TAHA Engineering Toolsby TAHA Knowledge Lab

HVAC & Building Services

Air Sensible & Latent Heat Calculator

Sensible, latent and total heat of an air stream — or the airflow or temperature change for a given load.

Inputs

Calculate from
Duct with an airflow arrow entering on the left at temperature T1 and humidity ratio W1, passing a coil in the middle, and leaving on the right at T2 and W2. A heat arrow Q leaves the coil.V̇ — airflowIn: T₁, W₁Out: T₂, W₂Qcoil
Air passes a coil (or a room). Its temperature changes from T₁ to T₂ (sensible heat) and its humidity ratio from W₁ to W₂ (latent heat). Diagram not to scale.

Volume flow of the air stream (supply air, outside air or air through a coil).

The size of the temperature change, entered as a positive number for both cooling and heating, e.g. room 24 °C and supply 14 °C → ΔT = 10 K. Enter it as a difference, not as a temperature.

Optional, for the latent heat. The size of the change in humidity ratio, entered as a positive number for both moisture removal (cooling coil) and moisture addition (humidifier), e.g. 10 g/kg → 8 g/kg → ΔW = 2 g/kg. Leave empty for sensible heat only.

Standard air ≈ 1.2 kg/m³ (1.204 kg/m³ at 20 °C and 101.325 kPa). Use a lower value at high altitude or high temperature.

2501 kJ/kg is the value used in the ASHRAE moist-air enthalpy equation.

Result

Sensible heat
6.036
Mass flow of air
0.6
Working
Qs = ρ × V̇ × cp × ΔT = 1.2 × 0.5 × 1.006 × 10 = 6.036 kW

The air stream carries about 6.036 kW of sensible heat.

Educational estimate — check the assumptions below.

About this calculator

Air carries heat in two ways. Sensible heat changes the air’s temperature — what a thermometer shows. Latent heat is the energy in its water vapour: it is removed when a cooling coil condenses moisture out of the air, and added when air is humidified. Use this calculator to find the heat picked up or removed by supply air, outside air or air passing a coil, or to size the airflow for a room’s sensible load.

It uses the basic energy balance for moist air with property values you can change. It does not calculate a building’s cooling load; that needs a full load calculation.

Formula

Heat from airflow

Qs = ρ × V̇ × cp × ΔT

QL = ρ × V̇ × hfg × ΔW    Qt = Qs + QL    SHR = Qs ÷ Qt

ρ = air density (kg/m³), V̇ = airflow (m³/s), cp = specific heat of air (J/(kg·K)), ΔT = temperature change (K), hfg = latent heat of water vapour (J/kg), ΔW = change in humidity ratio (kg of water per kg of dry air).

With the default values, ρ × cp = 1.2 × 1.006 = 1.207 kJ/(m³·K). In inch-pound units the same values give the familiar rule Qs (Btu/h) = 1.08 × cfm × ΔT (°F). For latent heat the inch-pound rule 0.68 × cfm × Δgr/lb uses slightly different property values, so it gives results about 1–2% lower than this calculator.

Airflow for a load

V̇ = Qs ÷ (ρ × cp × ΔT)

The airflow needed to carry a sensible heat load Qs with a temperature change ΔT. Inch-pound form: cfm = Btu/h ÷ (1.08 × ΔT °F).

ΔT for a load

ΔT = Qs ÷ (ρ × V̇ × cp)

The temperature change of an airflow V̇ carrying a sensible heat load Qs. Inch-pound form: ΔT (°F) = Btu/h ÷ (1.08 × cfm).

Worked example

  • Sensible heat: 0.5 m³/s cooled by 10 K → Qs = 1.2 × 0.5 × 1.006 × 10 = 6.04 kW.
  • Latent heat: the same air loses 2 g/kg of moisture (ΔW = 0.002) → QL = 1.2 × 0.5 × 2501 × 0.002 = 3.00 kW; total 9.04 kW; SHR = 6.04 ÷ 9.04 = 0.67.
  • Inch-pound check: 1000 cfm with ΔT = 20 °F → 1.08 × 1000 × 20 = 21 600 Btu/h (1.8 TR).
  • Airflow for a load: a 6 kW sensible load with a 10 K supply-air temperature difference needs 6 ÷ (1.2 × 1.006 × 10) = 0.497 m³/s (about 1790 m³/h).

Assumptions and limitations

  • Steady flow with the property values entered. The defaults are for standard air near sea level; density falls with altitude and temperature.
  • Sensible and latent heat are calculated separately with constant properties. This is the usual engineering approximation; a psychrometric (enthalpy) calculation is more exact.
  • ΔT and ΔW are entered as positive sizes of the change. The calculator gives the amount of heat; whether it is added to or removed from the air depends on your process (cooling or heating, dehumidifying or humidifying).
  • The humidity-ratio change must come from your own data or a psychrometric chart; this calculator does not work it out from relative humidity.
  • An air-side heat balance only. It is not a building cooling or heating load calculation.

References

  • ASHRAE Handbook — Fundamentals, chapter “Psychrometrics” (moist-air properties; h = 1.006 t + W (2501 + 1.86 t) kJ/kg).
  • First law of thermodynamics for a steady-flow air stream: Q = ṁ × cp × ΔT.