Heating up Humid Air
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Air handling, in AHU or in drying operations, requires the heating of humid air. It is then important to be able to calculate the energy required to bring air from a temperature \(T_1\) to a temperature \(T_2\).
Humid Air Heating Calculator
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 increases.
2. Calculation of humid air heating energy requirements
By calculation
The 1st step is to define the enthalpy of humid air:
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)
- \(T_0\) = temperature of reference (K)
- \(\omega\) = Absolute humidity of air (kg_water/kg_dry_air)
- \(\Lambda_0\) = vaporization enthalpy at \(T_0\) (J/kg)
In practice, at 273.15 K (0°C):
Considering a temperature \(T_A\) (starting temperature) and a temperature \(T_B\) (end temperature), the energy required to heat up humid air, at constant absolute humidity is then:
Engineering Rules of Thumb:
- AHU Face Velocity: Standard heating coils are sized for 2.0 to 3.0 m/s (400-600 fpm) to balance heat transfer and pressure drop.
- Max Temperature: For comfort heating, supply air is typically limited to 35-45°C to avoid stratification.
- Specific Heat: For dry air, \(Cp \approx 1.005 \text{ kJ/kg.K}\). For humid air, it increases significantly with moisture content.
- Safety Margin: Always add 10-15% to the calculated heating load for duct losses and startup transients.
Example of humid air heating calculation: Step by Step calculation
Air at 25°C and 50% RH is to be heated up until 35°C, 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
\[ \Delta H = (1005 + 1884 \cdot 0.010) \cdot (35 - 25) = 10238 \text{ J/kg of dry air} \]
Graphically
It is possible to calculate the energy required to heat up humid air by using a psychrometric chart, which illustrates the thermodynamic properties of moist air for drying applications. Knowing the starting conditions, it is possible to determine the final conditions by moving along the lines of constant specific humidity.
The value obtained graphically is close to the calculated value; the difference comes from the chart resolution and reading precision.
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FAQ: Air Heating
Q: Does absolute humidity change during heating?
A: No, unless water is added or removed, \(\omega\) remains constant during sensible heating.
Q: Why does Relative Humidity drop?
A: Warmer air has a higher capacity to hold water vapor (higher saturation pressure), so the same amount of water represents a smaller percentage of the maximum possible.