Duct Heat Loss and Outlet Temperature Calculator

Concepts behind this calculation

Estimate duct heat loss or gain and outlet air temperature using the original standard-air screening model or an ordered section model with explicit air properties and overall U-values.

Duct air gradually approaches the temperature of its surroundings as heat crosses the duct assembly. The exponential temperature response reflects a shrinking driving temperature difference along the run. Greater heat-transfer area or conductance increases the approach; greater air heat-capacity flow reduces the temperature change for the same exposure.

The single-run screen uses fixed standard-air properties and an added film resistance with the entered insulation R-value. Ordered sections instead use actual inlet flow, matching total-air density, compatible specific heat, and an independently established overall U for each section. The outlet of one section becomes the inlet of the next, so a cold space followed by a warm space cannot be replaced casually by one average ambient temperature.

How to use this calculator

1. Select Thermal calculation method and enter Inlet air temperature and Duct airflow.
2. For screening, enter Average surrounding temperature, Run length, Outside duct perimeter, and Insulation R-value.
3. For ordered sections, supply Inlet total-air density and Compatible total-air specific heat, document the U-area reference, and confirm Ordered sensible-model basis.
4. Enter Sections in airflow order and review the section trace before the net result.

Calculation method and applicability

U = 1 / (R_insulation + 0.85); A = perimeter × length; T_out = T_ambient + (T_in − T_ambient) × exp[−UA / (1.08 × CFM)] Ordered model: m=60×Qinlet×ρinlet; C=m×cp; Ai=Pi[in]/12×Li[ft]; Ti,out=Ta,i+(Ti,in−Ta,i)exp(−UiAi/C); qi=C(Ti,in−Ti,out); Ti+1,in=Ti,out. Net=Σqi; gross loss=Σmax(0,qi); gross gain=Σmax(0,−qi).

U = overall conductance (BTU/(h·ft²·°F)); A = heat-transfer area (ft²); m = air mass flow (lbm/h); C = thermal capacity rate (BTU/(h·°F)); q = heat transfer (BTU/h). T is °F. Section perimeter P is entered in inches and length L in feet.

Input definitions and units

Thermal calculation method

Retain the original standard-air single-run screen, or use explicit inlet mass flow and overall U values for an ordered section chain. Choices: Standard-air single-run screening; Ordered sections with explicit properties and U.

Inlet air temperature (°F)

Air temperature at the start of the run or section chain. Negative Fahrenheit is valid above absolute zero. Use the chosen method’s air-property and phase assumptions.

Average surrounding temperature (°F)

Use an approximately constant ambient temperature for this run, not a weather extreme applied to every space. Applies to Thermal calculation method: Standard-air single-run screening.

Duct airflow (CFM)

Screening uses the original standard-air basis. Ordered mode requires actual inlet volume flow at the same state as the supplied total-air density; SCFM is not interchangeable. The chain conserves mass flow, not local CFM.

Run length (ft)

Zero length is a valid boundary and returns the inlet temperature. Applies to Thermal calculation method: Standard-air single-run screening.

Outside duct perimeter (in)

For a rectangular duct use 2 × (outside width + outside height); for round use π × outside diameter. Applies to Thermal calculation method: Standard-air single-run screening.

Insulation R-value (h·ft²·°F/BTU)

Enter installed insulation thermal resistance. Zero represents no added insulation; the model still includes 0.85 combined film resistance. Applies to Thermal calculation method: Standard-air single-run screening.

Inlet total-air density (lbm/ft³)

Actual inlet total-air density in lbm/ft³, paired with inlet ACFM. Supply an independently established value; no altitude, weather or standard-air default. Applies to Thermal calculation method: Ordered sections with explicit properties and U.

Compatible total-air specific heat (BTU/(lbm·°F))

One applicable constant specific heat per pound of the same total-air mass basis as density, valid over all section temperatures. Do not pair dry-air-basis cp with moist total-air density. Applies to Thermal calculation method: Ordered sections with explicit properties and U.

Section order,properties and U-area reference

Identify the actual air-property basis, ordered locations, overall U sources and matching area/perimeter reference. Confirm U includes applicable films, wall and insulation and applies over the modeled temperatures. This reference is not authenticated. Applies to Thermal calculation method: Ordered sections with explicit properties and U.

Ordered sensible-model basis

Confirm one stream without leakage, compatible constant mass flow and cp, a single gas phase, steady sections and independently established overall U on the entered perimeter basis. Choices: Not established; Section and property basis documented. Applies to Thermal calculation method: Ordered sections with explicit properties and U.

Sections in airflow order (length ft, perimeter in, U BTU/(h·ft²·°F), surroundings °F)

Enter 1–100 numeric rows in airflow order, without branches, mixing or fan heat. Overall U includes all applicable resistances on the entered area basis; no fixed film resistance is added. U=0 is an ideal adiabatic boundary; length=0 is valid; perimeter must be positive. Applies to Thermal calculation method: Ordered sections with explicit properties and U.

How to interpret the result

Positive transfer is heat leaving the air; negative transfer is heat entering it. Inspect section temperatures and both gross totals, because a modest final temperature change can hide substantial intermediate transfer.

Worked examples

Assumptions and limits

• The original screening mode assumes one-dimensional steady heat transfer, constant U and specific heat, combined inside/outside film resistance of 0.85 h·ft²·°F/BTU, and no leakage.
• The original screening mode fixes density at 0.075 lb/ft³ and cp at 0.24 BTU/(lb·°F). Select ordered mode when using independently established actual inlet mass flow, compatible constant cp and overall U.
• Insulation compression, moisture, thermal bridges, vapor-control detailing and surface condensation are not evaluated. This does not certify an insulation thickness or code minimum.
• Ordered mode conserves mass flow from actual inlet CFM and matching total-air density, using one compatible constant total-air cp. Local CFM is not held constant or predicted. It handles 1–100 sequential sections without branches or mixing.
• Ordered mode requires independently established overall U on the entered perimeter/area basis, including applicable films, wall and insulation. It adds no fixed film resistance and does not derive U from material data.
• Both methods are steady sensible-only approximations. Moisture phase changes, latent loads, leakage, thermal storage, separate solar/radiant boundary solutions and fan heat are not modeled. Confirm a single gas phase and valid fixed properties; no saturation or condensation check is performed.
• For very small NTU, the outlet temperature can round to the inlet while the stable energy result remains nonzero. The heat balance uses unrounded transfer; no physical measurement precision is implied.

Sources

• NIA: Temperature Drop Calculator for Air DuctsPublic method and assumptions; it references ASHRAE 2009 Fundamentals, Chapter 4, Equation 48. Default worked case independently reproduced.
• U.S. DOE EnergyPlus 22.2: Node Temperature Calculations, original engineering-reference sourceThe primary reference gives the sensible outlet relation using mass flow, cp, overall U and area, then connects each duct outlet to the next inlet. This mode applies the constant-surroundings relation to one sequential stream; it does not implement the full AirflowNetwork, radiation or moisture model.