# Logarithmic Mean Temperature Differential

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Logarithmic mean temperature differential, abbreviated as LMTD, also called log mean temperature differential, is used to determine the temperature driving force for heat transfer usually in heat exchangers.

## Logarithmic mean temperature differential Formulas

 $$\large{ LMTD = \frac{ \Delta T_a\;-\;\Delta T_b }{ ln\;\left( \frac{\Delta T_a}{\Delta T_b} \right) } }$$ $$\large{ LMTD = \frac{ \Delta T_a\;-\;\Delta T_b }{ ln\;\Delta T_a\;-\;ln\; \Delta T_b } }$$

### Where:

 Units English Metric $$\large{ LMTD }$$ = logarithmic mean temperature differential $$\large{\frac{Btu}{lbm}}$$ $$\large{\frac{J}{kg}}$$ $$\large{ ln }$$ = natural logarithm $$\large{dimensionless}$$ $$\large{ \Delta T_a }$$ = temperature differential $$\large{F}$$ $$\large{K}$$ $$\large{ \Delta T_b }$$ = temperature differential $$\large{F}$$ $$\large{K}$$