5.2 Fenestration, Opaque Envelope & Internal Heat Gains

Fenestration, Opaque Envelope & Internal Heat Gains

Core Principle: Peak residential heat gain consists of external envelope loads (solar radiant gain, fenestration conduction, opaque wall/roof conduction, and foundation heat transfer) combined with internal gains (occupants, lighting, plug loads, and appliances). Each component must be separated into sensible heat (which raises dry-bulb temperature) and latent heat (which adds airborne moisture).

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Fenestration Heat Transfer (Windows, Glazed Doors & Skylights)

Fenestration is the most critical dynamic thermal component in residential load calculation. Glazed surfaces transmit heat through two concurrent mechanisms:

1. Conductive / Convective Heat Transmission ($q_{\text{cond}}$): $q_{\text{cond}} = U_{\text{window}} \times A_{\text{window}} \times \Delta T$
2. Solar Radiation Heat Gain ($q_{\text{solar}}$): $q_{\text{solar}} = A_{\text{window}} \times \text{SHGC} \times \text{SLF} \times \text{IAC}$
   • $\text{SHGC}$ (Solar Heat Gain Coefficient): The fraction of incident solar radiation admitted through a window, both directly transmitted and absorbed and released inward. Ranges from $0.0$ to $1.0$ (lower values mean less solar heat gain).
   • $\text{SLF}$ (Solar Load Factor): The peak solar irradiance value ($\text{BTU}/(\text{hr}\cdot\text{ft}^2)$) from Manual J Table 3, which varies by compass orientation (North, South, East, West, NE, NW, SE, SW), latitude, and month.
   • $\text{IAC}$ (Internal Appurtenance Coefficient): A multiplier accounting for internal shading devices (such as light-colored horizontal blinds, blackout drapes, or solar screens, typically $0.45 - 0.85$).

North Carolina Energy Conservation Code Fenestration Mandates

Under NCECC Table R402.1.2, replacement and new residential fenestration must satisfy strict prescriptive thermal thresholds:

Impact of Window Orientation on Peak Cooling Loads

Solar heat gain varies dramatically depending on window orientation:

• East-Facing Windows: Experience peak solar radiation in the early morning ($8:00\text{ AM} - 10:00\text{ AM}$) when outdoor dry-bulb temperatures are relatively low.
• West-Facing Windows: Experience peak solar radiation in the late afternoon ($3:00\text{ PM} - 5:00\text{ PM}$) which coincides exactly with the daily maximum outdoor dry-bulb temperature, creating the highest combined cooling load spikes in North Carolina homes.
• South-Facing Windows: Experience high solar angles in summer (causing lower direct gain if shaded by modest overhangs) but low solar angles in winter (providing beneficial passive solar heating).
• North-Facing Windows: Receive almost exclusively diffuse ambient sky radiation with minimal direct solar beam irradiance.

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Opaque Envelope Components: Walls, Roofs & Sol-Air Effects

Sol-Air Temperature & Cooling Load Temperature Difference (CLTD)

Sunlight striking opaque exterior surfaces (dark asphalt shingles, dark brick, fiber cement siding) heats the surface far above the ambient outdoor dry-bulb air temperature. This combined convective and radiant effect is defined as the sol-air temperature ($T_{\text{sol-air}}$).

In Manual J, this is simplified through Cooling Load Temperature Differences (CLTD) or direct Heat Transfer Multipliers (HTM):

$q = U \times A \times \text{CLTD} \quad \text{or} \quad q = A \times \text{HTM}$

• Attic / Ceiling Dynamics: An unconditioned attic under dark asphalt shingles in a North Carolina summer can reach temperatures of $130^\circ\text{F} - 140^\circ\text{F}$. With $R-38$ ceiling insulation, the temperature difference driving heat down into the living space is $\Delta T = 130^\circ\text{F} - 75^\circ\text{F} = 55^\circ\text{F}$, compared to an outdoor ambient $\Delta T$ of only $17^\circ\text{F}$.
• Radiant Barriers: Installing an approved radiant barrier (emittance $\epsilon \le 0.05$) under the roof decking reduces radiant transfer from the hot roof deck to the top of ceiling insulation, lowering attic air temperatures by $15^\circ\text{F} - 25^\circ\text{F}$ and reducing ceiling cooling loads.

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Foundation Heat Losses: Slabs, Basements & Crawlspaces

Foundations interact with the earth, which has substantial thermal mass. Heat loss is not modeled by simple one-dimensional outdoor $\Delta T$.

1. Slab-on-Grade Floors

In slab-on-grade construction, downward heat loss through the center of the concrete slab is minimal because the ground underneath stabilizes near deep-ground temperature ($55^\circ\text{F} - 60^\circ\text{F}$). Almost all heat loss occurs laterally through the exposed perimeter edge to ambient winter air.

Manual J calculates slab design heating loss using the slab perimeter formula:

$q_{\text{slab}} = F_p \times P \times (T_{\text{indoor}} - T_{\text{outdoor, heat}})$

where:

• $F_p$ = Slab perimeter heat loss coefficient ($\text{BTU}/(\text{hr}\cdot\text{linear ft}\cdot^\circ\text{F})$).
• $P$ = Length of the exposed exterior slab perimeter (linear feet).
• $\Delta T = 70^\circ\text{F} - T_{\text{outdoor, heat}}$.

