Refrigerated Transport Load Calculation

Reference ID: MET-543E | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

The Refrigerated Transport Load Calculation is a critical process engineering assessment used to determine the cooling capacity requirements for mobile thermal enclosures, such as refrigerated semi-trailers or rigid trucks. Accurate estimation is vital to ensure product integrity during transit, queuing, and multi-stop distribution cycles.

In process engineering, this calculation serves as the foundation for selecting refrigeration units (TRUs). It accounts for transient environmental conditions, including solar radiation, convective heat transfer during vehicle movement, and air infiltration due to door openings. Unlike stationary cold storage, transport refrigeration must manage the thermal flywheel effect of the trailer structure and the rapid pull-down requirements following loading or stop-and-go operations.

Methodology & Formulas

The total cooling load is determined by summing the heat gains from transmission, solar radiation, air infiltration, and internal heat sources. The following formulas define the physical model:

1. Transmission Load

The transmission load accounts for heat transfer through the enclosure boundaries based on the temperature differential between the ambient environment and the internal setpoint:

\[ \dot{Q}_{\text{trans}} = \sum \left( U_{i} \cdot A_{i} \cdot \Delta T_{i} \right) \]

Where the temperature differential for the roof incorporates the sol-air temperature to account for solar gain:

\[ T_{\text{sol-air}} = T_{\text{amb}} + \frac{\alpha_{\text{solar}} \cdot q_{\text{solar}}}{h_{o}} \]

\[ \Delta T_{\text{roof}} = T_{\text{sol-air}} - T_{\text{set}} \]

2. Infiltration Load

Infiltration represents the sensible heat gain from ambient air entering the enclosure, calculated based on the air change rate. The specific heat of air \(c_{p,\text{air}}\) is taken in kJ/(kg·K); the factor 3.6 in the denominator converts the result directly to watts:

\[ \dot{Q}_{\text{inf}} = \frac{V_{\text{cargo}} \cdot \text{ACH} \cdot \rho_{\text{air}} \cdot c_{p,\text{air}} \cdot (T_{\text{amb}} - T_{\text{set}})}{3.6} \]

3. Internal and Total Load

Internal loads include heat generated by evaporator fans and defrost cycles. The final sizing load includes a safety factor to account for operational uncertainties:

\[ \dot{Q}_{\text{int}} = P_{\text{fans}} + P_{\text{defrost}} \]

\[ \dot{Q}_{\text{total}} = \left( \dot{Q}_{\text{trans}} + \dot{Q}_{\text{inf}} + \dot{Q}_{\text{int}} \right) \cdot SF \]

Empirical Constraints and Validity

The following table outlines the operational limits and empirical bounds required for a valid calculation. Values outside these ranges indicate potential modeling errors or non-standard equipment configurations.

Parameter	Description	Valid Range
U_i	Overall Heat Transfer Coefficient (W/m²·K)	0.20 – 0.60
ACH	Air Changes per Hour	0.10 – 4.00
α_solar	Solar Absorptivity	0.15 – 0.95

To calculate the total heat load, you must aggregate the heat gain from all primary sources. Follow these steps:

Calculate the transmission load based on the surface area, insulation U-value, and the temperature differential between the ambient environment and the set point.
Determine the product respiration load if transporting fresh produce.
Account for air exchange loads caused by door openings or trailer leakage.
Include internal heat loads generated by fans, lights, or auxiliary equipment.

While the exact safety factor depends on the specific commodity and route, process engineers typically apply a margin of 15 to 25 percent. This buffer accounts for:

Degradation of insulation performance over the vehicle lifecycle.
Extreme ambient temperature spikes during transit.
Variations in loading density and airflow obstruction.

Improper stacking is a leading cause of thermal failure. To maintain efficiency, ensure the following:

Maintain a minimum gap between the load and the trailer walls to allow for cold air circulation.
Ensure the load does not block the return air bulkhead, which prevents short-cycling of the refrigeration unit.
Use pallets to facilitate airflow beneath the cargo, preventing heat transfer from the trailer floor.

Worked Example: Refrigerated Transport Load Calculation for Frozen Food

A frozen food distribution company operates a 16-meter semi-trailer carrying 20,000 kg of meat at -20 °C. The trailer is in transit on a summer day with ambient temperature 38 °C, peak solar radiation on the roof, and a ground temperature of 30 °C. The refrigeration unit must maintain the setpoint during steady-state highway travel. The following calculation determines the required cooling capacity using the sol-air method and standard load components.

