Heat Transfer
Log-mean temperature difference for a two-stream exchanger, plus duty Q if you supply U and area.
ΔT_lm = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂); Q = U A ΔT_lm
The log-mean temperature difference is the correct average driving force for a heat exchanger. Combined with the overall coefficient U and area A, it gives the heat duty.
Hot stream 150→90 °C against cold 25→70 °C, counter-current. LMTD ≈ 71 °C; multiply by U and A for the duty.
The temperature difference between the streams varies along the exchanger, and the driving force is non-linear. The log-mean is the exact average for constant-property, single-phase service.
For multi-pass shell-and-tube or cross-flow exchangers, multiply LMTD by a factor F (< 1) that accounts for the flow arrangement. Pure counter- or co-current flow needs no correction. Pick the '1 shell pass · 2+ tube passes' arrangement here and the tool computes F (Bowman equation) and the corrected MTD for you.
For some temperature combinations no 1–2 exchanger can meet the duty — the correction factor mathematically doesn't exist. The fix is more shells in series or a true counter-current design. As a design rule, keep F above about 0.75.
When the cold outlet exceeds the hot outlet. It's only achievable in counter-current flow and signals you should check your arrangement — co-current flow cannot do it.