Balanced sensible heat recovery

Estimate supply and exhaust outlet temperatures and sensible recovery for equal air heat-capacity rates.

How this calculation works

Begin with the outdoor and extract inlet temperatures and a sensible effectiveness applicable to the heat exchanger. The model is specifically balanced: both streams have the same mass flow and the same constant specific heat. Convert effectiveness from percent to a fraction and multiply it by the inlet temperature difference. This gives the supply temperature change and an equal opposite exhaust temperature change. Multiplying that change by either stream's heat-capacity rate gives the sensible transfer to the supply. A positive transfer warms incoming air; a negative transfer cools it. The calculation does not account for moisture transfer, condensation, frost control or fan heat. Unequal air heat-capacity rates need a different effectiveness treatment, so equal volume flows alone are not the stated balance condition.

Inputs and units

Outdoor inlet temperature (°C)
Extract inlet temperature (°C)
Sensible effectiveness (%)
Mass flow of each stream (kg/s)
Specific heat of each stream (kJ/(kg·K))

Method and formula

Tsupply,out = Toutdoor + ε(Textract−Toutdoor); Texhaust,out = Textract−ε(Textract−Toutdoor); Qto supply = m cp ε(Textract−Toutdoor), where ε is effectiveness/100.

Worked example

Example inputs

Outdoor inlet temperature: 0 °C
Extract inlet temperature: 22 °C
Sensible effectiveness: 75 %
Mass flow of each stream: 1 kg/s
Specific heat of each stream: 1.006 kJ/(kg·K)

Calculation steps

Effectiveness = 75 / 100 = 0.75. Supply temperature change = 0.75 × (22 − 0) = 16.5 K.
Supply outlet = 0 + 16.5 = 16.5 °C; exhaust outlet = 22 − 16.5 = 5.5 °C.
Sensible transfer to supply = 1 × 1.006 × 16.5 = 16.599 kW.

Example results

Supply outlet temperature: 16.5 °C
Exhaust outlet temperature: 5.5 °C
Sensible transfer to supply: 16.599 kW

Assumptions

Both streams have equal mass flow and equal constant specific heat.
Steady sensible-only exchange; positive duty heats the supply, negative duty cools it.

Limitations

No latent recovery, leakage, fan heat, defrost or unequal-flow correction.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

EnergyPlus Engineering Reference: Heat Exchangers: Section 16.8, equations 16.590–16.591: sensible effectiveness with heat-capacity-rate ratio
DOE Fundamentals: Thermodynamics: Specific heat, equation 1-17; first-law energy balance