What is enthalpy mixing of air?

When two air streams of different temperature and humidity are mixed in mass-flow proportion, the specific enthalpy and humidity ratio of the mixed air are mass-weighted averages of the two. This follows from energy and mass conservation and is the basic equation used to design the outdoor-air mixing box of an air-handling unit and to read mixing graphically on a psychrometric chart.

What does outdoor air fraction (OAF) mean?

Outdoor air fraction (OAF) is the mass-flow share of outdoor air in the mixed stream, defined as x = m_oa /(m_oa + m_ra). For example, OAF = 30% means that for every 100 units of mixed air, 30 are outdoor air and 70 are return air. The lower bound is set by indoor air quality requirements (minimum ventilation), and the value is kept as small as possible to save energy.

Can the mixed temperature be obtained as a simple weighted average?

Strictly, the mixed temperature is back-solved from the weighted averages of enthalpy and humidity ratio, because the specific heat of moist air depends on humidity. In the usual HVAC range, however, the humidity-ratio difference is small, so a temperature-weighted average is numerically almost identical (for example, mixing 32 °C and 26 °C at 3:7 gives about 27.8 °C either way). This tool uses the rigorous back-solve.

How does the mixed point move on the psychrometric chart?

The mixed point MA always lies on the straight line connecting the outdoor air point OA and the return air point RA on the psychrometric chart. As OAF varies, MA slides along that line — at OAF = 0% it coincides with RA and at 100% with OA. The chart in this tool updates the three points and the mixing line in real time as the sliders move, making the geometric meaning of mixing intuitive.

Outdoor & Return Air Enthalpy Mixing Simulator

Parameters

Outdoor dry bulb T_oa

°C

Outdoor RH RH_oa

Return-air dry bulb T_ra

°C

Outdoor air fraction OAF

Return-air RH is fixed at 50%, atmospheric pressure at 1013 hPa. OAF = 0% is full return-air recirculation; 100% is 100% outdoor air.

Results

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Mixed temperature T_ma

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Mixed humidity ratio w_ma

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Mixed enthalpy h_ma

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Mixed RH RH_ma (computed)

Mixing on the Psychrometric Chart (T–w)

Red = OA / Blue = RA / Green = MA. The three points are collinear, and MA moves between OA and RA as OAF changes.

Theory & Key Formulas

When outdoor air (mass flow $m_\text{oa}$) and return air (mass flow $m_\text{ra}$) mix, with the outdoor air fraction $x = m_\text{oa}/(m_\text{oa}+m_\text{ra})$, the humidity ratio and specific enthalpy of the mixed air are mass-weighted averages.

Mass conservation (humidity ratio):

$$w_\text{ma} = x\,w_\text{oa} + (1-x)\,w_\text{ra}$$

Energy conservation (specific enthalpy):

$$h_\text{ma} = x\,h_\text{oa} + (1-x)\,h_\text{ra}$$

Mixed temperature back-solved from the moist-air enthalpy ($w$ in kg/kg, $h$ in kJ/kg DA):

$$T_\text{ma} = \frac{h_\text{ma} - 2.501\,w_\text{ma}}{1.006 + 1.86\,w_\text{ma}}$$

The saturation vapor pressure uses the Magnus form $e_s(T)=6.112\exp[17.62\,T/(243.12+T)]$ hPa, and the humidity ratio is $w = 622\,e/(p-e)$ g/kg.

What is the Enthalpy Mixing Simulator

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An office air conditioner does not just bring in fresh outside air all the time, right? I heard that it mixes indoor air with outdoor air.

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Right. Bringing in 100% outdoor air and cooling it would be hugely expensive, so the unit mixes return air from the rooms with a fraction of outdoor air, and then cools and dehumidifies. The fraction is set by the "outdoor air fraction" (OAF) slider above. With OAF = 30%, the mixed stream is 30% outdoor air and 70% return air.

🙋

Can I just take a plain average of the two temperatures to get the mixed temperature?

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The strict approach is to weight-average enthalpy and humidity ratio, because the specific heat of moist air depends on humidity. The simple temperature average is off by less than 0.1 °C in the normal HVAC range, so it is fine for quick estimates. This tool uses the rigorous enthalpy back-solve, but for the defaults (32 °C and 26 °C at 3:7) the answer of 27.8 °C matches the simple average almost exactly.

🙋

The three points on the chart are on a straight line. Does that have a physical meaning?

🎓

A key point. Because mixing is set only by mass and energy conservation, MA must lie on the straight line joining OA and RA on the psychrometric chart. With OAF = 0% it sits on RA, and at 100% on OA, dividing the segment in proportion to the OAF — this is called the mixing line rule. In practice this chart guides the choice to keep OAF at the minimum ventilation rate on a hot summer day, and to push OAF to 100% on a cool shoulder-season day for free cooling.

