What is LMTD and How Do I Size a Heat Exchanger?
You are sizing a heat exchanger or checking an existing one and you need the log mean temperature difference. The temperature gap between hot and cold streams changes along the length of the exchanger, so a plain average is wrong - LMTD is the correct value to plug into the design equation Q = UA × LMTD.
What is the LMTD formula?
LMTD = (ΔT1 − ΔT2) ÷ ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the hot and cold streams at each end of the exchanger. For counterflow, ΔT1 = Thot,in − Tcold,out and ΔT2 = Thot,out − Tcold,in. For parallel flow, ΔT1 = Thot,in − Tcold,in and ΔT2 = Thot,out − Tcold,out.
When ΔT1 equals ΔT2 the natural log term collapses to zero, so the formula is undefined - but the limit is just that common value. If your end deltas are within 1% of each other, use either one directly. To skip the arithmetic, drop your inlet and outlet temperatures into the LMTD calculator.
How do I calculate LMTD for a counterflow exchanger?
Walk through a typical case: hot fluid enters at 90°C and leaves at 60°C, cold fluid enters at 20°C and leaves at 50°C. In counterflow the hot inlet meets the cold outlet, so ΔT1 = 90 − 50 = 40°C. The hot outlet meets the cold inlet, so ΔT2 = 60 − 20 = 40°C. Both ends have the same gap and LMTD = 40°C - a balanced design.
Now an unbalanced case: hot 100°C → 70°C and cold 30°C → 60°C. ΔT1 = 100 − 60 = 40°C, ΔT2 = 70 − 30 = 40°C. Still balanced. Try hot 100°C → 60°C and cold 20°C → 40°C: ΔT1 = 100 − 40 = 60°C, ΔT2 = 60 − 20 = 40°C. LMTD = (60 − 40) ÷ ln(60/40) = 20 ÷ 0.4055 = 49.3°C. The arithmetic mean would say 50°C, so ignoring the log understates required area by 1.5% - not huge here but it grows when ΔT1 and ΔT2 diverge.
How do I size a heat exchanger using LMTD?
The sizing equation is A = Q ÷ (U × LMTD × F) where Q is the heat duty in watts, U is the overall heat transfer coefficient in W/m²·K, A is the required surface area in m² and F is a correction factor (1.0 for true counterflow or parallel flow, 0.8 to 0.95 for shell-and-tube with multiple passes).
Example: transfer 100 kW with LMTD = 40°C and a typical shell-and-tube U of 500 W/m²·K. A = 100,000 ÷ (500 × 40 × 1.0) = 5 m² of heat transfer area. For an F of 0.85 (a 2-shell-pass exchanger) you would need 5 ÷ 0.85 = 5.9 m². Get U wrong by 2x and your exchanger is either half the size it needs to be or double the cost - tabulated U values for the fluid pair and geometry are critical.
Typical U values for heat exchanger sizing
| Fluid pair | Geometry | Typical U (W/m²·K) |
|---|---|---|
| Water to water | Shell-and-tube | 800 - 1500 |
| Water to water | Brazed plate | 3000 - 7000 |
| Steam to water (condensing) | Shell-and-tube | 1500 - 4000 |
| Light oil to water | Shell-and-tube | 200 - 400 |
| Air to water | Finned-tube | 25 - 60 |
| Refrigerant to air | Finned-tube evaporator | 300 - 700 |
Treat these as starting points - fouling and flow regime can shift U by a factor of two or more, because deposits on the tube wall add a thermal resistance in series with the fluid film coefficients.
What is the difference between counterflow and parallel flow LMTD?
Counterflow streams move in opposite directions, so the hot inlet meets the cold outlet at one end and the hot outlet meets the cold inlet at the other. The two end gaps tend to be similar, which keeps LMTD high. Parallel flow streams move the same direction, so both fluids start far apart and converge - the exit gap is small and the LMTD drops. For the same duty and U, parallel flow needs more area than counterflow. Parallel flow can never achieve a cold-outlet temperature higher than the hot-outlet temperature, while counterflow can - that is the key advantage when you need close approach temperatures.
When does LMTD break down?
LMTD assumes constant fluid heat capacities and no phase change along the path. Three cases require a different approach:
- Phase change (condensers, evaporators). One side is at constant temperature, so ΔT1 = ΔT2 in segments. Compute LMTD piecewise or use the effectiveness-NTU method instead.
- Variable specific heat. For wide temperature ranges where cp changes by more than 10%, split the exchanger into zones and sum the area for each.
- Multi-pass shell-and-tube. Use the LMTD correction factor F from TEMA charts (typically 0.75 - 0.95). If F drops below 0.75 the geometry is a poor match and you should add another shell pass.
For the standard single-pass counterflow or parallel-flow case, LMTD works cleanly. Plug your inlet and outlet temperatures into the LMTD calculator for instant results, or use the heat transfer calculator to work out the duty Q before sizing.