# Effectiveness–NTU Calculator (Heat Exchanger)

URL: https://speedycalculator.com/calculators/physics/effectiveness-ntu/
Last updated: 2026-10-30

> The effectiveness–NTU calculator finds the number of transfer units, effectiveness, heat duty and outlet temperatures of a parallel-flow, counter-flow, shell-and-tube or cross-flow heat exchanger from the flow rates, specific heats, inlet temperatures and UA.

## Inputs

- Exchanger type
- Hot fluid mass flow (kg/s, kg/h, g/s, lb/s, lb/min)
- Hot fluid specific heat (J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C))
- Hot inlet temperature (°C, °F, K)
- Cold fluid mass flow (kg/s, kg/h, g/s, lb/s, lb/min)
- Cold fluid specific heat (J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C))
- Cold inlet temperature (°C, °F, K)
- UA (W/K)

## Results

- Heat capacity ratio C_r
- NTU
- Effectiveness ε
- Heat transfer rate
- Hot outlet temperature
- Cold outlet temperature

## Formula

```
C = ṁ·c_p,  C_r = C_min/C_max,  NTU = UA/C_min · Counter-flow: ε = (1 − e^{−NTU(1−C_r)})/(1 − C_r·e^{−NTU(1−C_r)})
q = ε·C_min·(T_h,in − T_c,in),  T_h,out = T_h,in − q/C_h,  T_c,out = T_c,in + q/C_c
```

## Explanation

When outlet temperatures are unknown, the effectiveness–NTU method predicts how well a given heat exchanger will perform. Effectiveness is the fraction of the maximum possible heat transfer that actually happens.

### How to use the Effectiveness–NTU Calculator

- **Exchanger type**
- **Hot fluid mass flow**
- **Hot fluid specific heat**
- **Hot inlet temperature**
- **Cold fluid mass flow**
- **Cold fluid specific heat**
- **Cold inlet temperature**
- **UA (W/K)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the exchanger type, enter both streams' mass flow, specific heat and inlet temperature, and the product UA.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterExchanger typeChoose one: Parallel flow, Counter flow, Shell and tube (one shell pass), Cross flow, both fluids unmixed …Hot fluid mass flowUnits: kg/s, kg/h, g/s, lb/s, lb/minHot fluid specific heatUnits: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C)Hot inlet temperatureUnits: °C, °F, KCold fluid mass flowUnits: kg/s, kg/h, g/s, lb/s, lb/minCold fluid specific heatUnits: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C)Cold inlet temperatureUnits: °C, °F, KUA (W/K)A number

### What each result means

- **Heat capacity ratio C_r** = [Cmin]÷max([Ch], [Cc])
- **NTU** = [UA (W÷K)]÷[Cmin]
- **Heat transfer rate** = [Effectiveness ε]×[Cmin]×([Hot inlet temperature] - [Cold inlet temperature])÷1000
- **Hot outlet temperature** = [Hot inlet temperature] - [Heat transfer rate]×1000÷[Ch]
- **Cold outlet temperature** = [Cold inlet temperature] + [Heat transfer rate]×1000÷[Cc]

### Example values

How the main result changes when **Hot fluid mass flow** changes and everything else stays at the example values above:

Hot fluid mass flow (kg/s)Effectiveness ε0.250.90.3750.76840.50.65520.6250.56610.750.496410.4955

## Worked example

Inputs — Exchanger type: Counter flow; Hot fluid mass flow: 0.5 kg/s; Hot fluid specific heat: 4,182 J/(kg·K); Hot inlet temperature: 90 °C; Cold fluid mass flow: 0.8 kg/s; Cold fluid specific heat: 4,182 J/(kg·K); Cold inlet temperature: 15 °C; UA (W/K): 3,000.

Results — Heat capacity ratio C_r = 0.625; NTU = 1.4347; **Effectiveness ε = 0.65521**; Heat transfer rate = 102.75302 kW; Hot outlet temperature = 40.8594 °C; Cold outlet temperature = 45.7129 °C.

## Key terms

- **Effectiveness**: Actual heat transfer divided by the maximum possible.

## FAQ

**What is NTU?**
UA/C_min – the "thermal size" of the exchanger.

**Which type is most effective?**
Counter-flow, for the same NTU.

**When is the ε–NTU method used?**
When outlet temperatures are unknown (rating problems).

**What is C_r?**
Ratio of the smaller to the larger heat capacity rate.

**What formula does the Effectiveness–NTU Calculator use?**
C = ṁ·c_p,  C_r = C_min/C_max,  NTU = UA/C_min · Counter-flow: ε = (1 − e^{−NTU(1−C_r)})/(1 − C_r·e^{−NTU(1−C_r)}).


## Sources

- [Incropera – Fundamentals of Heat and Mass Transfer (reference text)](https://www.wiley.com/en-us/Fundamentals+of+Heat+and+Mass+Transfer%2C+8th+Edition-p-9781119320425)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)