How the area is calculated
A heat exchanger transfers heat in proportion to its area, the heat transfer coefficient and the temperature difference between the streams. Rearranged for the area:
A = Q ÷ (U · F · LMTD)
LMTD = (ΔT1 − ΔT2) ÷ ln(ΔT1 ÷ ΔT2)
For counterflow, ΔT1 = Thot,in − Tcold,out and ΔT2 = Thot,out − Tcold,in. For parallel flow both streams enter at the same end, so ΔT1 = Thot,in − Tcold,in and ΔT2 = Thot,out − Tcold,out.
Worked example
Oil cools from 120 °C to 70 °C while water heats from 20 °C to 60 °C, in counterflow. The end differences are 60 K and 50 K, so the LMTD is 54.8 K. For a duty of 150 kW and U = 800 W/m²K the exchanger needs 150,000 ÷ (800 × 54.8) = 3.42 m². In parallel flow the same temperatures give an LMTD of only 39.1 K and need 4.80 m².
Typical U-values
| Exchanger and fluids | U (W/m²K) |
|---|---|
| Plate, water to water | 3,000 – 7,000 |
| Shell and tube, water to water | 800 – 1,500 |
| Shell and tube, steam to water | 1,500 – 4,000 |
| Shell and tube, oil to water | 100 – 400 |
| Air-cooled finned tube, water to air | 25 – 50 |
| Gas to gas | 10 – 50 |
Ranges for first estimates. The real value depends on velocities, fouling and materials and comes from the exchanger supplier.
The correction factor F
The LMTD formula is exact only for pure counterflow and pure parallel flow. Shell and tube exchangers with several tube passes and cross-flow exchangers sit in between. Their effective temperature difference is LMTD × F, with F read from charts for the exchanger type. If F drops below about 0.8, the design is inefficient; use more shells in series or a different exchanger type.