I. Known Conditions
- Overall heat transfer capacity K·A = 1500 W/K;
- Hot side C_hot = 3000 W/K (i.e., m·cp);
- Cold side C_cold = 5000 W/K;
- Hot inlet 180°C, cold inlet 25°C.
II. Calculate NTU and Heat Capacity Ratio
Take the smaller one Cmin = 3000 W/K:
NTU = K·A / Cmin = 1500 / 3000 = 0.5
Cr = Cmin / Cmax = 3000 / 5000 = 0.6
III. Substitute into the Counter-Flow Effectiveness Formula
Counter flow: ε = (1 − exp(−NTU(1−Cr))) / (1 − Cr·exp(−NTU(1−Cr))).
First compute the exponential term: NTU·(1−Cr) = 0.5 × 0.4 = 0.2, exp(−0.2) ≈ 0.8187.
ε = (1 − 0.8187) / (1 − 0.6 × 0.8187) = 0.1813 / 0.5088 ≈ 0.356
IV. Calculate the Actual Heat Transfer
Maximum possible heat transfer Qmax = Cmin·(T_hot_in − T_cold_in) = 3000 × (180 − 25) = 465000 W.
Q = ε · Qmax = 0.356 × 465000 ≈ 165.5 kW
That is, this equipment actually transfers about 165 kW under the current operating condition. To improve efficiency, increasing K·A (raising NTU) or adjusting Cr (e.g., increasing cold-side flow to better match the two sides) will both raise the effectiveness.
The benefit of ε-NTU: no need to guess outlet temperatures; given the equipment capacity, you can measure what it can deliver.