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Humid Air - Heating

Enthalpy change and temperature rise when heating humid air without adding moisture.

The process of sensible heating of air - heating without adding moisture - can be visualized in the Mollier diagram as:

Moist air - heating in Mollier chart

Sensible heating of air changes the state of the air from A to B along the constant specific humidity - x - line. The supplied heat - dH - can be estimated as indicated in the diagram above.

The heating process can also be visualized in the psychrometric chart

Moist air - heating in pshycrometric chart

Note! - when sensible heating of air - the specific moisture remains constant - the relative humidity is decreased.

Calculating Enthalpy

The enthalpy of moist air can be calculated as:

h = c pa t + x [c pw t + h we ] (1)


h = specific enthalpy of moist air (kJ/kg)

c pa = 1.01 - specific heat capacity of air at constant pressure (kJ/kg oC, kWs/kgK)

t = air temperature (oC)

x = humidity ratio (kg/kg)

c pw = 1.84 - specific heat capacity of water vapor at constant pressure (kJ/kg. oC, kWs/kg.K)

h we = 2502 - evaporation heat of water at 0 oC (kJ/kg)

(1) can be modified to:

h = 1.01 (kJ/kg. oC) t + x [1.84 (kJ/kg. oC) t + 2502 (kJ/kg)] (1b)

The Enthalpy Difference

The enthalpy difference when heating air without adding moisture can be calculated as:

dh A-B = c pa t B + x [c pw t B + h we ] - c pa t A + x [c pw t A + h we ]

= c pa (t B - t A ) + x c pw (t B - t A ) (2)

Example - Enthalpy Change when Heating Air

The specific humidity of air at 25 oC and relative moisture 50% is 0.0115 kg/kg - check the Mollier diagram . The change in enthalpy when heating the air to 35 oC can be calculated as:

dh A-B = (1.01 kJ/kg oC)(35 oC - 25 oC) + (0.0115 kg/kg) (1.84 kJ/kg oC) (35 oC - 25 oC)

= (10.1 kJ/kg) + (0.2 kJ/kg)

= 10.3 (kJ/kg)

Note! - the contribution from the water vapor is relatively small and can for practical purposes often be neglected. (2) can then be modified to:

dh A-B = c pa ( t B - t A ) (2b)

Increase in Temperature when Heating Air

If heat is added to humid air the increase in air temperature can be calculated by modifying (2b) to:

t B - t A = dh A-B / c pa (2c)

Example - Heating Air and Temperature Rise

If 10.1 kJ is added to 1 kg air the temperature rise can be calculated as:

t B - t A = (10.1 kJ/kg) / (1.01 kJ/kg oC)

= 10 (oC)

Heat Flow in a Heating Coil

The total heat flow rate through a heating coil can be calculated as:

q = m (h B - h A ) (3)


q = heat flow rate (kJ/s, kW)

m = mass flow rate of air (kg/s)

The total heat flow can also be expressed as:

q s = L ρ (h B - h A ) (3a)


L = air flow rate (m3 /s)

ρ = density of air (kg/m3 )

Note! The density of air varies with temperature. At 0 oC the density is 1.293 kg/m3 . At 80 oC the density is 1.0 kg/m3 .

It's common to express sensible heat flow rate as:

q = m c pa (t B - t A ) (3b)

or alternatively:

q = L ρ c pa (t B - t A ) (3c)

Heating Coil Effectiveness

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 = (t B - t A ) / (t HC - t A ) (4)


μ = heating coil effectiveness

t HC = mean surface temperature of the heating coil (oC)

Example - Heating Air

1 m3 /s of air at 15 oC and relative humidity 60% (A) is heated to 30 oC (B). The surface temperature of the heating coil is 80 oC . The density of air at 20 oC 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 = (30 oC - 15 oC) / (80 oC - 15 oC)

= 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) (30 oC - 15 oC)

= 18.3 (kJ/s, kW)

Note! Due to the inaccuracy when working with diagrams there is a small difference between the total heat flow and the sum of the latent and sensible heat. In general - this inaccuracy is within acceptable limits.

Related Topics

  • Air Psychrometrics

    Moist and humid air calculations. Psychrometric charts and Mollier diagrams. Air-condition systems temperatures, absolute and relative humidities and moisture content in air.

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