How the ε-NTU method works
When you know the inlet temperatures and the exchanger's size but not the outlets, the effectiveness–NTU method gives the heat duty directly. NTU measures the exchanger's size relative to the smaller heat-capacity stream, and the effectiveness follows from NTU, the capacity ratio and the flow arrangement.
- Heat capacity rates:
C = ṁ·c_p;C_r = C_min/C_max - Size:
NTU = U·A/C_min - Counterflow:
ε = (1 − e^(−NTU(1−C_r))) / (1 − C_r·e^(−NTU(1−C_r))) - Duty:
Q = ε·C_min·(T_h,in − T_c,in)
Worked example: plate heat exchanger
Water at 80 °C and 1.0 kg/s heats water entering at 15 °C and 1.2 kg/s in a 2.5 m² counterflow plate exchanger with U = 3,000 W/m²·K. NTU is about 1.8 and the effectiveness about 68%, so the exchanger transfers about 184 kW. The hot side leaves at about 36 °C and the cold side at about 52 °C.
Good to know
- Beyond an NTU of about 4, added area returns very little extra heat.
- Pro adds fouling resistance and solves for the area needed to reach a target outlet temperature.