How to use the LMTD and heat transfer area calculator
Inside a heat exchanger the temperature difference between the two streams changes continuously from one end to the other, so sizing on a simple arithmetic average gives the wrong area. Designers use the log mean temperature difference instead. Enter the four stream temperatures along with the heat duty and the overall coefficient to get LMTD and the required surface area.
The formula is LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂), and area comes from A = Q ÷ (U × LMTD). In counter-flow, ΔT₁ is the hot inlet minus the cold outlet and ΔT₂ is the hot outlet minus the cold inlet. In parallel flow the two inlets are paired and the two outlets are paired. When the two differences are equal the logarithm becomes zero, so this calculator falls back to the arithmetic mean, which is the correct limiting value.
For the same temperatures, counter-flow produces a larger LMTD than parallel flow and therefore needs less surface. The overall coefficient U depends heavily on fluid type, velocity and fouling, running high for water to water plate units and much lower for gas to gas service.
The area shown is a pure counter-flow or parallel-flow value. Multi-pass shell and tube or cross-flow geometries need the LMTD correction factor F, and fouling allowance must be added separately, so confirm the final selection with manufacturer data before ordering.
Frequently asked questions
With ΔT₁ equal to ΔT₂ the term ln(1) is zero and the formula would divide by zero. The mathematical limit equals that same temperature difference, so this tool uses the average of the two values.
Apply it whenever flow is not true counter-flow, such as a 1-2 shell and tube unit or a cross-flow coil. Designs normally keep F above 0.8; below that it is better to change the pass arrangement.