Transmission Loads Calculation

Transmission loads represent heat transfer through the building envelope of refrigerated spaces due to temperature differences between inside and outside conditions. These loads constitute a major component of the total refrigeration load and require precise calculation for proper equipment sizing and energy analysis.

Fundamental Heat Transfer Equation

The basic heat transmission through building envelope components follows Fourier’s law adapted for one-dimensional steady-state conduction:

Q = U × A × ΔT

Where:

• Q = Heat transfer rate (Btu/h or W)
• U = Overall heat transfer coefficient (Btu/h·ft²·°F or W/m²·K)
• A = Surface area (ft² or m²)
• ΔT = Temperature difference between inside and outside (°F or K)

For refrigerated facilities, this equation must account for multiple envelope components with varying thermal properties and temperature gradients.

Overall Heat Transfer Coefficient (U-Value)

The U-value represents the rate of heat transfer through a building assembly, including all material layers and surface resistances.

Calculation Methodology

The overall thermal resistance (R-total) includes:

R-total = R-inside + R-1 + R-2 + … + R-n + R-outside

U = 1 / R-total

Where:

• R-inside = Inside surface film resistance (h·ft²·°F/Btu or m²·K/W)
• R-1, R-2, … R-n = Thermal resistance of each material layer (h·ft²·°F/Btu or m²·K/W)
• R-outside = Outside surface film resistance (h·ft²·°F/Btu or m²·K/W)

Surface Film Resistances

Surface film coefficients depend on air velocity, surface orientation, and emissivity.

Standard Surface Film Resistances (IP Units):

Standard Surface Film Resistances (SI Units):

Reference: ASHRAE Fundamentals Handbook, Chapter 27 - Heat, Air, and Moisture Control in Insulated Assemblies

Insulation R-Values

Thermal resistance of insulation materials is the primary barrier to heat transmission in refrigerated facilities.

Common Insulation Materials

Thermal Properties of Insulation Materials at 75°F Mean Temperature:

Note: Thermal conductivity (k-value) increases with increasing temperature and moisture content. For refrigerated applications, use k-values at mean operating temperature.

Temperature Effect on Insulation Performance

The thermal conductivity of insulation varies with temperature. For accurate calculations:

k(T) = k₀ + a·T + b·T²

Where:

• k(T) = Thermal conductivity at temperature T
• k₀ = Reference thermal conductivity
• a, b = Material-specific coefficients
• T = Mean temperature (°F or °C)

For polyurethane foam:

• k increases approximately 0.5-1.0% per 10°F temperature increase above 75°F

Recommended Insulation Thickness

Minimum Insulation R-Values for Refrigerated Spaces:

Reference: ASHRAE Refrigeration Handbook, Chapter 24 - Refrigerated-Facility Design

Thermal Bridging

Thermal bridges are localized areas of higher heat transfer that bypass insulation, creating paths of least resistance for heat flow.

Common Thermal Bridge Locations

1. Structural Penetrations:

   • Steel columns through insulated walls
   • Concrete or steel beams
   • Wall ties and fasteners
   • Suspended ceiling hangers

2. Envelope Discontinuities:

   • Wall-to-floor junctions
   • Wall-to-ceiling junctions
   • Corner assemblies
   • Door frames and jambs

3. Service Penetrations:

   • Electrical conduit
   • Piping penetrations
   • Ductwork penetrations
   • Cable trays

Thermal Bridge Calculation Methods

Method 1: Linear Thermal Transmittance

For edge and junction effects:

Q = Ψ × L × ΔT

Where:

• Ψ = Linear thermal transmittance (Btu/h·ft·°F or W/m·K)
• L = Length of thermal bridge (ft or m)
• ΔT = Temperature difference (°F or K)

Method 2: Point Thermal Transmittance

For isolated penetrations:

Q = χ × n × ΔT

Where:

• χ = Point thermal transmittance (Btu/h·°F or W/K)
• n = Number of identical penetrations
• ΔT = Temperature difference (°F or K)

Method 3: Effective U-Value Adjustment

For assemblies with distributed thermal bridges:

U-effective = U-clear × f-clear + U-bridge × f-bridge

Where:

• U-clear = U-value of clear wall section
• f-clear = Fraction of area with clear wall
• U-bridge = U-value at thermal bridge
• f-bridge = Fraction of area with thermal bridge

Thermal Bridge Impact

Typical Thermal Bridge Heat Gain Increases:

Mitigation Strategies

1. Thermal Breaks:

   • Use non-metallic spacers between metal components
   • Install thermal break materials at structural connections
   • Select insulated panel systems with thermal breaks at joints

2. Structural Design:

   • Place structural members outside insulated envelope
   • Use insulated concrete forms (ICF)
   • Minimize penetrations through insulation

3. Installation Details:

   • Continuous insulation layers
   • Staggered stud walls for deep insulation
   • Proper sealing of all penetrations

Ground Contact Floors

Heat transfer through ground contact floors requires special consideration due to soil thermal properties and depth effects.

