What is the ε-NTU method?

It relates a heat exchanger's effectiveness to its Number of Transfer Units, NTU, which equals UA divided by the smaller heat-capacity rate. Effectiveness is the ratio of actual heat transfer to the maximum thermodynamically possible. The method avoids the trial-and-error of the LMTD approach when outlet temperatures are unknown.

How is effectiveness calculated for counter-flow?

For a counter-flow exchanger with capacity ratio Cr below 1, effectiveness is one minus the exponential of negative NTU times one-minus-Cr, all divided by one minus Cr times that same exponential. When Cr equals 1 it simplifies to NTU divided by one plus NTU.

Why does counter-flow beat parallel-flow?

In counter-flow the streams move in opposite directions, so a temperature difference is maintained along the whole length and the cold outlet can in theory approach the hot inlet. In parallel-flow both outlets converge toward a common temperature, capping effectiveness well below the counter-flow value for the same NTU.

What specific heat should I use for water and air?

Liquid water is about 4,186 J/kg·K and dry air near room conditions is about 1,005 J/kg·K. Use the value for the actual fluid and temperature; for an HRV core moving air, both streams use the air figure, while a water-to-water exchanger uses the water figure on both sides.

What does the cross-flow result assume?

It uses the standard Kays and London correlation for a cross-flow exchanger with both fluids unmixed, which is the common case for plate-fin and HRV cores. Mixed-stream or multi-pass shell-and-tube geometries use different relations and will read slightly differently.

What is the Heat Exchanger NTU-Effectiveness Calculator?

Compute heat exchanger effectiveness, heat transfer rate, and hot and cold outlet temperatures using the ε-NTU method for counter-flow, parallel-flow, and cross-flow units from mass flows, specific heats, UA, and inlet temperatures. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Heat Exchanger NTU-Effectiveness Calculator

Name: Heat Exchanger NTU-Effectiveness Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

When you know a heat exchanger’s size — captured by its overall conductance UA — but not the outlet temperatures, the ε-NTU method is the fastest way to find the heat duty. It expresses performance as a single dimensionless effectiveness that depends only on NTU, the ratio of the two streams’ heat-capacity rates, and the flow geometry. This calculator handles counter-flow, parallel-flow, and unmixed cross-flow units.

How it works

Each stream’s heat-capacity rate is its mass flow times specific heat, C = ṁ·cp. The smaller of the two is Cmin and the ratio Cr = Cmin/Cmax. The Number of Transfer Units is:

NTU = UA / Cmin
Cr  = Cmin / Cmax

Effectiveness follows the arrangement. For counter-flow with Cr below 1:

eff = (1 - exp(-NTU(1 - Cr))) / (1 - Cr*exp(-NTU(1 - Cr)))

Parallel-flow uses (1 - exp(-NTU(1 + Cr))) / (1 + Cr), and unmixed cross-flow uses the Kays and London correlation. The actual duty and outlet temperatures then come from the maximum possible transfer:

q_max = Cmin * (T_hot_in - T_cold_in)
q     = eff * q_max
T_hot_out  = T_hot_in  - q / C_hot
T_cold_out = T_cold_in + q / C_cold

Example and notes

Take a water-to-water counter-flow exchanger: hot stream 0.5 kg/s, cold 0.8 kg/s, both cp 4,186 J/kg·K, UA of 2,000 W/K, hot in 80°C, cold in 15°C. Cmin is the hot stream at 2,093 W/K, Cr is 0.625, NTU is about 0.956, and effectiveness lands near 0.55. The hot stream leaves around 44°C and the cold stream rises to roughly 36°C.

Effectiveness never exceeds 1, and for a fixed UA the only way to raise it is to lower the flow rates (raising NTU) or switch to a counter-flow layout. Use this to size HRV cores, hydronic plate exchangers, and water-to-water loops; for multi-pass shell-and-tube units apply the appropriate correction factor instead.

Counter-flow vs parallel-flow: the practical difference

For the same NTU and capacity ratio, a counter-flow arrangement always achieves higher effectiveness than parallel-flow. At NTU = 2 and Cr = 0.5, for example:

Counter-flow effectiveness ≈ 0.83
Parallel-flow effectiveness ≈ 0.64

The difference grows with NTU. This is why virtually all high-performance heat exchangers — plate heat exchangers, HRV/ERV cores, and compact brazed-plate units — are designed for counter-flow or near-counter-flow geometry. Parallel-flow is occasionally used when a limited outlet temperature difference is needed for process reasons, but for maximising energy recovery it is always the inferior choice.

HRV and ERV sizing context

For residential heat recovery ventilators (HRV) and energy recovery ventilators (ERV), the ε-NTU method directly predicts sensible effectiveness, which is the key performance metric quoted on HRV certification data sheets (HVI standard). Enter the ventilation airflow rate as both the hot and cold mass flows (they are approximately equal in a balanced HRV), use cp = 1,005 J/kg·K for air, and enter the UA from the manufacturer’s specification or back-calculate from the certified effectiveness and flow rates at rated conditions. The result lets you predict performance at off-design flow rates, such as when the HRV runs at low speed.

Notes on the cross-flow result

The cross-flow formula used here assumes both fluids unmixed — the standard assumption for plate-fin and air-to-air cores where each fluid streams through many narrow parallel passages without lateral mixing. If one fluid is well-mixed (for example, the shell side of a small shell-and-tube unit), the correct effectiveness formula differs. Multi-pass and shell-and-tube geometries with baffles use correction factors on the LMTD method or their own NTU-effectiveness relations, which are beyond this calculator’s scope.