Streams
- Hot inlet temperature
- Hot outlet temperature
- Cold inlet temperature
- Hot mass flow
- Cold mass flow
- Specific heat of water (~50 °C)
- Overall coefficient, clean plate HX
Thermal · worked example · 3 pages
Heat exchanger sizing
Sizing the area of a water-to-water counterflow exchanger by the LMTD method: the duty from the hot stream, the cold outlet from an energy balance, the log-mean temperature difference for counterflow, then the area from an assumed overall coefficient. The ε-NTU method suits rating problems; for sizing with all four temperatures known, LMTD is direct.
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What this calculation covers
Duty and the cold outlet
- Heat duty from the hot stream
- Cold outlet from the energy balance
- Heat picked up by the cold stream
- Energy balance closes
Log-mean temperature difference (counterflow)
The differences carry °C tags; dividing each by K first makes the log-mean come out as a plain kelvin difference. When the two ends are (near) equal the log-mean formula becomes 0/0 — its limit is simply that common value, so the calculation switches to the arithmetic mean there.
- Terminal difference, hot-in end
- Terminal difference, hot-out end
- Hot-in end difference, in kelvin
- Hot-out end difference, in kelvin
- Log-mean temperature difference (mean at the equal limit)
Required area
- Heat-transfer area required
Operating comparisons
Parallel flow with the same temperatures would give ΔT ends of 60 K and 24 K — LMTD 39.3 K — needing about 7% more area, and it could never cool the hot stream below the cold outlet.
- Area needed at an overall coefficient U
- Fouled service (U = 500)
Results summary
- Cooling 1.2 kg/s of water from 80 °C to 60 °C is a 100 kW duty that warms the 1.5 kg/s cold stream to 36 °C. With counterflow LMTD of 42 K and U = 850 W/m²K the exchanger needs about 2.8 m² — call it 3 m² with margin; fouling to U = 500 would demand 4.8 m².
Try changing…
- Halve the cold flow — the cold outlet climbs to 52 °C, ΔT_lm shrinks, and the area grows.
- Ask for T_h2 = 40 °C — double the duty, tighter approaches, and area more than doubles.
- Set both flows equal — the terminal differences equalise and LMTD tends to their common value.