LMTD (Log Mean Temperature Difference) is the effective average temperature driving force for heat transfer in a heat exchanger. It accounts for the varying temperature difference between hot and cold fluids along the exchanger length using a logarithmic mean.

How is LMTD calculated?

LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂). For counter flow: ΔT₁ = T_h,in − T_c,out and ΔT₂ = T_h,out − T_c,in. For parallel flow: ΔT₁ = T_h,in − T_c,in and ΔT₂ = T_h,out − T_c,out.

Why is counter flow more efficient than parallel flow?

Counter flow produces a higher LMTD for the same inlet/outlet temperatures, meaning less heat transfer area is needed. The cold fluid can also be heated closer to the hot fluid inlet temperature, which is impossible in parallel flow.

When is LMTD undefined?

When ΔT₁ = ΔT₂ (equal temperature differences at both ends), the formula gives 0/0. In this special case, LMTD simply equals ΔT₁ = ΔT₂ (arithmetic mean equals log mean when both are equal).

What is Q = U × A × LMTD?

This is the basic heat exchanger design equation. Q is heat duty (W), U is overall heat transfer coefficient (W/m²K), A is heat transfer area (m²), and LMTD is the log mean temperature difference (K). Given any three, you can find the fourth.

Free Engineering Tool

Heat Exchanger LMTD Calculator

Calculate Log Mean Temperature Difference for parallel and counter flow heat exchangers. Optional Q=U·A·LMTD sizing.

LMTDCounter & Parallel#181

Results

Counter Flow LMTD

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Parallel Flow LMTD

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Counter Flow Area (if U & Q given)

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Parallel Flow Area (if U & Q given)

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Hot Side ΔT

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Cold Side ΔT

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Temperature Profile (Counter Flow)

LMTD Formula

Counter Flow

ΔT₁ = T_h,in − T_c,out | ΔT₂ = T_h,out − T_c,in

Parallel Flow

ΔT₁ = T_h,in − T_c,in | ΔT₂ = T_h,out − T_c,out

Design Equation

Counter flow always produces a higher LMTD than parallel flow for the same temperatures, meaning less area is needed.

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