LMTD Calculator — Log Mean Temperature Difference for Heat Exchangers
LMTD (log mean temperature difference) is the correct average temperature driving force for sizing and rating heat exchangers. This free calculator computes LMTD for counter-flow and parallel-flow arrangements, the Bowman–Mueller–Nagle correction factor F for 1-shell-pass exchangers (exact analytic formula — no chart reading), heat duty Q = U·A·F·LMTD, and the NTU–effectiveness method. Everything runs 100% in your browser.
Flow arrangement
LMTD depends only on temperature differences: °C and K give identical results.
Log mean temperature difference
–K
ΔT1 (end difference)
–
ΔT2 (end difference)
–
AMTD (arithmetic mean, for comparison)
–
LMTD / AMTD ratio
–
Step-by-step
For 1 shell pass + an even number of tube passes (1-2, 1-4, …). Evaluates the analytic Bowman–Mueller–Nagle formula — the same curves as the textbook charts, without interpolation error. Pure counter-flow / parallel-flow needs no correction (F = 1).
P = (Tc,out − Tc,in) / (Th,in − Tc,in)
R = (Th,in − Th,out) / (Tc,out − Tc,in)
LMTD correction factor (1 shell pass)
–
–
F reference table (Bowman–Mueller–Nagle)
P ↓ / R →
Rows: P (cold-fluid effectiveness). Columns: R (capacity-rate ratio). Dashes mark infeasible regions (temperature cross).
Heat duty Q = U·A·F·LMTD
–W
Use this when outlet temperatures are unknown (rating an existing exchanger). If all four terminal temperatures are known, the LMTD tab is the direct route.
Heat exchanger effectiveness ε
–
NTU
–
Cr
–
Qmax = Cmin·ΔTmax
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Actual Q = ε·Qmax
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Worked example: shell-and-tube heat duty
A counter-flow exchanger cools a hot stream from 150 °C → 80 °C while heating a cold stream from 20 °C → 70 °C. Overall coefficient U = 1200 W/m²·K, area A = 8 m², one shell pass with two tube passes.
End differences: ΔT1 = 150 − 70 = 80 K; ΔT2 = 80 − 20 = 60 K.
LMTD = (80 − 60) / ln(80/60) = 69.52 K.
P = (70 − 20)/(150 − 20) = 0.3846; R = (150 − 80)/(70 − 20) = 1.4.
Bowman–Mueller–Nagle: F = 0.864 (comfortably above the 0.75 rule-of-thumb minimum).
Try it: the LMTD tab preset “Shell-and-tube case” loads these temperatures; the Heat duty tab preset matches U, A, F and LMTD.
LMTD formula and flow-arrangement definitions
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2) If ΔT1 = ΔT2, the limit applies: LMTD = ΔT1.
Arrangement
ΔT1
ΔT2
Correction F
Counter-flow (opposite ends)
Th,in − Tc,out
Th,out − Tc,in
1 (exact)
Parallel-flow (same end)
Th,in − Tc,in
Th,out − Tc,out
1 (exact)
1 shell pass, 2+ tube passes
counter-flow LMTD, then ΔTm = F·LMTD
Bowman–Mueller–Nagle
Phase change (one fluid isothermal)
use the constant saturation temperature for that stream
1
Q = U · A · F · LMTD · A = Q / (U · F · LMTD) U = overall heat transfer coefficient, A = area, F = correction factor.
LMTD vs AMTD: why the logarithmic mean matters
AMTD = (ΔT1 + ΔT2)/2 always overestimates the true driving force. The error is small when ΔT1/ΔT2 < 1.5 but grows fast beyond that — e.g. ΔT1 = 65, ΔT2 = 10 gives AMTD = 37.5 but LMTD = 29.38, a 28% overestimate that would undersize your exchanger. The LMTD tab shows both values side by side for every calculation.
Scope boundary
This tool covers the log mean temperature difference of heat exchangers: counter/parallel-flow LMTD, the F correction factor, heat duty Q = U·A·F·LMTD, and NTU–effectiveness. It does not compute the overall heat transfer coefficient U from wall layers — that is the job of our heat transfer coefficient (U-value) calculator (multi-layer walls per EN ISO 6946, building heat loss Q = U·A·ΔT). Use the U-value tool to find U, then return here to evaluate exchanger duty. See also the full tool directory.
LMTD calculator — frequently asked questions
What is LMTD (log mean temperature difference)?
LMTD is the effective average temperature difference between the hot and cold fluids in a heat exchanger. Because the local temperature difference changes along the length of the exchanger, a simple arithmetic average would be wrong; the logarithmic mean LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2) is the exact average driving force for heat transfer when the overall heat transfer coefficient U is constant.
