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 (darjah Celsius)

Hot outlet Tₕ,ₒ (darjah Celsius)

Cold inlet T𝒄,ᵢ (darjah Celsius)

Cold outlet T𝒄,ₒ (darjah Celsius)

Documented heat duty Q (kW)

Duty/energy-balance source

Nilai U keseluruhan (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.