Heat Exchanger Lmtd⚠ unverified
Physics / Heat Transfer · Compute the log mean temperature difference for a heat exchanger
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| T1_in | T1in | K | 1.0 | Hot-stream inlet temperature |
| T1_out | T1out | K | 1.0 | Hot-stream outlet temperature |
| T2_in | T2in | K | 1.0 | Cold-stream inlet temperature |
| T2_out | T2out | K | 1.0 | Cold-stream outlet temperature |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | LMTD | K | Log mean temperature difference, in kelvin (K). Returns the endpoint difference when the two end differences are equal, and 0.0 when the end differences have opposite signs (or one is zero) |
The science & history
Understanding the Parameters
-
Terminal temperatures — define the two end $\Delta T$s; configuration (counter/parallel) sets which pairing is $\Delta T_1$ vs $\Delta T_2$.
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LMTD — always between the arithmetic extremes; requires $\Delta T_1 \neq \Delta T_2$ and same sign (no internal pinch for the pure formula).
Derivation (Approaching a Proof)
For constant $U$ and capacity rates, $dQ = U\Delta T\,dA$ with $\Delta T$ linear in $Q$ along the exchanger integrates to $Q = UA\,\mathrm{LMTD}$ with the log-mean of the end differences.
History
LMTD sizing is classical heat-exchanger design (TEMA, Kern method); effectiveness–NTU is the common alternative.
Related Concepts: Heat Exchanger Effectiveness, Overall Heat Transfer Coefficient, Convection Heat Transfer
Notes: Registry calculator heat-exchanger-lmtd (unverified). Confirm counterflow vs parallel
pairing in ToolBox. Filename uses ASCII Lmtd.