How to use the NTU-Effectiveness Calculator
- 1. Pick the problemRating (area known, find outlets) or sizing (target outlet, find area).
- 2. Choose the exchangerCounter, parallel, shell and tube, three cross-flow cases, or phase change.
- 3. Enter the fluidsInlet temperatures, flow rates, cp and U to get the full answer.
ε-NTU method
Capacity rates are C = ṁ·cp for each fluid. With Cmin the smaller one and Cr = Cmin/Cmax:
- NTU = UA / Cmin
- Qmax = Cmin (Th,in − Tc,in) and Q = ε·Qmax
- Counter flow: ε = [1 − e^(−NTU(1−Cr))] / [1 − Cr·e^(−NTU(1−Cr))]
- Parallel flow: ε = [1 − e^(−NTU(1+Cr))] / (1 + Cr)
- Boiling or condensing (Cr = 0): ε = 1 − e^(−NTU) for every type
The shell and tube and cross-flow relations are the standard ones in Cengel's tables. For sizing, the tool uses the inverse relation (or a numerical solve for the both-unmixed cross-flow case) to get NTU from ε.
Worked example and exam tips
Oil (0.5 kg/s, cp 2.1) at 150 °C is cooled by water (0.4 kg/s, cp 4.18) at 20 °C in a 5 m² counter-flow exchanger with U = 300 W/m²K. Ch = 1.05 kW/K = Cmin, Cc = 1.672 kW/K, so Cr = 0.628 and NTU = 1500 / 1050 = 1.43. This gives ε = 0.653, so Q = 0.653 × 1.05 × 130 = 89.2 kW. The oil leaves at 65 °C and the water at 73 °C.
- Qmax always uses Cmin, never Cmax.
- A parallel-flow exchanger can never pass ε = 1/(1 + Cr), however large it is.
- Check your answer: ṁcpΔT must be the same Q for both fluids.
Frequently asked questions
What is effectiveness?
The actual heat transfer divided by the largest heat transfer the inlet temperatures allow. It runs from 0 to 1.
What does NTU mean physically?
NTU measures the size of the exchanger compared with the smaller capacity rate. A larger NTU means more area per unit of flow.
Why does phase change give Cr = 0?
A boiling or condensing fluid stays at a constant temperature, so it behaves as if its capacity rate were infinite.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.