Size a house heat exchanger from its duty, its overall heat-transfer coefficient and the logarithmic mean temperature difference between the two streams: area = Q ÷ (U × LMTD). For 4 kW with district water entering at 80 °C and leaving at 45 °C, and the house loop heated from 40 to 70 °C in counterflow, the LMTD is 7.21 K, so a copper coil in a tank at an assumed U of 200 W/m²K needs 2.77 m² (about 59 m of 15 mm tube) and a plate exchanger at an assumed 1,000 W/m²K needs 0.55 m². A warmer primary return shrinks the area but raises the network’s return temperature.
Part of District Heating
Sizing the exchanger or coil that transfers heat from the village main to a house’s own heating loop.
The Equation
For a heat exchanger carrying duty Q between two streams, Q = U × A × LMTD, where U is the overall heat-transfer coefficient (W/m²K), A the heat-transfer area and LMTD the logarithmic mean temperature difference. For counterflow (the streams in opposite directions), with the temperature differences at the two ends ΔT_a and ΔT_b:
LMTD = (ΔT_a − ΔT_b) ÷ ln(ΔT_a ÷ ΔT_b)
When the two end differences are equal, LMTD is that value.
Worked Example: One House, Three Primary Return Temperatures
Inputs: Q = 4 kW; district water enters at 80 °C; the house loop is heated from 40 °C to 70 °C (flow 70, return 40); counterflow. Warm end difference: 80 − 70 = 10 K. Cold end difference: primary outlet − 40.
| Primary outlet | Cold end ΔT | LMTD | Primary flow | Area at U = 200 | Area at U = 1,000 |
|---|---|---|---|---|---|
| 45 °C | 5 K | (10 − 5) ÷ ln 2 = 7.21 K | 0.027 kg/s | 2.77 m² | 0.55 m² |
| 50 °C | 10 K | 10.0 K | 0.032 kg/s | 2.00 m² | 0.40 m² |
| 55 °C | 15 K | (15 − 10) ÷ ln 1.5 = 12.3 K | 0.038 kg/s | 1.62 m² | 0.32 m² |
Working, first row: primary flow = 4 ÷ (4.18 × (80 − 45)) = 0.0273 kg/s; area = 4,000 ÷ (200 × 7.21) = 2.77 m²; a 15 mm copper tube has area π × 0.015 = 0.0471 m² per metre, so 2.77 ÷ 0.0471 = 59 m of tube.
The two U values are assumptions: 200 W/m²K for a coil in a tank where the tank side moves only by natural convection, and 1,000 W/m²K for a plate exchanger with forced flow on both sides. Neither is a corpus figure; both vary with design and fouling, and a bare copper coil measurement is the only way to know. Measure your first unit before building thirty (see below).
Reading The Table
- Moving from a 55 °C to a 45 °C primary return raises the area by 12.3 ÷ 7.21 = 1.7 times. The cooler return saves pumping and loss but costs copper.
- The cold-end approach, the gap between primary outlet and house return, is what the area depends on. A closer approach is cheaper to run and dearer to build.
- A plate exchanger is far smaller than a coil: salvaged plate units from heating equipment are valuable for this reason (the carrier page notes this).
Method: Build And Measure A Coil
- Wind the coil from copper tube, with soldered or brazed joints (the temperatures, 230 to 350 °C and 600 to 900 °C, are in Metalworking & Soldering, which describes the work with a solar dish), inside an insulated tank, low in the tank so that the water it heats rises past the rest of the tank by natural convection.
- Fill both sides and vent the air.
- Run the primary at a known flow (bucket and stopwatch) and read the four temperatures.
- Compute the duty from the primary side, Q = m × c × (T_in − T_out), and divide by A × LMTD to get the real U.
- Use the measured U for the other houses, and size from it.
Pressure, Leaks And Separation
An exchanger has two sides; a pinhole leak lets water cross from the higher pressure to the lower. For a domestic hot water coil, keep the potable side at the higher pressure so a leak puts potable water into the loop and not the other way (a recalled convention), or use a double-wall unit where one is available. Salvaged plate units must be pressure-tested on both sides.
Common Mistakes
- Using an arithmetic mean temperature difference. For a 10 K and 5 K end, the LMTD is 7.21 K; the arithmetic mean is 7.5 K, an error that grows with the range.
- Sizing at the design temperature and running cooler. When the primary supply is lower than 80 °C the LMTD falls and the exchanger delivers less.
- Ignoring fouling. Scale on the potable side cuts U with time.
Safety
Hot side meets drinking water
A cracked or corroded coil can put district water, with its rust and any treatment additives, into the house water, and 80 °C water into a tank rated for 60 °C. Keep district water chemically clean (no additives you would not drink), test the coil at 1.5 times pressure, and fit a relief on the house side.
What’s Next
- Learn next: Radiator & Underfloor Heating — what the secondary loop feeds
- Combine with: Domestic Hot Water Takeoff — the tank-side coil