Heat Transfer Mechanisms

Heat flow from refrigerated spaces to ground occurs through:

1. Conduction through floor slab and underlying soil
2. Heat storage in soil mass (transient effects)
3. Moisture migration and phase change

Calculation Methods

Method 1: Simplified Steady-State

For preliminary calculations:

Q = A × ΔT / (R-floor + R-soil)

Where:

• R-floor = Thermal resistance of floor assembly and insulation
• R-soil = Effective soil resistance (typically 2-4 h·ft²·°F/Btu)

Method 2: ASHRAE Ground Heat Transfer Model

The ground heat transfer coefficient depends on floor dimensions and perimeter characteristics:

U-ground = (P/A) × F + k-soil/d

Where:

• P = Floor perimeter (ft or m)
• A = Floor area (ft² or m²)
• F = Perimeter heat loss factor (Btu/h·ft·°F or W/m·K)
• k-soil = Soil thermal conductivity (Btu/h·ft·°F or W/m·K)
• d = Depth below grade (ft or m)

Soil Thermal Properties:

Reference: ASHRAE Fundamentals Handbook, Chapter 18 - Nonresidential Cooling and Heating Load Calculations

Floor Insulation Configuration

Recommended Floor Insulation:

Under-Floor Heating

For spaces below 35°F, under-floor heating prevents:

• Soil freezing and heaving
• Moisture migration and ice lens formation
• Structural damage to floor slab

Under-Floor Heating Load:

Q-heater = Q-refrigerated + Q-downward-loss + Safety-factor

Typical under-floor heating density: 1.5-3.0 W/ft² (16-32 W/m²)

Control strategy: Maintain sub-slab temperature between 40-50°F (4-10°C)

Sun-Exposed Surfaces

Solar radiation significantly increases heat gain through exposed surfaces, particularly roofs.

Solar Heat Gain Components

Total heat gain through sun-exposed surfaces:

Q-total = Q-conduction + Q-solar

Q-solar = U × A × (TETD) × CLF

Where:

• TETD = Total equivalent temperature difference (°F or K)
• CLF = Cooling load factor (accounts for thermal mass)

Sol-Air Temperature

Sol-air temperature combines outdoor air temperature with solar radiation effects:

T-sol-air = T-outdoor + (α × I-total / h-o) - ε × ΔR / h-o

Where:

• α = Solar absorptance of surface (0.3-0.9)
• I-total = Total solar radiation intensity (Btu/h·ft² or W/m²)
• h-o = Outside surface heat transfer coefficient (Btu/h·ft²·°F or W/m²·K)
• ε = Surface emissivity (0.8-0.95)
• ΔR = Difference between long-wave radiation from surface and surroundings (typically 20 Btu/h·ft² or 63 W/m²)

Solar Absorptance by Surface Color:

Peak Sol-Air Temperatures

Representative Peak Sol-Air Temperatures (95°F Design Day):

Mitigation Strategies

1. Cool Roofing:

   • High solar reflectance (SR > 0.65)
   • High thermal emittance (ε > 0.85)
   • Reduces peak sol-air temperature by 30-50°F

2. Additional Insulation:

   • Increase roof insulation to R-40 minimum
   • Use insulation with low thermal diffusivity

3. Ventilated Roof Systems:

   • Air gap between roof membrane and insulation
   • Reduces heat gain by 15-25%

Adjacent Space Temperature Differences

Heat transmission from adjacent unconditioned or conditioned spaces requires separate calculation.

Temperature Differential Categories

Typical Adjacent Space Conditions:

Multi-Temperature Zone Calculations

For refrigerated facilities with multiple temperature zones:

Q-1to2 = U × A × (T-2 - T-1)

Where zones are numbered from coldest (1) to warmest (2).

Design Considerations:

1. Zone Arrangement:

   • Place coldest zones in building core
   • Minimize surface area between zones with large ΔT
   • Use buffer zones to reduce temperature steps

2. Insulation Strategy:

   • Lower R-values acceptable between similar temperature zones
   • Higher R-values required between extreme temperature differences

Recommended R-Values Between Temperature Zones:

Transmission Load Calculation Procedures

Step-by-Step Calculation Process

Step 1: Define Envelope Components

Identify and quantify all envelope surfaces:

• Exterior walls (by orientation)
• Roof or ceiling
• Floor (ground contact or elevated)
• Walls adjacent to other spaces
• Doors and openings (calculate separately)

Step 2: Determine Design Temperatures

Establish temperature differentials:

