Air heat loads
Sensible heat in an air stream (Q = ρ cp q ΔT)
- where
- sensible heat (kW)
- air density (kg/m³)
- specific heat capacity of moist air (kJ/kg·K)
- air volume flow rate (m³/s)
- air temperature difference (K)
- sensible heat (W)
Explain this equation
Works out how much heat an air stream picks up or gives away when only its temperature changes. Use it for sizing a heater battery, checking a cooling coil's sensible duty, or finding what a supply grille delivers to a room.
V̇ is the volume of air moving each second. Multiplying by ρ turns it into a mass flow, and cp is the energy needed to warm one kilogram of that air by one kelvin. ΔT is how much the air is heated or cooled. Q_W is the same answer in watts.
Heat equals mass times specific heat times temperature change; applying that to a flowing stream every second gives a rate in kW. With ρ = 1.2 and cp = 1.025 the product is 1.23, the familiar ASHRAE factor.
Sense check: 1 m³/s (1000 l/s) warmed by 10 K carries about 12 kW. Halve the temperature difference and the duty halves.
Watch out: if the coil also removes moisture, that is extra latent duty not counted here.
Works out the sensible heat an air stream carries or delivers for a given airflow and temperature change. Use it for heater batteries, cooling coils and supply air to a room.
Enter your values to see the result.
Good to know
ρ = 1.2 kg/m³ is standard air at about 20 °C at sea level. cp = 1.025 kJ/(kg·K) is moist air at about 10 g/kg, which with ρ = 1.2 reproduces ASHRAE’s 1.23 W per (l/s·K). Using dry-air cp 1.005 gives about 2 % less. 1 m³/s = 1000 l/s.
Common mistake
Mixing up volume flow and mass flow, or using l/s in an equation written for m³/s, which gives answers 1000 times out.
Limits
Sensible heat only: any change in moisture content is latent heat and needs the latent calculator. Density falls with temperature and altitude; for hot or high-altitude air use the actual density.
Sources
- ASHRAE Handbook — Fundamentals (2017), chapter 18 Nonresidential cooling and heating load calculations, Table 1 heat gain from occupants (moderately active office work: 75 W sensible, 55 W latent); simplified air equations qs = 1.23 Q Δt and ql = 3010 Q ΔW (Q in L/s)
- CIBSE Guide C: Reference data (2007), chapter 1 (properties of humid air) and chapter 4 (flow of fluids in pipes and ducts)
- CIBSE Guide A: Environmental design (2015), chapters 5 and 6 (thermal design, internal heat gains from people, lighting and equipment)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.