What does the LMTD calculator calculate?

It calculates the log mean temperature difference of a heat exchanger for parallel-flow or counter-flow operation.

What temperature inputs are required?

You need the hot-stream inlet and outlet temperatures and the cold-stream inlet and outlet temperatures.

What units does the calculator use for LMTD?

The result is reported in kelvin (K). Temperature differences in °C equal differences in K, while Fahrenheit differences are converted to K.

Can it calculate heat transfer rate?

Yes. Enter both U and A to calculate Q = U·A·LMTD in watts.

What happens if a terminal temperature difference is zero or negative?

The calculator rejects the input because a non-positive terminal difference indicates a physically impossible temperature cross.

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Heat Exchanger LMTD Calculator (Log Mean Temperature Difference)

Compute the Log Mean Temperature Difference (LMTD) of a heat exchanger for parallel or counter flow. Parallel flow: ΔT₁ = T_h,in - T_c,in and ΔT₂ = T_h,out - T_c,out; counter flow: ΔT₁ = T_h,in - T_c,out and ΔT₂ = T_h,out - T_c,in. LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂), or ΔT₁ when ΔT₁ = ΔT₂. A non-positive terminal difference (temperature cross) is physically impossible and is rejected. Optionally, with the overall heat transfer coefficient U (W/(m²·K)) and the heat transfer area A (m²), the heat transfer rate Q = U·A·LMTD (W) is returned. Temperatures are used only as differences: Δ°C = ΔK and Δ°F ×5/9 = ΔK; the LMTD is reported in K.

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2 examples

Counter-flow exchanger: T_h,in=100°C, T_h,out=60°C, T_c,in=20°C, T_c,out=50°C -> ΔT₁=50 K, ΔT₂=40 K, LMTD≈44.81 K

Counter flow. ΔT₁=T_h,in-T_c,out=100-50=50 K, ΔT₂=T_h,out-T_c,in=60-20=40 K. LMTD=(50-40)/ln(50/40)=10/0.2231≈44.81 K (per code).

{"result":"Heat exchanger LMTD (counter flow). T_h,in=100 °C, T_h,out=60 °C, T_c,in=20 °C, T_c,out=50 °C. ΔT₁=50 K, ΔT₂=40 K. LMTD = 44.8142 K.","metadata":{"input":{"flowType":"counter","hotInletTemp":100,"hotOutletTemp":60,"coldInletTemp":20,"coldOutletTemp":50,"tempUnit":"°C"},"result":{"lmtd_K":44.8142,"deltaT1_K":50,"deltaT2_K":40,"flowType":"counter","heatFlowRate_W":null,"overallHeatTransferCoeff":null,"area_m2":null}}}

Parallel-flow exchanger with U,A: T_h,in=120°C, T_h,out=70°C, T_c,in=30°C, T_c,out=60°C, U=500, A=2 m² -> LMTD≈36.41 K, Q≈36409 W

Parallel flow. ΔT₁=T_h,in-T_c,in=120-30=90 K, ΔT₂=T_h,out-T_c,out=70-60=10 K. LMTD=(90-10)/ln(90/10)=80/ln(9)≈36.41 K. Q=U·A·LMTD=500·2·36.41≈36409 W (per code).

{"result":"Heat exchanger LMTD (parallel flow). T_h,in=120 °C, T_h,out=70 °C, T_c,in=30 °C, T_c,out=60 °C. ΔT₁=90 K, ΔT₂=10 K. LMTD = 36.4096 K. Q = U·A·LMTD = 500 W/(m²·K) · 2 m² · 36.4096 K = 36409.5691 W.","metadata":{"input":{"flowType":"parallel","hotInletTemp":120,"hotOutletTemp":70,"coldInletTemp":30,"coldOutletTemp":60,"tempUnit":"°C","heatTransferCoeff":500,"area":2},"result":{"lmtd_K":36.4096,"deltaT1_K":90,"deltaT2_K":10,"flowType":"parallel","heatFlowRate_W":36409.5691,"overallHeatTransferCoeff":500,"area_m2":2}}}

Inputs

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9 options

SettingsAdjust formats, ranges, numbers, and modes.9

Flow ArrangementselectOptionalFlow arrangement: Parallel Flow (both streams in the same direction) or Counter Flow (opposite directions).Hot Stream Inlet T_h,innumberRequiredHot-stream inlet temperature T_h,in, in the selected Temperature Unit.Hot Stream Outlet T_h,outnumberRequiredHot-stream outlet temperature T_h,out, in the selected Temperature Unit.Cold Stream Inlet T_c,innumberRequiredCold-stream inlet temperature T_c,in, in the selected Temperature Unit.Cold Stream Outlet T_c,outnumberRequiredCold-stream outlet temperature T_c,out, in the selected Temperature Unit.Temperature UnitselectOptionalUnit of the four stream temperatures. Only differences matter: Δ°C = ΔK and Δ°F ×5/9 = ΔK.Overall Heat Transfer Coefficient U (optional)numberOptionalOverall heat transfer coefficient U in W/(m²·K). Optional; when supplied together with A, the heat transfer rate Q = U·A·LMTD is computed.Heat Transfer Area A (optional)numberOptionalHeat transfer area A in m². Optional; when supplied together with U, the heat transfer rate Q = U·A·LMTD is computed.Decimal PlacesnumberOptional

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Heat Exchanger LMTD Calculator (Log Mean Temperature Difference)

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Examples

1. Counter-flow LMTD calculation

2. Parallel-flow heat transfer rate

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