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Heating up Humid Air

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1. Cooling humid air without condensation
2. Cooling humid air with condensation : dehumidification

Air handling, in AHU or or in drying operations, require the heating of humid air. It is then important to be able to calculate the energy required to bring air from a temperature T1 to a temperature T2.

1. Heating up humid air

Humid air is heated up, without change of state of the water, at constant specific humidity, but not at constant relative humidity, as the relative humidity decreases if the temperature.

2. Calculation of humid air heating energy requirements

By calculation

The 1st step is to define the enthalpy of humid air :

H' = Cp'.(T-T0) + ω.Λ0

With :

H' = enthalpy of humid air (J/kg_dry_air)
Cp' = specific heat of humid air (J/K/kg_dry_air)
T = temperature of calculation (K)
T0 = temperature of reference (K)
ω = Absolute humidity of air (-)
Λ0 = vaporization enthalpy at T0 (J/kg)

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In practice, at 273 K, H' = (1005 + 1884*ω).(T-273) + 2.5023.106.ω

Considering a temperature TA (starting temperature) and a temperature TB (end temperature), the energy required to heat up humid air, at constant absolute humidity is then :

HB-HA = (1005+1884*ω)*TB-(1005+1884*ω)*TA

Example of humid air heating calculation : Step by Step calculation

Air a 25c and 50% RH is to be heated up until 35c, what is the energy required ?

STEP 1 : determine the absolute humidity of the air

It can be determined on a Mollier diagram or psychrometric chart : the absolute humidity is ~0.010 kg water / kg of dry air

STEP 2 : calculate the difference in enthalpy in between states

HB-HA = (1005+1884*0.010)*(273.15+35)-(1005+1884*0.010)*(273.15+25) = 10238 J/kg of dry air

Graphically

It is possible to calculate the energy required to heat up humid air by using a psychrometric chart. Knowing the starting conditions, it is possible to determine the final conditions by moving along the lines of constant specific humidity. The difference of enthalpy read on the graph between the starting and final conditions allows to calculate the energy required to heat up the humid air considered.

Psychrometric diagram : heat up humid air

The value obtained graphically is close to the calculated value, the difference is coming from the chart used, how easy it is to precisely define the different values.