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Cooling and Heating Equations

Latent and sensible cooling and heating equations - imperial units

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Sensible Heat

The sensible heat in a heating or cooling process of air (heating or cooling capacity) can be calculated in SI-units as

hs = cp ρ q dt                                              (1)


hs = sensible heat (kW)

cp = specific heat of air (1.006 kJ/kg oC)

ρ = density of air (1.202 kg/m3)

q = air volume flow (m3/s)

dt = temperature difference (oC)

Or in Imperial units as

hs = 1.08 q dt                                            (1b)


hs = sensible heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dt = temperature difference (oF)

Latent Heat

Latent heat due to the moisture in air can be calculated in SI-units as:

hl = q ρ hwe dwkg                                      (2)


hl = latent heat (kW)

ρ = density of air (1.202 kg/m3)

q = air volume flow (m3/s)

hwe = latent heat evaporization water (2454 kJ/kg - in air at atmospheric pressure and 20oC)

dwkg = humidity ratio difference (kg water/kg dry air)

Latent evaporation heat for water can be calculated as

hwe = 2494 - 2.2 t                  (2a)


t = evaporation temperature (oC)

Or for Imperial units:

hl = 0.68 q dwgr                                      (2b)


hl = 4840 q dwlb                                     (2c)


hl= latent heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dwgr = humidity ratio difference (grains water/lb dry air)

dwlb = humidity ratio difference (lb water/lb dry air)

Total Heat - Latent and Sensible Heat

Total heat due to both temperature and moisture can be expressed in SI units as:

ht = q ρ dh                                            (3)


ht = total heat (kW)

q = air volume flow (m3/s)

ρ = density of air (1.202 kg/m3)

dh = enthalpy difference (kJ/kg)

Or - in imperial units:

ht = 4.5 q dh                                        (3b)


ht= total heat (Btu/hr)

q = air volume flow (cfm, cubic feet per minute)

dh = enthalpy difference (btu/lb dry air)

Total heat can also be expressed as:

ht = hs + hl

    = 1.08 q dt + 0.68 q dwgr                                      (4)

Example - Heating Air

An air flow of one cfm is heated from 32 to 52oF. Using (1) the sensible heat added to the air can be expressed as:

hs = 1.08 (1 cfm) ((52 oF) - (32 oF))      

    = 21.6 (Btu/hr)

Sensible Heat Load and Required Air Volume Chart

Sensible heat load and required air volume to keep the temperature constant at various temperature differences between make up air and room air:

Sensible Load - heat required for air volume to keep room temperature constant

Latent Heat Load and Required Air Volume Chart

Latent heat load - humidifying and dehumidifying - and required air volume to keep temperature constant at various temperature differences between entering air and room air are indicated in the chart below:

Latent heat - required air volume keep moisture content constant

SHR - Sensible Heat Ratio

The Sensible Heat Ratio can be expressed as

SHR = hs / ht                              (6)


SHR = Sensible Heat Ratio

hs = sensible heat

ht = total heat (sensible and latent)

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