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Enter the flows, specific heats and temperatures of both streams to get the heat duty, cold outlet temperature and log-mean temperature difference ΔTlm; add the overall coefficient U to get the required area. Defaults are the benchmark from Incropera Example 11.1.
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Inputs: Hot (oil) 0.1 kg/s, cₚ 2131 J/(kg·K), 100 → 60 °C; cold (water) 0.2 kg/s, cₚ 4178 J/(kg·K), inlet 30 °C; counter-flow
| Log-mean temperature difference ΔTlm | 43.2 K |
|---|---|
| Heat duty Q | 8.524 kW |
| Cold outlet temperature | 40.2 °C |
| Terminal difference ΔT₁ | 59.8 K |
| Terminal difference ΔT₂ | 30 K |
| UA = Q / ΔTlm | 197.3 W/K |
The example matches industry benchmark GC-IND-HX-LMTD-001 in our repository (expected values derived independently with 50-digit decimals and checked by automated tests).
The temperature difference varies exponentially along the surface; integrating it gives the log-mean. When both terminal differences are close the two are similar, but the arithmetic mean becomes increasingly wrong as they diverge.
For the same terminal temperatures counter-flow gives a larger LMTD and needs less area, and the cold outlet can exceed the hot outlet. In parallel flow the cold outlet can never exceed the hot outlet.
A terminal difference of zero or less, so heat cannot flow from the hot to the cold stream. The page tells you when it happens; switch to counter-flow or change the flows or temperatures.
Compute the counter-flow LMTD and multiply by the correction factor F from TEMA charts or equations. This tool does not include F.
It depends on the fluids, velocities and fouling and should come from heat transfer correlations or handbooks. The 300 W/(m²·K) default is only an example.
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