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.

Heat Exchanger NTU-Effectiveness Calculator

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.