2. Vented Crawlspaces vs. Closed (Conditioned) Crawlspaces

North Carolina homes feature two distinct crawlspace configurations:

• Vented Crawlspaces: Open foundation vents expose the subfloor to outdoor ambient temperatures and humid summer air. The floor above must be insulated to $R-19$ (Zone 4) or $R-13$ (Zone 3). In summer, hot humid air entering through vents condenses on cold ductwork and floor joists, creating severe moisture problems.
• Closed / Conditioned Crawlspaces (NCRC Section R408.3 & Appendix E): Vents are completely eliminated. The ground is covered with a continuous, sealed minimum $6\text{ mil}$ (or $10\text{ mil}$) vapor retarder turned up $6"$ on foundation walls. Foundation perimeter walls are insulated with $R-10$ continuous rigid foam or $R-13$ cavity insulation. The crawlspace is conditioned with either supply air ($1\text{ CFM}$ per $50\text{ sq ft}$ of crawlspace area) or a dedicated crawlspace dehumidifier. The living space floor requires no subfloor insulation, and floor heat loss is virtually eliminated.

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Internal Heat Gains (Sensible & Latent)

Internal heat gains originate from people, appliances, and lighting inside the conditioned envelope. These gains increase cooling loads and are credited in full during summer, but are generally excluded from heating load calculations to ensure heating systems can warm the structure when unoccupied.

1. Occupant Heat Gains (Manual J Bedroom Rule)

Manual J standardizes residential occupant allowances based on the physical capacity of the home:

$\text{Design Occupants} = N_{\text{bedrooms}} + 1$ (Example: A 3-bedroom home is designed for $3 + 1 = 4$ occupants; a 4-bedroom home is designed for $4 + 1 = 5$ occupants).

Heat generated per sedentary occupant:

• Sensible Heat: $230\text{ BTU/h}$ per person
• Latent Heat: $200\text{ BTU/h}$ per person
• Total Heat: $430\text{ BTU/h}$ per person

2. Appliance & Plug Load Allowances

• Standard Kitchen Appliance Baseline: $1{,}200\text{ BTU/h sensible}$ and $0\text{ BTU/h latent}$ (assumes range hood exhaust fan discharges cooking moisture outdoors).
• Additional Kitchen / Bar Refrigerators: $400\text{ BTU/h}$ sensible each.
• Home Electronics & Computers: Actual rated wattage $\times 3.412\text{ BTU/h per Watt}$ (or default Manual J allowances of $400 - 800\text{ BTU/h}$ for home office equipment).

3. Lighting Heat Gains

Lighting generates purely sensible heat: $q_{\text{lighting}} = \text{Total Watts} \times 3.412\text{ BTU/h per Watt}$ Under modern energy codes utilizing high-efficacy LED lighting, standard Manual J residential lighting allowance is typically $0.80\text{ BTU}/(\text{hr}\cdot\text{sq ft})$ or based on actual connected fixtures.

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Comprehensive Worked Example: Envelope & Internal Cooling Load

Problem Data (Living Room in Raleigh, NC)

• South-Facing Window: Area $60\text{ sq ft}$, $U = 0.30$, $\text{SHGC} = 0.25$, $\text{SLF} = 45\text{ BTU}/(\text{hr}\cdot\text{ft}^2)$, $\text{IAC} = 0.70$, $\Delta T = 17^\circ\text{F}$.
• West-Facing Window: Area $40\text{ sq ft}$, $U = 0.30$, $\text{SHGC} = 0.25$, $\text{SLF} = 150\text{ BTU}/(\text{hr}\cdot\text{ft}^2)$, $\text{IAC} = 0.70$, $\Delta T = 17^\circ\text{F}$.
• Occupants: 4 people in living zone.
• Lighting & Electronics: $300\text{ Watts}$ LED lighting and TV.

Step 1: Fenestration Conduction Heat Gain

$q_{\text{cond, south}} = 0.30 \times 60\text{ sq ft} \times 17^\circ\text{F} = 306\text{ BTU/h}$ $q_{\text{cond, west}} = 0.30 \times 40\text{ sq ft} \times 17^\circ\text{F} = 204\text{ BTU/h}$ $\text{Total Fenestration Conduction} = 306 + 204 = 510\text{ BTU/h}$

Step 2: Fenestration Solar Radiant Heat Gain

$q_{\text{solar, south}} = 60\text{ sq ft} \times 0.25 \times 45 \times 0.70 = 472.5\text{ BTU/h}$ $q_{\text{solar, west}} = 40\text{ sq ft} \times 0.25 \times 150 \times 0.70 = 1{,}050.0\text{ BTU/h}$ $\text{Total Fenestration Solar Gain} = 472.5 + 1{,}050.0 = 1{,}522.5\text{ BTU/h}$ (Note how the smaller $40\text{ sq ft}$ west window delivers more than double the solar heat of the $60\text{ sq ft}$ south window due to afternoon peak irradiance).

Step 3: Occupant Heat Gain (4 People)

$q_{\text{sensible, people}} = 4 \times 230\text{ BTU/h} = 920\text{ BTU/h}$ $q_{\text{latent, people}} = 4 \times 200\text{ BTU/h} = 800\text{ BTU/h}$

Step 4: Lighting and Equipment Heat Gain

$q_{\text{sensible, equipment}} = 300\text{ W} \times 3.412\text{ BTU/(hr}\cdot\text{W)} = 1{,}023.6\text{ BTU/h}$

Step 5: Subtotal Living Room Heat Gains

• Total Sensible Gain: $510 + 1{,}522.5 + 920 + 1{,}023.6 = 3{,}976.1\text{ BTU/h}$
• Total Latent Gain: $800\text{ BTU/h}$
• Total Combined Load: $3{,}976.1 + 800 = 4{,}776.1\text{ BTU/h}$