Liquid-to-Liquid Heat Transfer

This methodology works with hourly data only and each measurement is taken at the start of the hour. If the system operates seasonally, measurements should be taken for the duration of the season at one-hour intervals. If the system is not weather dependent, then a minimum of six (6) weeks of hourly data is required for this methodology to work.

The following equations are used to calculate the sensible heat transferred by the heat exchanger for a full year. All data used in this section should be measured with data loggers per the measurements techniques above.

1. Calculate the mass flow rate of fluid 1 and fluid 2 leaving the heat exchanger for each hour interval.

\begin{equation} \dot{m_1} = Q_1 * 0.13368 * d \end{equation}

Where,

$\dot{m_1} =$ hourly mass flow rate of fluid 1 leaving the heat exchanger ($lb_m$/min)

$Q_1 =$ hourly flow rate of fluid 1 leaving the heat exchanger (GPM)

$d =$ density of water, 62 $(lb/ft^3)$

$0.13368 =$ unit conversion, GPM to $(ft^3/min)$

\begin{equation} \dot{m_2} = Q_2 * 0.13368 * d \end{equation}

Where,

$\dot{m_2} =$ hourly mass flow rate of fluid 2 leaving the heat exchanger ($lb_m$/min)

$Q_2 =$ hourly flow rate of fluid 2 leaving the heat exchanger (GPM)

$d =$ density of water, 62 $(lb/ft^3)$

$0.13368 =$ unit conversion, GPM to $(ft^3/min)$

2. Heat transfer should be calculated only when the heat exchanger is operating. This can be determined by checking the temperature difference across the recovery system in both the supply side and waste heat stream side. Another condition is that water flow should exist across the heat exchanger.

\begin{equation} \text{If} \hspace{2mm} \begin{cases} T_1 - T_2 > 1 & \text{if heat transfer occurs}\\ T_1 - T_2 < -1 & \text{if heat transfer occurs} \\ -1 < T_1 - T_2 < 1 & \text{if no heat transfer occurs} \end{cases} \end{equation}

Where,

$T_1 =$ meausured hourly temperature of fluid 1 entering the heat exchanger (F)

$T_2 =$ meausured hourly temperature of fluid 1 leaving the heat exchanger (F)

\begin{equation} \text{If} \hspace{2mm} \begin{cases} T_3 - T_4 > 1 & \text{if heat transfer occurs}\\ T_3 - T_4 < -1 & \text{if heat transfer occurs} \\ -1 < T_3 - T_4 < 1 & \text{if no heat transfer occurs} \end{cases} \end{equation}

Where,

$T_3 =$ meausured hourly temperature of fluid 1 entering the heat exchanger (F)

$T_4 =$ meausured hourly temperature of fluid 1 leaving the heat exchanger (F)

\begin{equation} \text{If} \hspace{2mm} \begin{cases} Q_1 > 0 & \text{if heat transfer occurs}\\ Q_1 < 0 & \text{if no heat transfer occurs} \end{cases} \end{equation}

Where,

$Q_1 =$ hourly flow rate of fluid 1 leaving the heat exchanger (GPM)

3. Calculate the sensible heat transferred by the heat exchanger for each hour interval.

\begin{equation} q_{s1} = \dot{m_1} * 60 * (T_1 - T_2) \end{equation}

Where,

$q_{s1} =$ sensible heat transferred by the heat exchanger every hour for fluid 1(Btu/h)

$60 =$ unit conversion, (min/hour)

$\dot{m_1} =$ hourly mass flow rate of fluid 1 leaving the heat exchanger ($lb_m$\min)

$T_1 =$ hourly fluid 1 entering the heat exchanger temperature (F)

$T_2 =$ hourly fluid 1 leaving the heat exchanger temperature (F)

\begin{equation} q_{s2} = \dot{m_2} * 60 * (T_3 - T_4) \end{equation}

Where,

$q_{s2} =$ sensible heat transferred by the heat exchanger every hour for fluid 2(Btu/h)

$60 =$ unit conversion, (min/hour)

$\dot{m_2} =$ hourly mass flow rate of fluid 2 leaving the heat exchanger ($lb_m$\min)

$T_3 =$ hourly fluid 2 entering the heat exchanger temperature (F)

$T_4 =$ hourly fluid 2 leaving the heat exchanger temperature (F)

4. Calculate the total heat transfer by the heat exchanger for a whole year.

\begin{equation} Q_s = \sum_{t=0}^{8760} q_s \end{equation}

Where,

$Q_s =$ total sensible heat transfer for a whole year (Btu/h)

$q_s =$ sensible heat transferred by the heat exchanger every hour (Btu/h)

$t =$ hours