What is the LMTD formula?
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the hot and cold streams at the two ends of the heat exchanger. If ΔT1 equals ΔT2, the limit of the formula applies and LMTD = ΔT1 = ΔT2.
How do ΔT1 and ΔT2 differ between counter-flow and parallel-flow?
For counter-flow (streams enter at opposite ends): ΔT1 = Th,in − Tc,out and ΔT2 = Th,out − Tc,in. For parallel-flow (streams enter at the same end): ΔT1 = Th,in − Tc,in and ΔT2 = Th,out − Tc,out. The same inlet and outlet temperatures give a larger LMTD in counter-flow, which is why counter-flow exchangers need less area.
What is the LMTD correction factor F?
The correction factor F adjusts the counter-flow LMTD for exchangers that are not pure counter-flow, such as shell-and-tube exchangers with one shell pass and multiple tube passes. The true mean temperature difference is ΔTm = F × LMTD(counter-flow), with F ≤ 1. For pure counter-flow or parallel-flow, F = 1 and no correction is needed.
How are P and R calculated for the correction factor?
P = (Tc,out − Tc,in) / (Th,in − Tc,in) is the temperature effectiveness of the cold fluid, and R = (Th,in − Th,out) / (Tc,out − Tc,in) is the heat-capacity-rate ratio. Together they locate the operating point on the Bowman–Mueller–Nagle charts; this calculator evaluates the analytic Bowman–Mueller–Nagle formula directly, so no chart reading is needed.
When is the correction factor F equal to 1?
F = 1 for pure counter-flow and pure parallel-flow (double-pipe) exchangers, because the LMTD formula already describes those arrangements exactly. F drops below 1 for shell-and-tube or cross-flow geometries; values below about 0.75 usually mean the design should use more shell passes.
How do you calculate heat duty Q from LMTD?
Q = U × A × F × LMTD, where U is the overall heat transfer coefficient, A is the heat transfer area, F is the LMTD correction factor (1 for pure counter/parallel flow), and LMTD is the log mean temperature difference. Rearranged, the required area is A = Q / (U × F × LMTD).
What is the difference between LMTD and AMTD?
AMTD = (ΔT1 + ΔT2) / 2 is the arithmetic mean of the two end temperature differences, while LMTD is the logarithmic mean. LMTD is always smaller than AMTD (for ΔT1 ≠ ΔT2) and is the correct driving force for sizing; using AMTD overestimates performance, with the error growing as the ratio ΔT1/ΔT2 grows.
Can LMTD be negative? What does it mean?
A negative or undefined LMTD means one of the end temperature differences is zero or negative — a temperature cross, where the cold stream would leave hotter than the hot stream at some point. That is physically impossible in a simple exchanger and almost always means the inlet/outlet temperatures were entered incorrectly or the wrong flow arrangement was selected.
What units should I use for LMTD — °C, °F, or K?
LMTD depends only on temperature differences, so °C and K give identical results, and °F differences convert with a factor of 5/9. Just keep all four terminal temperatures in the same unit; this calculator accepts °C, °F, or K and converts internally.
When should I use the NTU–effectiveness method instead of LMTD?
Use LMTD when all four terminal temperatures are known and you want the heat duty or required area. Use the NTU–effectiveness method when outlet temperatures are unknown — for example, rating an existing exchanger: compute NTU = U·A/Cmin and the capacity ratio Cr, look up the effectiveness ε for your flow arrangement, then Q = ε × Cmin × (Th,in − Tc,in).
My correction factor F is very low (below 0.75). What should I do?
F below roughly 0.75 indicates a temperature cross is developing inside the shells — the chosen 1-shell-pass arrangement is thermodynamically inefficient for those temperatures. The standard fix is to split the duty across two or more shells in series, which raises F back toward 1.
Does LMTD work for condensers and evaporators (phase change)?
Yes, with a simplification: when one fluid changes phase at constant temperature, its capacity rate is effectively infinite, so R = 0 (or Cr = 0). The LMTD formula still applies using the constant saturation temperature for that stream, and the correction factor F becomes 1.
How is this LMTD tool different from a heat transfer coefficient (U-value) calculator?
This tool computes the log mean temperature difference, the F correction factor, and heat duty for heat exchangers. A heat transfer coefficient calculator (such as our U-value tool for walls) computes the overall coefficient U itself from material layers and film resistances. The two are complementary: U comes from the coefficient tool, then Q = U·A·F·LMTD is evaluated here.
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