One documented arrangement and thermal basis

Terminal-Temperature LMTD & Area Calculator

Calculate a numerically stable log-mean temperature difference for one documented counterflow or parallel-flow arrangement, then apply a documented correction factor, duty and overall U-value.

Stable log1p LMTDQ = UAFΔTlmNo configuration ranking

Project / exchanger identifier

Documented idealized arrangement

Terminal-temperature source, operating case and revision

Stream/profile basis, including any documented isothermal phase change

Hot inlet Tₕ,ᵢ (°C)

Hot outlet Tₕ,ₒ (°C)

Cold inlet T𝒄,ᵢ (°C)

Cold outlet T𝒄,ₒ (°C)

Documented heat duty Q (kW)

Duty/energy-balance source

Ukupna U-vrijednost (W/(m²·K))

U-value, fouling and area-basis source

Documented correction factor F (0<F≤1)

F source / configuration basis

Applicability gate: terminal temperatures must belong to the same documented steady case; hot temperature must not increase and cold temperature must not decrease unless a different signed convention/model is explicitly developed. Both paired terminal differences must remain strictly positive.

Documented LMTD result

Terminal difference ΔT₁

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Terminal difference ΔT₂

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Log-mean difference ΔTlm

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Corrected driving force FΔTlm

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Area from entered Q,U,F

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Implemented terminal pairings

Counterflow: ΔT₁=Tₕ,ᵢ−T𝒄,ₒ ; ΔT₂=Tₕ,ₒ−T𝒄,ᵢ
Parallel flow: ΔT₁=Tₕ,ᵢ−T𝒄,ᵢ ; ΔT₂=Tₕ,ₒ−T𝒄,ₒ
ΔT_lm=(ΔT₁−ΔT₂)/ln(ΔT₁/ΔT₂)
A=Q/(UFΔT_lm)

Temperature differences in kelvins and degrees Celsius have the same numerical magnitude. The implementation uses log1p for close terminal differences and the exact continuous limit ΔTlm=ΔT when ΔT₁=ΔT₂.

Source and scope

A NASA heat-exchanger design report uses the general relation q=UAΔTlm and defines the terminal log-mean temperature difference. This page adds a user-documented correction factor F for arrangements where the chosen idealized pairing does not alone represent the actual geometry. F=1 is not assumed; it must be entered with its source.

Why the former comparison was removed

The former page computed counterflow and parallel-flow results from the same four outlet temperatures and announced that counterflow was more efficient and always preferred. Changing arrangement generally changes outlet temperatures, duty, U and feasible construction, so those two arithmetic pairings were not a controlled design comparison. The page also estimated both areas with no correction factor or Q/U provenance.

Not exchanger design approval: verify stream energy balance, phase/property changes, pressure drop, fouling, U/area definition, correction-factor method, minimum approach, flow distribution, transient/off-design cases and mechanical/process-code requirements.