Heat exchanger calculations
The equations behind heat exchanger rating and performance monitoring — heat duty, LMTD, the overall coefficient U and fouling — with worked examples and calculators.
Heat duty and the heat balance
Q = ṁ cp (Tin − Tout) (sensible heat) Q = ṁ λ (condensing or boiling)
Work out the duty from both sides. If the hot-side and cold-side duties disagree by more than a few percent, a flow meter or a thermometer is wrong — find that before you calculate anything else. Heat capacity and latent heat change with temperature; the PlantCalcKit tools take them from the built-in fluid property library.
Log mean temperature difference (LMTD)
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)
For counter-current flow ΔT₁ = Th,in − Tc,out and ΔT₂ = Th,out − Tc,in. Example. Hot oil cooled from 150 to 90 °C by water heated from 30 to 70 °C: ΔT₁ = 80 K, ΔT₂ = 60 K, LMTD = 20 / ln(80/60) = 69.5 K. Multi-pass shell-and-tube exchangers are not purely counter-current, so the LMTD is multiplied by a correction factor F (Bowman, Mueller and Nagle; TEMA). A design with F below about 0.8 is sensitive to small temperature changes and usually needs another shell in series.
Overall heat transfer coefficient and area
Q = U A F LMTD
From measured temperatures and flows you can turn this round to get the U the exchanger is achieving today. U itself is built up from the film coefficients on each side, the wall, and the fouling resistances (Kern, Process Heat Transfer; Perry's Chemical Engineers' Handbook, Section 11).
Fouling resistance
Rf = 1/Uactual − 1/Uclean
Tracking Rf over time shows how fast an exchanger fouls and when cleaning pays back: the lost duty has a cost in extra steam, fuel or cooling water, set against the cost and downtime of cleaning. TEMA Standards tabulate design fouling resistances by service for comparison.
Effectiveness–NTU
When outlet temperatures are unknown — predicting what an existing exchanger will do at new flows — the effectiveness method is simpler than LMTD: ε = Q / Qmax, with Qmax = Cmin (Th,in − Tc,in), and ε a function of NTU = UA / Cmin and the flow arrangement.
Condensers, reboilers, plate exchangers and gas coolers
Condensers and reboilers are dominated by latent heat and by how the condensing or boiling curve shapes the temperature difference. Plate exchangers use chevron-plate correlations and are almost purely counter-current. Gas coolers and compressor intercoolers must account for water condensing out of the gas. Each has its own PlantCalcKit tool below.
Calculators for this
Free calculators
- Heat duty and LMTD — Duty, heat balance, LMTD, F correction factor and the area you need — for shell-and-tube and double-pipe exchangers.
- Fouling and cleaning — Actual U, fouling resistance, duty lost to fouling, its yearly cost and how fast cleaning pays back.
- Effectiveness–NTU rating — Duty and outlet temperatures of an existing exchanger from its area and U — shell-and-tube, counter-flow, cross flow.
- Tube-side heat transfer coefficient — Film coefficient inside tubes by Gnielinski, Dittus–Boelter and Sieder–Tate, with water properties built in.
Online tools and Excel tools
- Shell and Tube Heat Exchanger Performance and Fouling — Actual U, fouling resistance and cleanliness from plant readings — with the duty lost to fouling, its yearly cost and the best cleaning interval. Use online · Excel tool, USD 49
- Condenser and Reboiler Performance — Process condensers, steam surface condensers and reboilers, rated zone by zone — with the back-pressure and lost output a dirty condenser costs. Use online · Excel tool, USD 49
- Plate Heat Exchanger Performance — Plate exchanger performance from a test, and the clean duty and pressure drop predicted from the plate geometry. Use online · Excel tool, USD 49
- Gas Cooler and Compressor Intercooler — Wet-gas coolers and intercoolers: dew point, condensate load, sensible and latent duty, U and fouling — and the extra compressor power a warm intercooler costs. Use online · Excel tool, USD 49
- Heat Duty and Utility Consumption — Heat duty for up to 10 process streams, the steam, cooling water, refrigeration or fuel each one needs, and the yearly utility bill. Use online · Excel tool, USD 39
- Waste Heat Recovery — How much heat a hot gas or flue gas can give back — as steam or to heat another stream — with fuel saved, CO₂ avoided and payback. Use online · Excel tool, USD 49
Field guide
- Heat Exchangers Made Simple — A 174-page plain-language field guide for operators and young engineers: how exchangers work, every main type, monitoring, testing, fouling, troubleshooting, cleaning and economics.
Questions
How do I calculate LMTD?
LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂), where ΔT₁ and ΔT₂ are the temperature differences at the two ends of the exchanger. For multi-pass exchangers multiply by the F correction factor.
How do I know if my heat exchanger is fouled?
Calculate the actual U from today's flows and temperatures and compare it with the clean (design or after-cleaning) U. The fouling resistance is 1/U_actual − 1/U_clean.
What if the hot-side and cold-side duties don't match?
A heat balance error of more than a few percent points to a faulty flow meter or temperature reading. Fix the data before calculating U.
More calculation guides
- Process engineering calculations
- Pump calculations
- Pipe pressure drop and orifice sizing
- Fluid properties for process calculations
- Cooling tower calculations
These guides and calculators give engineering estimates for screening, troubleshooting and training. Check important decisions against site data, your equipment maker and your plant's approved procedures.