• Interior design temperature (refrigerated space)
• Exterior design temperature (ASHRAE design conditions)
• Adjacent space temperatures
• Sol-air temperatures for exposed surfaces

Step 3: Calculate Component U-Values

For each envelope component:

a) List all material layers with thickness and k-values b) Calculate R-value for each layer: R = thickness / k c) Add surface film resistances d) Sum total R-value: R-total = R-inside + ΣR-layers + R-outside e) Calculate U-value: U = 1 / R-total f) Adjust for thermal bridging if significant

Step 4: Calculate Surface Areas

Measure or calculate area for each component:

• Use net areas (subtract openings)
• Account for building geometry
• Verify area calculations

Step 5: Apply Heat Transfer Equation

For each component:

Q = U × A × ΔT

Sum all components for total transmission load:

Q-transmission-total = ΣQ-components

Step 6: Apply Safety Factors

Add appropriate safety factors:

• Insulation aging/settling: 5-10%
• Installation imperfections: 5-10%
• Thermal bridging (if not explicitly calculated): 10-20%
• Overall uncertainty: 10-15%

Example Calculation

Given:

• Cooler space: 35°F
• Exterior design temperature: 95°F
• Wall construction: 4" polyurethane insulation between metal skins
• Wall dimensions: 40 ft × 12 ft high

Calculation:

1. Temperature difference:

   • ΔT = 95°F - 35°F = 60°F

2. Calculate U-value:

   • Outside film resistance: R = 0.17
   • Outside metal skin (0.05"): R = 0.05 / 300 = 0.0002 (negligible)
   • Polyurethane insulation (4"): R = 4 × 6.7 = 26.8
   • Inside metal skin (0.05"): R = 0.0002 (negligible)
   • Inside film resistance: R = 0.68
   • R-total = 0.17 + 26.8 + 0.68 = 27.65
   • U = 1 / 27.65 = 0.0362 Btu/h·ft²·°F

3. Calculate area:

   • A = 40 ft × 12 ft = 480 ft²

4. Calculate heat gain:

   • Q = 0.0362 × 480 × 60 = 1,043 Btu/h

5. Apply thermal bridging factor (panel joints, 15%):

   • Q-adjusted = 1,043 × 1.15 = 1,199 Btu/h

Advanced Considerations

Transient Heat Transfer

For facilities with variable operation or cycling:

Q(t) = U × A × Σ[ΔT-i × CTF-i]

Where:

• CTF-i = Conduction transfer function coefficients
• ΔT-i = Temperature difference at previous time intervals

Reference: ASHRAE Fundamentals Handbook, Chapter 18 - Nonresidential Cooling and Heating Load Calculations

Moisture Effects

Moisture accumulation in insulation degrades thermal performance:

k-wet = k-dry × (1 + m × MC)

Where:

• k-wet = Thermal conductivity with moisture
• k-dry = Dry thermal conductivity
• m = Material-specific moisture coefficient
• MC = Moisture content (% by volume)

Typical degradation: 3-5% increase in k-value per 1% moisture content by volume

Three-Dimensional Heat Transfer

At corners and complex geometries, two-dimensional or three-dimensional finite element analysis provides accurate results where simplified methods underestimate heat transfer by 10-30%.

Quality Assurance

Verification Checklist

• All envelope components identified and measured
• Thermal properties verified for actual installed materials
• Temperature differentials confirmed for design conditions
• Surface film resistances appropriate for orientation and exposure
• Thermal bridges identified and quantified
• Ground contact calculations include soil properties
• Solar effects included for exposed surfaces
• Adjacent space temperatures verified or estimated conservatively
• Safety factors applied appropriately
• Calculations peer-reviewed

Common Errors

1. Using nominal vs. actual insulation thickness

   • Impact: 10-20% underestimation of heat gain

2. Neglecting thermal bridging

   • Impact: 15-50% underestimation depending on construction

3. Incorrect sol-air temperatures

   • Impact: 20-40% underestimation for roof loads

4. Assuming uniform ground temperature

   • Impact: 15-25% error in floor loads

5. Not accounting for insulation aging

   • Impact: 5-15% underestimation over equipment life

Summary

Accurate transmission load calculations require:

1. Detailed envelope component analysis with actual material properties
2. Proper accounting for thermal bridges and envelope discontinuities
3. Recognition of ground contact and solar exposure effects
4. Consideration of adjacent space temperature impacts
5. Application of appropriate safety factors for uncertainty

These calculations form the foundation for refrigeration system sizing and must be performed with rigor to ensure adequate capacity, energy efficiency, and space temperature control.

Reference: ASHRAE Refrigeration Handbook, Chapter 24 - Refrigerated-Facility Design; ASHRAE Fundamentals Handbook, Chapter 27 - Heat, Air, and Moisture Control in Insulated Assemblies

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