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The process of sensible heating of air can be expressed in the Mollier diagram as:

Heating of air moves the air condition from A to B along a constant specific humidity - x - line. The supplied heat - dH - can be read in the diagram as shown.
The heating process of air expressed can also be expressed in the psychrometric chart as:

Note! When heating air the specific moisture remains constant and the relative humidity decreases.
The enthalpy of moist air can be expressed as:
h = cpa t + x [cpw t + hwe] (1)
where
h = specific enthalpy of moist air (kJ/kg)
cpa = 1.01 - specific heat capacity of air at constant pressure (kJ/kg.oC, kWs/kg.K)
t = air temperature (oC)
x = humidity ratio (kg/kg)
cpw = 1.84 - specific heat capacity of water vapor at constant pressure (kJ/kg.oC, kWs/kg.K)
hwe = 2,502 - evaporation heat of water at 0oC (kJ/kg)
(1) can be modified as:
h = 1.01 (kJ/kg.oC) t + x [1.84 (kJ/kg.oC) t + 2,502 (kJ/kg)] (1b)
The enthalpy difference when heating air without changing moisture content can be expressed as:
dhA-B = cpa tB + x [cpw tB + hwe] - cpa tA + x [cpw tA + hwe]
= cpa(tB - tA) + x cpw (tB - tA) (2)
The specific humidity of air at 25oC and relative moisture 50% is 0.0115 kg/kg - check the Mollier diagram. The change in enthalpy when heating the air to 35oC can be calculated as:
dhA-B = (1.01 kJ/kg.oC)(35oC - 25oC) + (0.0115 kg/kg) (1.84 kJ/kg.oC) (35oC - 25oC)
= 10.1 kJ/kg + 0.2 kJ/kg
= 10.3 kJ/kg
Note! The contribution from the water vapor is relatively small and for practical purposes it may often be neglected. (2) can then be modified to:
dhA-B = cpa( tB - tA) (2b)
If heat is added to humid air the increase air temperature can be calculated by modifying (2b) [(2) to be more exact]:
tB - tA = dhA-B / cpa (2b)
If 10.1 kJ is added to 1 kg air, the temperature rise can be calculated as:
tB - tA = (10.1 kJ/kg) / (1.01 kJ/kg.oC)
= 10oC
The total heat flow rate through a heating coil can be calculated as:
q = m (hB - hA) (3)
where
q = heat flow rate (kJ/s, kW)
m = mass flow rate of air (kg/s)
The total heat flow can also be expressed as:
qs = v ρ (hB - hA) (3a)
where
v = volume flow (m3/s)
ρ = density of air (kg/m3)
Note! The density vary with temperature. At 0oC the density is 1.293 kg/m3. At 80oC the density is 1.0 kg/m3.
It's common to express the sensible heat flow rate as:
q = m cpa (tB - tA) (3b)
or alternatively:
q = v ρ cpa (tB - tA) (3c)
For a limited heating coil surface the average surface temperature will always be higher than the outlet air temperature. The effectiveness of a heating coil can be expressed as:
μ = (tB - tA) / (tHC - tA) (4)
where
μ = heating coil effectiveness
tHC = mean surface temperature of the heating coil (oC)
1 m3/s of air at 15oC and relative humidity 60% (A) is heated to 30oC (B). The surface temperature of the heating coil is 80oC. The density of air at 20oC is 1.205 kg/m3.
From the Mollier diagram the enthalpy in (A) is 31 kJ/kg and in (B) 46 kJ/kg.
The heating coil effectiveness can be calculated as:
μ = (30oC - 15oC) / (80oC - 15oC)
= 0.23
The heat flow can be calculated as:
q = (1 m3/s) (1.205 kg/m3) ((46 kJ/kg) - (31 kJ/kg))
= 18 (kJ/s, kW)
As an alternative, as one of the most common methods:
q = (1 m3/s) (1.205 kg/m3) (1.01 kJ/kg.oC) (30oC - 15oC)
= 18.3 (kJ/s, kW)
Note! Due to inaccuracy when working diagrams there is a small difference between the total heat flow and the sum of the latent and sensible heat. This inaccuracy is in general within acceptable limits.
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