Risk

Dewpoint temperature: Temperature at which moisture condenses

At each layer interface, check:

$$T_{interface} > T_{dewpoint}$$

If $T_{interface} < T_{dewpoint}$, condensation occurs.

Condensation prevention strategies:

1. Warm-side vapor retarder: Prevent moisture entry into wall
2. Exterior insulation: Keep sheathing warm (above dewpoint)
3. Ventilation: Remove moisture from building
4. Dehumidification: Control indoor humidity (< 40% RH winter)

Related Technical Guides:

• Material Thermal Properties
• Heat Transfer Fundamentals
• Heating Load Calculations
• Cooling Load Calculations
• Psychrometric Fundamentals

References:

• ASHRAE Fundamentals Handbook, Chapter 26: Heat, Air, and Moisture Control in Building Assemblies
• ASHRAE Fundamentals Handbook, Chapter 25: Thermal and Water Vapor Transmission Data
• Building Science Corporation: www.buildingscience.com
• Lstiburek, J., “Builder’s Guide to Cold Climates”
• Straube, J., “High Performance Enclosures”