Heat Exchanger (LMTD + ε-NTU)
Two methods: LMTD (Q = U·A·F·ΔTlm) from the four stream temperatures, and ε-NTU (method = ntu) from inlets + UA for counter, parallel, cross, and 1-2 shell-and-tube arrangements.
Hot stream
Cold stream
Sizing
NTU streams
Frequently asked
- How does the LMTD method work?
- Q = U·A·ΔT_lm, where ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂) from the two end differences. Counter-flow pairs hot-in with cold-out; parallel-flow pairs hot-in with cold-in. Give any two of U, A, Q and the calculator solves the third.
- Why does it reject some temperatures?
- LMTD needs ΔT > 0 at both ends. A temperature crossing (cold outlet above hot outlet in counter-flow, etc.) makes the log-mean undefined — that's a physical impossibility for a passive exchanger, so the solver refuses it.
- How does the ε-NTU method work?
- Set NTU = UA/C_min and R = C_min/C_max, read effectiveness ε from the arrangement formula, then Q = ε·C_min·(T_h,in − T_c,in). It is the method of choice when outlet temperatures are unknown — no iteration needed, and it covers counter-flow, parallel, cross-flow (unmixed and mixed) and 1-2 shell-and-tube.
- When do I use LMTD vs ε-NTU?
- LMTD is direct when all four stream temperatures are known (rating by duty). ε-NTU is direct when only inlets and UA are known (rating by outlet temperatures) — the two methods are algebraically equivalent for the same exchanger.