HVAC Humidifier Sensible Heat Gain Calculation in Excel

HVAC Humidifier Sensible Heat Gain is the amount of heat added to the air by the humidification process. Humidification is the process of adding moisture to the air to increase its relative humidity. Relative humidity is the ratio of the amount of water vapor in the air to the maximum amount of water vapor that the air can hold at a given temperature.

Humidification can be done by various methods, such as spraying water, evaporating water, or injecting steam into the air. Each method has a different effect on the temperature and humidity of the air. For example, spraying water lowers the temperature and increases the humidity of the air, while injecting steam raises the temperature and increases the humidity of the air.

The sensible heat gain from humidification depends on the method, the amount, and the temperature of the water or steam added to the air. The sensible heat gain is calculated by multiplying the mass flow rate of the water or steam by the difference between the temperature of the water or steam and the temperature of the air before humidification. The sensible heat gain increases the cooling load of the HVAC system, which means that more energy is required to cool the air to the desired temperature and humidity.

The sensible heat gain from humidification can be reduced by choosing a method that minimizes the temperature difference between the water or steam and the air, such as evaporating water at a low pressure or using a heat exchanger to pre-cool the water or steam before humidification. Alternatively, the sensible heat gain can be offset by increasing the latent heat removal from the air, which means that more moisture is extracted from the air by the cooling coil or dehumidifier. The latent heat removal lowers the humidity and the temperature of the air, which reduces the cooling load of the HVAC system.

Basic Theory

The sensible heat gain (Q_sensible) due to a humidifier can be calculated using the formula:

$Q_{\text{sensible}} = \dot{m} \cdot c \cdot (\text{T}_{\text{outlet}} - \text{T}_{\text{inlet}})$

Where:

$\dot{m}$ is the mass flow rate of air (kg/s),
$c$ is the specific heat of air (kJ/kg·°C),
$\text{T}_{\text{outlet}}$ is the outlet air temperature (°C),
$\text{T}_{\text{inlet}}$ is the inlet air temperature (°C).

Procedures

Determine the Required Airflow ( $\dot{m}$ ):
- Evaluate the required airflow for the space based on factors such as room size, occupancy, and heat sources.
Specify Inlet and Outlet Air Temperatures ( $\text{T}_{\text{inlet}}$ and $\text{T}_{\text{outlet}}$ ):
- Determine the desired indoor air temperature ( $\text{T}_{\text{outlet}}$ ).
- Measure the initial air temperature ( $\text{T}_{\text{inlet}}$ ).
Gather Constants:
- Obtain the specific heat of air ( $c$ ).
Calculate Sensible Heat Gain:
- Use the formula to find the sensible heat gain introduced by the humidifier.

Scenario: Office Humidification

Let’s consider an office space with the following parameters:

Required airflow ( $\dot{m}$ ): 1.5 kg/s
Inlet air temperature ( $\text{T}_{\text{inlet}}$ ): 20°C
Outlet air temperature ( $\text{T}_{\text{outlet}}$ ): 25°C
Specific heat of air ( $c$ ): 1.006 kJ/kg·°C

Excel Calculation

Create an Excel table with the following columns:

$\dot{m}$ (kg/s)
$c$ (kJ/kg·°C)
$\text{T}_{\text{outlet}}$ (°C)
$\text{T}_{\text{inlet}}$ (°C)
Sensible Heat Gain ( $Q_{\text{sensible}}$ ) (kJ/s)

Input the scenario values into the respective columns and use the formula to calculate $Q_{\text{sensible}}$ .


            =A2 * B2 * (C2 - D2)

The result in the last column will give you the sensible heat gain.

Result

For our scenario:

$\dot{m}$ = 1.5 kg/s
$c$ = 1.006 kJ/kg·°C
$\text{T}_{\text{outlet}}$ = 25°C
$\text{T}_{\text{inlet}}$ = 20°C

Using the formula, we find $Q_{\text{sensible}}$ is 7.53 kJ/s.

MATLAB Comparison

For a MATLAB comparison, the same formula can be implemented using MATLAB code:


            % Constants
            m_dot = 1.5; % kg/s
            c = 1.006; % kJ/kg·°C
            T_outlet = 25; % °C
            T_inlet = 20; % °C

            % Sensible Heat Gain Calculation
            Q_sensible = m_dot * c * (T_outlet - T_inlet);
            disp(['Sensible Heat Gain (MATLAB): ' num2str(Q_sensible) ' kJ/s']);

Running this MATLAB code will yield the same sensible heat gain result for comparison.