Heat Recovery Efficiency

Overview

Engineering reference data for Heat Recovery Efficiency in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Heat Recovery Principles

Heat recovery units in ventilation and air conditioning systems operate on several common principles, each with distinct characteristics for transferring sensible and latent heat:

• Return Air Recovery Units: Outlet air is mixed directly into the supply air stream, transferring both sensible and latent heat without an intermediate medium.
• Rotating Heat Exchangers: A wheel alternately passes through outlet and supply air flows, transferring heat. Hygroscopic wheels enhance moisture (latent heat) transfer; non-hygroscopic wheels drain condensate.
• Air-Fluid-Air Exchangers: Heat is transferred from outlet air to a circulating fluid, then from the fluid to supply air. Moisture may condense but is not transferred to the supply stream.
• Cross Flow Heat Exchangers: Heat transfers directly through separating walls between air streams. Latent heat can be recovered via condensation, but moisture is not transferred.
• Heat Pumps: Utilize additional energy (typically 1/3 to 1/5 of recovered energy) to boost heat recovery, transferring both sensible and latent heat. Condensation occurs, but moisture is not transferred.

Transfer Efficiency Calculations

Efficiency metrics for heat recovery units quantify how effectively heat, moisture, or enthalpy is transferred between air streams. These are defined as follows:

Temperature Transfer Efficiency

$$\mu_t = \frac{t_2 - t_1}{t_3 - t_1}$$

Where:

• $\mu_t$ is the temperature transfer efficiency.
• $t_1$ is the temperature of outside make-up air before the heat exchanger (°C or °F).
• $t_2$ is the temperature of outside make-up air after the heat exchanger (°C or °F).
• $t_3$ is the temperature of outlet air before the heat exchanger (°C or °F).

Moisture Transfer Efficiency

$$\mu_m = \frac{x_2 - x_1}{x_3 - x_1}$$

Where:

• $\mu_m$ is the moisture transfer efficiency.
• $x_1$ is the moisture content of outside make-up air before the heat exchanger (kg/kg or grains/lb).
• $x_2$ is the moisture content of outside make-up air after the heat exchanger (kg/kg or grains/lb).
• $x_3$ is the moisture content of outlet air before the heat exchanger (kg/kg or grains/lb).

Enthalpy Transfer Efficiency

$$\mu_e = \frac{h_2 - h_1}{h_3 - h_1}$$

Where:

• $\mu_e$ is the enthalpy transfer efficiency.
• $h_1$ is the enthalpy of outside make-up air before the heat exchanger (kJ/kg or Btu/lb).
• $h_2$ is the enthalpy of outside make-up air after the heat exchanger (kJ/kg or Btu/lb).
• $h_3$ is the enthalpy of outlet air before the heat exchanger (kJ/kg or Btu/lb).

Psychrometric Visualization

Heating processes with heat recovery can be visualized in psychrometric diagrams. For systems without moisture transfer (e.g., cross flow exchangers), the supply air temperature rises while humidity remains constant. For systems with moisture transfer (e.g., rotating wheels), both temperature and humidity increase in the supply air stream. These processes illustrate how sensible and latent energy changes affect air state, relevant for design and performance analysis.

References

• Original Source