Calculate the log mean temperature difference for counterflow or parallel flow, then the heat duty, required heat transfer area and water flow on each side.
Counterflow gives a larger LMTD than parallel flow for the same temperatures, so it needs less area, and it allows the cold outlet to be hotter than the hot outlet (a temperature cross). Plate heat exchangers are close to true counterflow (F ≈ 1). Multi-pass shell and tube exchangers need a correction factor F, usually 0.8–1.0, from the manufacturer or TEMA charts.
| Exchanger and fluids | U (W/m²·K) | U (Btu/h·ft²·°F) |
|---|---|---|
| Plate heat exchanger, water to water | 3,000 – 7,000 | 530 – 1,230 |
| Shell and tube, water to water | 800 – 1,500 | 140 – 260 |
| Shell and tube, steam to water | 1,500 – 4,000 | 260 – 700 |
| Water to glycol plate exchanger | 2,000 – 4,500 | 350 – 790 |
| Finned air coil (air side area) | 25 – 60 | 4 – 11 |
Typical design ranges for preliminary sizing. Fouling, velocity and plate pattern change U; use the manufacturer's selection for final design.
Related: Chilled Water Flow Calculator, Cooling Tower Calculator, and the guide to types of HVAC systems (district cooling and chilled water).
The log mean temperature difference is the effective average temperature difference between the hot and cold fluids along a heat exchanger. Heat duty Q = U × A × LMTD, so LMTD links the temperatures to the area needed.
ΔT₁ = hot inlet − cold outlet and ΔT₂ = hot outlet − cold inlet, then LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂). If ΔT₁ = ΔT₂, the LMTD equals that value.
For the same temperatures it gives a higher LMTD, so less area is needed, and it allows the cold outlet temperature to rise above the hot outlet temperature, which parallel flow cannot do.
The smallest temperature difference between the two fluids at either end of the exchanger. A closer approach recovers more heat but needs much more area; 1–2 K is common in plate exchangers for district cooling and free cooling.
A = Q ÷ (U × LMTD × F). Find Q from the flow and temperature change, the LMTD from the four temperatures, U from typical values or the manufacturer, and F = 1 for plate or true counterflow exchangers.
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