Logarithmic Mean Temperature Difference Formula |
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\( LMTD \;=\; \dfrac{ \Delta T_1 - \Delta T_2 }{ ln \cdot \dfrac{ \Delta T_1 }{ \Delta T_2 } }\) \( LMTD \;=\; \dfrac{ \Delta T_1 - \Delta T_2 }{ ln \Delta T_1 - ln \Delta T_2 }\) |
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| Symbol | English | Metric |
| \( LMTD \) = Logarithmic Mean Temperature Difference | \(^\circ F\) | \(^\circ K\) |
| \( ln \) = Natural Logarithm | \(dimensionless\) | \(dimensionless\) |
| \( \Delta T_1 \) = Temperature Difference Between the Hot and Cold Fluids at One End of the Heat Exchanger | \(^\circ F\) | \(^\circ K\) |
| \( \Delta T_2 \) = Temperature Difference Between the Hot and Cold Fluids at the Other End of the Heat Exchanger | \(^\circ F\) | \(^\circ K\) |
Logarithmic mean temperature difference, abbreviated as \(LMDT\), is a specialized measure used in heat exchanger analysis to represent the effective average temperature difference between two fluids whose temperatures change as they flow through the exchanger. Unlike a simple arithmetic average, the \(LMDT\) accounts for the fact that the temperature difference between hot and cold fluids is not constant along the heat exchanger’s length, it may start large and gradually decrease or increase depending on the flow arrangement (parallel flow or counterflow). By using a logarithmic relationship, the \(LMDT\) provides an accurate “driving force” for heat transfer when temperatures vary, allowing engineers to correctly calculate the overall heat transfer rate. This makes \(LMDT\) an essential concept in the design and analysis of heat exchangers, ensuring that thermal performance is predicted realistically under changing temperature conditions.
