Latent Heat Flow

Overview

Engineering reference data for Latent Heat Flow in HVAC systems.

Key Formulas

Sensible Heat

$Q = \dot{m} c_p \Delta T$

Heat causing temperature change.

Latent Heat

$Q = \dot{m} h_{fg} \Delta\omega$

Heat causing moisture change.

COP (Cooling)

$COP = Q_c / W$

Coefficient of performance.

Variables

Example - Latent Heat Flow

Step-by-Step Calculation

The latent heat flow due to moisture in air can be calculated using the SI-unit formula:

$Q_l = \frac{h_{we} \cdot \rho \cdot q \cdot \Delta x}{3600}$

Given Data:

• Air flow rate: $q = 10000 \, \text{m}^3/\text{h}$
• Supply air conditions: $0^\circ \text{C}$, $100\%$ relative humidity
  • Humidity ratio from Mollier diagram: $x_{supply} = 0.0037 \, \text{kg}_{\text{H}_2\text{O}}/\text{kg}_{\text{dry air}}$
• Room air conditions: $20^\circ \text{C}$, $40\%$ relative humidity
  • Humidity ratio from Mollier diagram: $x_{room} = 0.0057 \, \text{kg}_{\text{H}_2\text{O}}/\text{kg}_{\text{dry air}}$

Standard Properties:

• Latent heat of vaporization: $h_{we} = 2454 \, \text{kJ/kg}$ (at atmospheric pressure and $20^\circ \text{C}$)
• Air density: $\rho = 1.202 \, \text{kg/m}^3$

Humidity Ratio Difference: $\Delta x = x_{room} - x_{supply} = 0.0057 - 0.0037 = 0.002 \, \text{kg}_{\text{H}_2\text{O}}/\text{kg}_{\text{dry air}}$

Calculation: $Q_l = \frac{2454 \times 1.202 \times 10000 \times 0.002}{3600} = 16.5 \, \text{kW}$

Note: The example uses $h_{we} = 2465.56 \, \text{kJ/kg}$ instead of the standard 2454 kJ/kg, which may account for temperature variations or specific conditions.

Properties and Measurement Notes

Air Property Variations

• Temperature Dependence: The latent heat of vaporization ($h_{we}$), air density ($\rho$), and humidity ratios all vary with temperature and pressure.
• Interpolation: When calculating latent heat flow at non-standard conditions, interpolate property values if exact data isn't available.
• Measurement Tools: Humidity ratios ($\Delta x$) are typically obtained from:
  • Mollier Diagrams (Psychrometric charts)
  • Hygrometers (direct measurement)
  • Calculated from wet-bulb/dry-bulb temperatures

Humidity Ratio ($\Delta x$) Significance

• Positive $\Delta x$: Indicates moisture is being added to the air (humidification)
• Negative $\Delta x$: Indicates moisture is being removed (dehumidification)
• Unit Consistency: Ensure all humidity ratios use the same base units ($\text{kg}_{\text{H}_2\text{O}}/\text{kg}_{\text{dry air}}$ or $\text{lb}_{\text{H}_2\text{O}}/\text{lb}_{\text{dry air}}$)

Imperial vs. SI Unit Conversion

When converting between systems, note:

• $1 \, \text{kW} = 3412 \, \text{Btu/hr}$
• $1 \, \text{m}^3/\text{h} = 0.5886 \, \text{ft}^3/\text{min}$
• Density and latent heat values change with unit system and measurement conditions

References

• Original Source