The log mean temperature difference of a heat exchanger and the heat duty it transfers (Q = U·A·LMTD) — for counterflow or parallel-flow, with a check for an impossible temperature cross.
The Right Average for a Changing Gap
In a heat exchanger the temperature difference between the hot and cold streams is not constant — it is largest at one end and smallest at the other. To size the exchanger you need a single representative driving difference, and the correct one is not the simple average but the log mean, which accounts for the exponential way the gap narrows along the length.
ΔT₁ and ΔT₂ are the temperature differences at the two ends. Multiply the LMTD by the overall heat-transfer coefficient U and the area A and you get the heat duty Q the exchanger transfers. Rearranged, it tells you the area needed for a target duty.
Counterflow Beats Parallel Flow
Run the streams in opposite directions (counterflow) and the temperature gap stays more uniform along the length, giving a higher LMTD and more heat transfer for the same area. Run them the same way (parallel flow) and the gap collapses quickly; the cold outlet can never even reach the hot outlet. For the same four temperatures, counterflow always wins — switch the arrangement here and watch the LMTD change.
Frequently Asked Questions
Why a log mean and not a simple average?
Because the temperature difference decays exponentially along the exchanger, not linearly. The log mean is the exact average driving force for that exponential profile; a plain average overestimates the duty.
What is the correction factor F?
Real shell-and-tube and crossflow units are not pure counterflow, so the duty is Q = F U A LMTD, where F (between 0 and 1) comes from charts based on the temperature ratios. This tool gives the ideal single-pass case with F = 1.
What is a temperature cross?
When the required outlet temperatures would force a negative end difference – impossible for that arrangement. Parallel flow crosses easily; counterflow tolerates more. The calculator flags it.
Related calculators
- Heat Transfer Calculator — conduction and convection rates.
- Sensible Heat Calculator — the duty to change a stream temperature.
- Pipe Heat Loss Calculator — loss from insulated pipe.
- Engineering Unit Converter — power, area and temperature units.