Heat exchanger duty and LMTD
Duty, heat balance, LMTD, F correction factor and the area you need — for shell-and-tube, double-pipe and plate exchangers.
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The Shell and Tube Heat Exchanger Performance and Fouling Excel tool does everything here and more: actual U, fouling resistance and cleanliness from plant readings — with the duty lost to fouling, its yearly cost and the best cleaning interval. Print-ready report, any units, visible formulas, no macros.
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How this calculator works
Duty on each side = flow × specific heat × temperature change; the average is used and the difference shows how well your readings close. The log-mean temperature difference (LMTD) is taken for counter-current flow (or co-current, if chosen). For shell-and-tube exchangers the LMTD is multiplied by the correction factor F, worked out from the two ratios R = hot range ÷ cold range and P = cold range ÷ (hot inlet − cold inlet). Area needed = duty ÷ (U × F × LMTD).
F is calculated exactly from the Bowman, Mueller and Nagle equations rather than read off a chart; for 2 shells in series the per-shell effectiveness method is used. As a check, the same exchanger is rated a second way by the effectiveness-NTU method and both routes give the same outlet temperatures.
The example is a heat-recovery exchanger: 50,000 kg/h of hot process liquid cooled from 120 to 70 °C while it heats 100,000 kg/h of water from 30 to 45 °C in a 1-2 shell-and-tube unit. Duty about 1,740 kW, LMTD 55.7 °C, F 0.957, so 72.5 m² is needed at U = 450 W/m²·K — the installed 80 m² gives about 10 % spare area.
Limits: constant specific heats, no phase change (for condensers and reboilers, enter the duty-weighted values with care), the same U along the whole exchanger. References: Perry's Chemical Engineers' Handbook §11; Kern, Process Heat Transfer; Bowman, Mueller and Nagle, Trans. ASME 62 (1940); Heat Exchanger Design Handbook; TEMA Standards.