LMTD Calculator
Calculate log mean temperature difference for counterflow and parallel flow heat exchangers.
Log Mean Temperature Difference
The log mean temperature difference (LMTD) estimates the effective temperature driving force in a heat exchanger. It is used with the overall heat transfer coefficient, area, and mass flow to size shell-and-tube, plate, and other exchangers.
Formula
$$LMTD = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$$For counter flow, \(\Delta T_1 = T_{hi} - T_{co}\) and \(\Delta T_2 = T_{ho} - T_{ci}\). For parallel flow, \(\Delta T_1 = T_{hi} - T_{ci}\) and \(\Delta T_2 = T_{ho} - T_{co}\).
Why LMTD Instead of a Simple Average?
Fluid temperatures change exponentially along the exchanger length. The arithmetic mean of inlet and outlet differences overestimates the driving force when \(\Delta T_1\) and \(\Delta T_2\) differ significantly. LMTD tracks that logarithmic profile and gives a more accurate mean temperature difference for design.
Counter flow generally yields a higher LMTD than parallel flow for the same inlet and outlet temperatures, so less surface area is needed for the same heat duty.
Frequently Asked Questions
What is LMTD used for?
LMTD is used in heat exchanger design to relate heat transfer rate to area, overall heat transfer coefficient, and the logarithmic mean of the hot and cold side temperature differences.
When are ΔT₁ and ΔT₂ equal?
When both temperature differences are the same, LMTD equals that common value. This is the limiting case as ΔT₁ approaches ΔT₂.
Why does counter flow give a higher LMTD?
In counter flow, the hot fluid meets the coldest cold fluid at one end, maintaining a larger temperature difference along the exchanger compared with parallel flow.
What if a temperature difference is zero or negative?
Both ΔT₁ and ΔT₂ must be positive for a valid LMTD. Negative or zero values indicate impossible or reversed temperature profiles for the selected flow arrangement.
Do I need a correction factor?
Shell-and-tube and cross-flow exchangers often use an LMTD correction factor based on flow passes and geometry. This calculator covers basic parallel and counter flow arrangements.
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