🙋

The mixed RH is also shown. Why is it about 55%, even though OA is 60% and RA is 50%?

🎓

Relative humidity does not simply weight-average. Mixing is done on humidity ratio (kg/kg), and only afterwards the new RH is computed by comparing the mixed humidity ratio against the saturation pressure at the new temperature. Because the relationship is non-linear, you must work in humidity ratio for the mass balance and read RH back from the result. Taking a weighted RH directly can be off by several percent — a rule worth remembering near condensation limits.

Frequently Asked Questions

Moist-air energy is the sum of the dry-air sensible and the water-vapour sensible and latent contents, and specific enthalpy bundles them into a single quantity. Energy conservation holds for (enthalpy × mass flow), so the mixed enthalpy is a strict mass-weighted average. Temperature alone does not, because the moist-air specific heat depends on humidity.

A minimum OAF follows from the required outdoor-air per person in ventilation codes (such as ASHRAE 62.1) times the occupancy. In typical offices it is 20 to 40%. Under extreme outdoor conditions OAF is held at the minimum to save energy, but in mild seasons, when outdoor enthalpy is below indoor enthalpy, raising OAF to 100% gives substantial free-cooling savings (the air-side economizer mode).

At high altitudes (about 899 hPa at 1000 m, about 630 hPa at the top of Mount Fuji) the humidity-ratio and enthalpy values change. The pressure $p$ in $w = 622\,e/(p-e)$ is smaller, so the same temperature and RH give a larger humidity ratio. This tool is tuned for sea level (1013 hPa). For high-altitude work, apply a correction or use a dedicated high-altitude psychrometric chart.

In principle, yes. When warm humid outdoor air is mixed with cold dry return air, the mixing line can temporarily pass above the saturation curve and the mixture becomes supersaturated, forming microscopic droplets — known as "mixing fog". The default range in this tool does not produce it, but in extreme parameter combinations the mixed point may enter the saturated region, indicating condensation and drain water inside the air-handling unit. In practice this drives the sizing of the dehumidifying coil.

Real-World Applications

Mixing-box design in central air-handling units (AHU): In a building or factory central system, rooftop outdoor air and return air from the floors meet in the mixing box and are then cooled and dehumidified by a coil. Predicting the temperature and humidity of the mixed air sets the required coil capacity and chiller load. This tool implements exactly the equations used to find the mixing-box outlet state.

Air-side economizer decisions: In spring and autumn, there are hours when outdoor enthalpy falls below the indoor target enthalpy. At those times pushing OAF to 100% gives cooling without running the chiller. Implementation requires an enthalpy comparison, and you can feel the savings potential by reading off the OA and RA enthalpies in this tool.

Temperature and humidity control in data centers: Free cooling of high-density IT equipment with outdoor air is very effective, but mismanaging humidity risks static electricity or condensation. You need to track the mixed humidity ratio and the mixed RH separately, so understanding how they evolve with this tool sharpens the design decision.

Boundary conditions for CFD and BEM: In building energy modeling (BEM) and AHU-internal CFD, the AHU-inlet air state is given as the mixed state of outdoor and return air. The same mass-weighted averaging used in this tool sits inside the HVAC component models of EnergyPlus, TRNSYS, Modelica and similar tools.

Common Misconceptions and Cautions

The most common misconception is to assume that relative humidity can be weight-averaged as well. As OAF varies in this simulator, the mixed RH is not a plain weighted average of the two RH values. Mixing 60% outdoor air with 50% return air at 3:7 does not give 53% — it gives about 55%, because mass balance is done on humidity ratio and RH is read back from the saturation pressure at the new temperature. For condensation-margin checks, always work in humidity ratio.

The next pitfall is to think that increasing OAF always improves air quality "for free". More outdoor air does dilute CO2 and VOCs, but in summer it adds cooling load and in winter it adds humidification load. Raising OAF above the ventilation minimum can square the energy penalty, so combining it with demand-controlled ventilation (DCV) based on CO2 sensors — bringing in extra outdoor air only when needed — is usually the best compromise. Compare the enthalpy of mixed air in this tool with OAF at 30% vs 80% to feel the increase in load.

Finally, watch out for "mixing fog". When very humid outdoor air is mixed with cold dry return air, the mixing line can cross the saturation curve, taking the air through an invisible supersaturated state. The resulting condensation drains inside the AHU, wetting fans and silencers — a real-world failure mode. Whether the OA–RA line crosses the saturation curve is easy to read off the chart in this tool. Always check the extreme seasonal OA / RA combinations during design.

Outdoor & Return Air Enthalpy Mixing Simulator

What is the Enthalpy Mixing Simulator

Frequently Asked Questions

Real-World Applications

Common Misconceptions and Cautions

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