LMTD Calculator – Log Mean Temperature Difference

In heat exchanger design, temperature differences between fluids change continuously along the length of the flow path. The LMTD method provides a logarithmic average of the temperature differences between the hot and cold fluids at each end of the exchanger. The fundamental formula is defined as LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 represent the temperature differences at the two opposite ends (inlet and outlet). For parallel flow arrangements, ΔT1 = T_hot,in - T_cold,in and ΔT2 = T_hot,out - T_cold,out. For counter-flow systems, the outlet temperature orientation is inverted accordingly, accounting for the reversed direction of fluid travel to ensure accurate thermal driving force calculations.

Consider a counter-flow heat exchanger where a hot fluid enters at 350 K (T_hot,in) and leaves at 280 K (T_hot,out). Meanwhile, the cold fluid enters at 250 K (T_cold,in) and exits at 300 K (T_cold,out). First, determine the temperature differences at both ends: ΔT1 = T_hot,in - T_cold,out = 350 - 300 = 50 K. Next, find ΔT2 = T_hot,out - T_cold,in = 280 - 250 = 30 K. Applying the LMTD equation, we compute the numerator as ΔT1 - ΔT2 = 50 - 30 = 20. The denominator is the natural logarithm of the ratio, ln(50 / 30) = ln(1.6667) approximately equal to 0.5108. Dividing the numerator by the denominator gives LMTD = 20 / 0.5108 = 39.15 K. This value accurately represents the effective thermal driving force across the exchanger.

Always verify your temperature unit consistency; mixing Celsius and Kelvin will invalidate logarithmic calculations. Pay close attention to whether your system utilizes parallel or counter-flow configurations, as swapping fluid outlet positions will drastically alter your ΔT values. Finally, if you are analyzing shell-and-tube or multi-pass cross-flow heat exchangers, remember that a correction factor (F) must be applied to the pure counter-flow LMTD result to account for multidirectional fluid mixing.