LMTD Calculator - Heat Exchanger Log Mean ΔT

An LMTD calculator solves the log mean temperature difference for a heat exchanger from the four inlet and outlet stream temperatures, then returns the driving ΔT used inside the standard heat-transfer equation Q = U · A · LMTD.

• • Heat exchanger rating: Estimate the heat duty of an existing shell-and-tube or double-pipe exchanger from field temperatures.
• • Heat exchanger sizing: Back out the required surface area from a known overall coefficient U and a target duty.
• • Process cooling loops: Compare counterflow and parallel flow to see which configuration gives the larger driving ΔT.
• • Homework and lab verification: Check the arithmetic on counterflow and parallel flow assignments before submitting heat-transfer problem sets.

The result lives inside Q = U · A · LMTD, so a clean LMTD number lets you solve for any of the other three variables when you know two of them.

Counterflow exchangers almost always return a larger LMTD than parallel flow on the same duty, which is why they dominate industrial designs when the fluid pair allows it.

When you move from a single conductive wall to a two-fluid exchanger, the same temperature logic shows up in the Heat Transfer Conduction Calculator for Fourier's law.

The LMTD formula takes the two end-point temperature differences of the exchanger and combines them through the natural logarithm, so a single number represents the temperature driving force across the whole unit.

• ΔT1: Temperature difference at one end of the exchanger. Counterflow: Th_in − Tc_out. Parallel: Th_in − Tc_in.
• ΔT2: Temperature difference at the opposite end. Counterflow: Th_out − Tc_in. Parallel: Th_out − Tc_out.
• ln: Natural logarithm of the ΔT1/ΔT2 ratio; undefined when the ratio is 1.
• LMTD: Log mean temperature difference, in the same units as the input temperatures (typically °C or K).

For counterflow the hot-outlet/cold-inlet pair swaps compared to parallel flow, which is why the same temperatures can give two different LMTD values.

When ΔT1 and ΔT2 are nearly equal, the ratio inside the logarithm approaches 1 and ln(1) = 0; in that limit the LMTD collapses to the arithmetic mean (ΔT1 + ΔT2) / 2, which is what this calculator returns automatically.

According to MIT Unified Engineering - Heat Exchangers, the logarithmic mean temperature difference for a general counterflow heat exchanger is ΔT_LM = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), derived from a local heat balance along the exchanger.

Before trusting an LMTD number, check whether the streams are turbulent or laminar with the Reynolds Number Calculator, because the overall heat-transfer coefficient U depends on that flow regime.

Four terms keep showing up whenever you read about LMTD - understanding them is what separates a number from an answer.

LMTD measures the real driving ΔT across a real exchanger, while the Carnot Efficiency Calculator gives the theoretical ceiling on how that ΔT can ever be converted to work.

Enter the four stream temperatures and pick the flow configuration. The tool applies the correct endpoint pairing and reports the LMTD plus the supporting numbers.

1. 1 Enter the hot stream temperatures: Type the inlet and outlet temperature of the hot stream in °C, leaving them blank only if you really have an isothermal hot stream.
2. 2 Enter the cold stream temperatures: Type the inlet and outlet temperature of the cold stream in °C. Negative values are allowed for sub-zero chilled-water loops.
3. 3 Pick the flow configuration: Choose Counterflow for the usual industrial arrangement or Parallel flow for co-current service.
4. 4 Read ΔT1, ΔT2, and the ln ratio: Check that the endpoint differences match your physical picture of the exchanger before trusting the final LMTD.
5. 5 Use LMTD in Q = U · A · LMTD: Plug the LMTD value, your overall heat-transfer coefficient U in W/(m²·K), and the heat-transfer area A in m² into Q = U · A · LMTD to recover the duty in watts.

Example: with Th_in = 150 °C, Th_out = 80 °C, Tc_in = 30 °C, Tc_out = 90 °C, and counterflow selected, the calculator returns ΔT1 = 60 °C, ΔT2 = 50 °C, ln(ΔT1/ΔT2) = 0.1823, and LMTD = 54.85 °C - which then feeds straight into Q = U · A · LMTD.

The tool handles the bookkeeping so you can spend your time on the heat-exchanger decisions that actually matter.

• • Right endpoint pairing every time: The counterflow / parallel flow toggle pairs ΔT1 and ΔT2 the way your textbook expects, with no off-by-one swap between the two ends.
• • Auditable intermediate values: ΔT1, ΔT2, and ln(ΔT1/ΔT2) are exposed so you can sanity-check the calculation against a worked example or a homework solution.
• • Degenerate-case handling: When ΔT1 and ΔT2 collapse toward each other, the tool returns the arithmetic mean instead of dividing by ln(1) = 0 and producing NaN.
• • Temperature-cross warning: Opposite-sign deltas flag a temperature cross so you know that the bare LMTD no longer applies and an F-factor correction is needed.
• • Sub-zero and high-temp support: Inputs down to −273.15 °C and up to 2000 °C cover cryogenic, district-heating, and furnace-service applications without breaking the math.
• • Direct fit into Q = U · A · LMTD: The output unit is exactly the same ΔT unit you need for the standard heat-transfer equation, so no conversion step is required.

When a stream crosses a phase boundary inside the exchanger, switch from LMTD to Q = m·L from the Latent Heat Calculator since the constant-U assumption no longer holds.

The LMTD is a clean closed-form value, but several physical effects decide whether that clean number actually matches the heat duty of a real exchanger.

• • LMTD is undefined when ΔT1 and ΔT2 have opposite signs (temperature cross); the bare formula cannot describe such an exchanger and an F-factor must be applied.
• • LMTD is only exact when the overall heat-transfer coefficient U is constant along the exchanger, so strongly varying U, large property changes, or phase change should send you to the effectiveness-NTU method instead.

According to Wikipedia - Log mean temperature difference, the log mean temperature difference is derived assuming constant overall heat-transfer coefficient along the exchanger, and it becomes undefined when the two end-point temperature differences have opposite signs (a temperature cross).

If the temperature swing changes the stream density enough to shift the mass flow balance, the Ideal Gas Calculator helps you check whether the LMTD you computed still matches the real heat capacity rate on each side.