Known Parameters

Wall: area \(A_{\text{wall}} = 123.0 \, \text{m}^2\), U-value \(U_{\text{wall}} = 0.35 \, \text{W/(m}^2\!\cdot\!\text{K)}\)
Roof: area \(A_{\text{roof}} = 34.0 \, \text{m}^2\), U-value \(U_{\text{roof}} = 0.40 \, \text{W/(m}^2\!\cdot\!\text{K)}\)
Floor: area \(A_{\text{floor}} = 34.0 \, \text{m}^2\), U-value \(U_{\text{floor}} = 0.40 \, \text{W/(m}^2\!\cdot\!\text{K)}\)
Temperatures: ambient \(T_{\text{amb}} = 38.0 \, ^\circ \text{C}\), setpoint \(T_{\text{set}} = -20.0 \, ^\circ \text{C}\), ground \(T_{\text{floor}} = 30.0 \, ^\circ \text{C}\)
Solar: irradiance \(q_{\text{solar}} = 800.0 \, \text{W/m}^2\), absorptivity \(\alpha = 0.75\), convective coefficient \(h_{o} = 25.0 \, \text{W/(m}^2\!\cdot\!\text{K)}\)
Cargo volume \(V_{\text{cargo}} = 92.0 \, \text{m}^3\), air changes per hour \(ACH = 1.0\)
Air density \(\rho_{\text{air}} = 1.2 \, \text{kg/m}^3\), specific heat \(c_{p,\text{air}} = 1.006 \, \text{kJ/(kg}\!\cdot\!\text{K)}\)
Internal loads: evaporator fan power \(P_{\text{fan}} = 2500.0 \, \text{W}\), defrost power \(P_{\text{defrost}} = 1000.0 \, \text{W}\)
Safety factor \(SF = 1.2\)

Temperature differences for transmission
\[ \Delta T_{\text{wall}} = T_{\text{amb}} - T_{\text{set}} = 38.0 - (-20.0) = 58.0 \, \text{K} \]

Sol-air roof temperature:

\[ T_{\text{sol-air, roof}} = T_{\text{amb}} + \frac{\alpha \cdot q_{\text{solar}}}{h_{o}} = 38.0 + \frac{0.75 \cdot 800.0}{25.0} = 62.0 \, ^\circ \text{C} \]

\[ \Delta T_{\text{roof}} = T_{\text{sol-air, roof}} - T_{\text{set}} = 62.0 - (-20.0) = 82.0 \, \text{K} \]

\[ \Delta T_{\text{floor}} = T_{\text{floor}} - T_{\text{set}} = 30.0 - (-20.0) = 50.0 \, \text{K} \]
Transmission load
\[ \dot{Q}_{\text{trans, wall}} = U_{\text{wall}} \cdot A_{\text{wall}} \cdot \Delta T_{\text{wall}} = 0.35 \cdot 123.0 \cdot 58.0 = 2496.9 \, \text{W} \]

\[ \dot{Q}_{\text{trans, roof}} = U_{\text{roof}} \cdot A_{\text{roof}} \cdot \Delta T_{\text{roof}} = 0.40 \cdot 34.0 \cdot 82.0 = 1115.2 \, \text{W} \]

\[ \dot{Q}_{\text{trans, floor}} = U_{\text{floor}} \cdot A_{\text{floor}} \cdot \Delta T_{\text{floor}} = 0.40 \cdot 34.0 \cdot 50.0 = 680.0 \, \text{W} \]

Total transmission:

\[ \dot{Q}_{\text{trans, total}} = 2496.9 + 1115.2 + 680.0 = 4292.1 \, \text{W} \]
Infiltration load
\[ \dot{Q}_{\text{inf}} = \frac{V_{\text{cargo}} \cdot ACH \cdot \rho_{\text{air}} \cdot c_{p,\text{air}} \cdot (T_{\text{amb}} - T_{\text{set}})}{3.6} \]

\[ \dot{Q}_{\text{inf}} = \frac{92.0 \cdot 1.0 \cdot 1.2 \cdot 1.006 \cdot 58.0}{3.6} = 1789.339 \, \text{W} \]
Internal loads
\[ \dot{Q}_{\text{int}} = P_{\text{fan}} + P_{\text{defrost}} = 2500.0 + 1000.0 = 3500.0 \, \text{W} \]
Total raw cooling load
\[ \dot{Q}_{\text{total, raw}} = \dot{Q}_{\text{trans, total}} + \dot{Q}_{\text{inf}} + \dot{Q}_{\text{int}} = 4292.1 + 1789.339 + 3500.0 = 9581.439 \, \text{W} \]
Final sizing load with safety factor
\[ \dot{Q}_{\text{sizing}} = \dot{Q}_{\text{total, raw}} \cdot SF = 9581.439 \cdot 1.2 = 11497.726 \, \text{W} \]

Final Answer: The required cooling capacity is 11497.726 W (approximately 11.5 kW). Based on this, a unit such as the Carrier Vector 1850 or Thermo King T-800, providing 10–12 kW at -20 °C box temperature, would be appropriate. A safety factor of 20% is already included; no further oversizing is needed.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle