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Heating Humid Air

Reference data and engineering information about heating humid air for air psychrometrics applications.

heatinghumidair

Overview

Engineering reference data for Heating Humid Air in air psychrometrics.

Key Formulas

Humidity Ratio

ω=0.622PvPa\omega = 0.622 \frac{P_v}{P_a}

Mass of water vapor per mass of dry air.

Relative Humidity

ϕ=PvPvs×100%\phi = \frac{P_v}{P_{vs}} \times 100\%

Ratio of actual to saturation vapor pressure.

Wet Bulb Temperature

Twb=Tdb−Pvs−PvγT_{wb} = T_{db} - \frac{P_{vs} - P_v}{\gamma}

Temperature measured by wet-bulb thermometer.

Enthalpy of Moist Air

h=cpT+ωhgh = c_p T + \omega h_g

Sensible + latent heat per unit mass of dry air.

Variables

SymbolDescriptionUnit
ω\omegaHumidity ratiokg/kg
ϕ\phiRelative humidity%
PvP_vVapor pressurePa
PvsP_{vs}Saturation vapor pressurePa
TdbT_{db}Dry bulb temperature°C
TwbT_{wb}Wet bulb temperature°C

Sensible Heating Process

When heating humid air without adding moisture (sensible heating), the specific humidity (xx) remains constant while the relative humidity decreases. This process moves along a constant-xx line on a Mollier or psychrometric diagram.

Detailed Examples

Example: Enthalpy Change Calculation

Given air at 25∘C25^\circ\text{C} with a specific humidity of 0.0115 kg/kg0.0115\,\text{kg/kg}, the enthalpy change when heating to 35∘C35^\circ\text{C} is: ΔhA−B=(1.01 kJkg⋅∘C)(35−25)∘C+(0.0115 kgkg)(1.84 kJkg⋅∘C)(35−25)∘C≈10.3 kJkg\Delta h_{A-B} = (1.01\,\frac{\text{kJ}}{\text{kg}\cdot^\circ\text{C}})(35 - 25)^\circ\text{C} + (0.0115\,\frac{\text{kg}}{\text{kg}})(1.84\,\frac{\text{kJ}}{\text{kg}\cdot^\circ\text{C}})(35 - 25)^\circ\text{C} \approx 10.3\,\frac{\text{kJ}}{\text{kg}} Note: The water vapor contribution is small and often negligible in practice, allowing the simplified formula ΔhA−B=cpa(tB−tA)\Delta h_{A-B} = c_{pa}(t_B - t_A).

Example: Temperature Rise from Added Heat

Adding 10.1 kJ10.1\,\text{kJ} to 1 kg1\,\text{kg} of air results in a temperature rise: tB−tA=10.1 kJ/kg1.01 kJ/(kg⋅∘C)=10∘Ct_B - t_A = \frac{10.1\,\text{kJ/kg}}{1.01\,\text{kJ/(kg}\cdot^\circ\text{C)}} = 10^\circ\text{C}

Example: Heating Coil Analysis

Heating 1 m3/s1\,\text{m}^3\text{/s} of air from 15∘C15^\circ\text{C} (enthalpy 31 kJ/kg31\,\text{kJ/kg}) to 30∘C30^\circ\text{C} (enthalpy 46 kJ/kg46\,\text{kJ/kg}) with a coil surface at 80∘C80^\circ\text{C}:

  • Heating Coil Effectiveness: μ=30−1580−15≈0.23\mu = \frac{30 - 15}{80 - 15} \approx 0.23
  • Heat Flow Rate (Total): q=(1 m3/s)(1.205 kg/m3)(46−31 kJ/kg)=18 kWq = (1\,\text{m}^3\text{/s})(1.205\,\text{kg/m}^3)(46 - 31\,\text{kJ/kg}) = 18\,\text{kW}
  • Heat Flow Rate (Sensible): q=(1 m3/s)(1.205 kg/m3)(1.01 kJkg⋅∘C)(30−15)∘C=18.3 kWq = (1\,\text{m}^3\text{/s})(1.205\,\text{kg/m}^3)(1.01\,\frac{\text{kJ}}{\text{kg}\cdot^\circ\text{C}})(30 - 15)^\circ\text{C} = 18.3\,\text{kW}

Note: Minor discrepancies between total and sensible heat calculations are due to diagram reading inaccuracies and are typically within engineering tolerance.

Practical Formulas & Properties

Key relationships for designing heating systems:

Sensible Heat Flow (Simplified): q=m˙cpa(tB−tA)=Lρcpa(tB−tA)q = \dot{m} c_{pa} (t_B - t_A) = L \rho c_{pa} (t_B - t_A)

Air Density Variation: Density (ρ\rho) changes with temperature. Key reference values:

  • At 0∘C0^\circ\text{C}: ρ≈1.293 kg/m3\rho \approx 1.293\,\text{kg/m}^3
  • At 80∘C80^\circ\text{C}: ρ≈1.0 kg/m3\rho \approx 1.0\,\text{kg/m}^3 Use density at the mean air temperature for accuracy.

References

Source: engineeringtoolbox.com