# Heat Exchanger ε-NTU Calculator (Effectiveness-NTU Method)

Compute the effectiveness (ε) of a heat exchanger by the ε-NTU method. C*=C_min/C_max (0..1), NTU=U·A/C_min, q_max=C_min·(T_h,in-T_c,in), and ε=q_actual/q_max. Supports four arrangements: Parallel flow ε=[1-exp(-NTU(1+C*))]/(1+C*); Counter flow ε=[1-exp(-NTU(1-C*))]/[1-C*·exp(-NTU(1-C*))], or NTU/(1+NTU) when C*=1; Shell-and-tube 1-2 ε=2/[1+C*+√(1+C*²)·(1+exp(-NTU√(1+C*²)))/(1-exp(-NTU√(1+C*²)))]; Crossflow (both unmixed) ε=1-exp{(NTU^0.22/C*)·[exp(-C*·NTU^0.78)-1]}. When C*=0 (phase change on one side, boiler/condenser) every arrangement gives ε=1-exp(-NTU). Optionally supply T_h,in and T_c,in to recover the actual heat-transfer rate q=ε·q_max and both outlet temperatures. Temperatures are used only as differences: Δ°C=ΔK and Δ°F×5/9=ΔK.

> Canonical page: https://elysiatools.com/en/tools/heat-exchanger-ntu

- **Category:** Math & Numbers

- **Keywords:** NTU, effectiveness, ε-NTU, heat exchanger, parallel flow, counter flow, shell and tube, crossflow, C*, capacity rate, thermal design

## Overview

Calculate heat exchanger effectiveness with the ε-NTU method for parallel-flow, counter-flow, shell-and-tube 1-2, or crossflow arrangements. Enter both heat-capacity rates, the overall heat transfer coefficient, and heat transfer area to obtain C*, NTU, and ε; optionally add inlet temperatures to calculate heat-transfer rate and outlet temperatures.

## Inputs

- **Exchanger Type** (select): Exchanger arrangement: Parallel Flow, Counter Flow, Shell-and-Tube (1 shell pass / 2 tube passes), or Crossflow (single pass, both fluids unmixed).
- **Hot-side Capacity Rate C_h** (number): Hot-side heat-capacity rate C_h = ṁ_h·c_p,h in W/K.
- **Cold-side Capacity Rate C_c** (number): Cold-side heat-capacity rate C_c = ṁ_c·c_p,c in W/K.
- **Overall Heat Transfer Coefficient U** (number): Overall heat transfer coefficient U in W/(m²·K).
- **Heat Transfer Area A** (number): Heat transfer area A in m².
- **Hot Inlet T_h,in (optional)** (number): Hot-side inlet temperature T_h,in, in the selected Temperature Unit. Optional; when supplied together with T_c,in the actual heat-transfer rate and both outlet temperatures are returned.
- **Cold Inlet T_c,in (optional)** (number): Cold-side inlet temperature T_c,in, in the selected Temperature Unit. Optional; when supplied together with T_h,in the actual heat-transfer rate and both outlet temperatures are returned.
- **Temperature Unit** (select): Unit of the inlet temperatures. Only differences matter: Δ°C = ΔK and Δ°F ×5/9 = ΔK.
- **Decimal Places** (number)

## When to use

- Estimate heat exchanger effectiveness when inlet and outlet temperatures are not yet known.
- Compare parallel-flow, counter-flow, shell-and-tube 1-2, and crossflow arrangements using the same operating data.
- Calculate actual heat transfer and both outlet temperatures when hot- and cold-side inlet temperatures are available.

## How it works

- Enter the hot-side capacity rate C_h, cold-side capacity rate C_c, overall coefficient U, and heat transfer area A.
- Select the exchanger arrangement; the calculator determines C_min, C_max, C*=C_min/C_max, and NTU=U·A/C_min.
- The appropriate ε-NTU relation is applied to calculate heat exchanger effectiveness.
- Optionally provide both inlet temperatures to calculate q_max, actual heat transfer q, and the hot- and cold-side outlet temperatures.

## Use cases

- Thermal design checks for process, HVAC, and energy systems.
- Early comparison of heat exchanger flow arrangements.
- Estimating heat duty and outlet temperatures from capacity rates and inlet conditions.

## Frequently asked questions

### What inputs are required?

Enter C_h, C_c, U, and A. The exchanger type is selectable, with counter flow used by default.

### Which exchanger arrangements are supported?

The calculator supports parallel flow, counter flow, shell-and-tube 1-2, and crossflow with both fluids unmixed.

### What does NTU mean?

NTU is the number of transfer units, calculated as U·A/C_min.

### Are inlet temperatures required?

No. They are optional. Provide both inlet temperatures to calculate actual heat transfer and outlet temperatures.

### Which temperature units can I use?

Use Kelvin, Celsius, or Fahrenheit. The calculation uses temperature differences, with Δ°C=ΔK and Δ°F×5/9=ΔK.

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