Underfloor Heating Output & Loop Designer

The upward model is derived here from steady Laplace conduction around an infinite periodic row of small circular pipes, with a Robin boundary at the screed top. It is a 2D refinement of the usual fin/spreading-resistance approximation, not a transcription of EN 1264 tables.

Use the logarithmic mean water-to-room temperature difference:

The published base curve is $q=8.92(\Delta T_s/1\,\mathrm K)^{1.1}\,\mathrm{W/m^2}$, hence the mean finished-floor temperature is $T_a+(q/8.92)^{1/1.1}$ in °C. Its secant coefficient is $h_s=q/\Delta T_s$. VALTEC 2025–2026, printed pp. 9–10 and 105–107, motivates the surface and pipe resistances; the requested base curve is the EN 1264-2:2021 convention.

For pipe pitch $s$, outside radius $r$, centre depth $H$, screed conductivity $k$, and $U=(R_c+1/h_s)^{-1}$, set $a_n=2\pi n/s$ and $b_n=(ka_n-U)/(ka_n+U)$. The derived spreading resistance is

It is based on a line source and a circular-wall mean, accurate when pipe radius is small compared with pitch and depth. The displayed 2D field uses the same Fourier Green function, cropped above the pipe crowns to exclude source singularities. Surface ripple is reconstructed through the thin covering with the mean secant coefficient; it is not a nonlinear finite-element solution.

For each trial flux, $T_p=T_a+\Delta T_s+q(R_c+R_{sp})$, $q_d=(T_p-T_b)/R_d$ and

Bisection requires a sign-changing bracket from exactly zero upward flux and verifies a water-temperature residual within 1 µK. At zero upward flux, the wall is at room temperature and the water supplies only downward loss: $T_{w,0}=T_a+[(T_a-T_b)/R_d]R_p$. Water colder than this requires heat from the room, which is outside the heating-only model. Such a root is rejected rather than replaced by a small positive flux. The return must also exceed this threshold so the complete loop stays in the upward-heating domain.

The inlet calculation repeats the positive-root solution at supply temperature. The surface-only supply threshold is constrained by the effective-water range 20–50 °C, supply range 20–60 °C and return range 16–55 °C at the selected drop. The implied return must remain above the room and zero-upward-flux threshold. If no valid pair exists, no maximum supply or limited-capacity value is reported; reduce the drop. A model-range warning qualifies a ceiling determined by water-temperature validity rather than the surface limit.

Selected useful heat uses the lower of the entered supply and the valid ceiling, keeping the drop fixed. Maximum useful heat uses the valid ceiling, independent of the entered temperature level. If only selected output is insufficient, raise both temperatures toward the displayed pair and recalculate hydraulics. If even maximum output is insufficient, change the floor design or add heating. Changing spacing changes both resistance and output, so retune the water temperatures and recheck the inlet hot spot.

Pipe length is $A/s$ plus two leads per loop. Water flow follows $\dot m=Q_w/(c_p\Delta T_w)$. Equal loops share the flow. Darcy–Weisbach pressure loss uses Churchill's full-range Darcy factor (1977, Eq. 18), followed by the user's branch allowance. This is pump differential head, not elevation lift in a closed circuit.

VALTEC thermal benchmarks are intentionally approximate: the model predicts about 73 versus 83 W/m² for tile and 54 versus 60 W/m² for carpet, with 15% tolerances. The manual uses different spreading assumptions and fixed 10% downward losses; no coefficient is fitted to its table. The 10 kW flow example differs by 0.33% because the tool uses 4187 rather than 4200 J/(kg·K).

• Steady heating, identical equally spaced pipes fully bonded into homogeneous screed; no plates or contact gaps.
• The upper screed spreading equations are derived here. Lower heat escape is a separate lumped resistance at the mean outer pipe wall; its spatial field is not solved.
• The logarithmic water temperature approximates the along-loop variation. A separate all-pipes-at-supply section estimates an inlet hot spot conservatively; it does not resolve a serpentine or counterflow spiral.
• Covering is a thin through-thickness resistance; its lateral conduction is neglected.
• Homogeneous plastic pipe with the entered conductivity; composite and metal pipes require a suitable effective resistance.
• Fixed water-film coefficient 400 W/(m²·K), following VALTEC printed p. 106. Hydraulic water properties are fixed: density 1000 kg/m³ and heat capacity 4187 J/(kg·K), following VALTEC printed p. 95, with viscosity 0.72 mPa·s approximating water at 35 °C. Fluid-property variation is not coupled to flow.
• Active areas and branch lengths are equal. Manifold leads are insulated and do not heat the modeled room. Pipe quantity is an area estimate without a bend/waste percentage; verify an actual layout before ordering.

For preliminary and comparative sizing of water-heated embedded plastic-pipe floors: pitch 75–300 mm, pipe outside diameter 12–25 mm, screed cover 20–80 mm, conductivity 0.6–2.5 W/(m·K), covering resistance 0–0.20 m²·K/W, effective water temperature 20–50 °C, manifold supply 20–60 °C, return 16–55 °C and water drop 0.5–15 K. These temperature bounds are enforced; the return must also exceed the zero-upward-heat threshold imposed by downward loss. Normal room temperatures 18–25 °C best match the base curve. Values outside that room range or above 35 °C surface temperature need separate assessment. A 15% agreement allowance in two manufacturer examples is not a guaranteed uncertainty bound.

European presets refer to EN 1264-2:2021 / EN 1264-3:2021 conventions (29 °C occupied, 33 °C bathroom, 35 °C perimeter); local maxima are checked conservatively. Russian presets follow SP 60.13330.2020 §14.18, as reproduced in VALTEC 2025–2026 printed p. 115: mean 29 °C occupied, 31 °C temporary occupancy, 23 °C preschool, with 35 °C local maximum where applicable. Reviewed 27 October 2026. Older 26 °C guidance must not be substituted for the current occupied-zone preset. A covering supplier may require a lower value: use Custom. Check against the standard in force; these presets are not a complete compliance assessment.

No building heat-loss calculation, structural/screed approval, expansion-joint layout, pipe bending assessment, cooling/condensation, glycol, transient response or detailed pump/mixing-valve selection. Small bores, transitional flow, low flow rates and contact defects can change output or pressure loss materially. Cover under 30 mm and covering resistance over 0.15 m²·K/W need supplier-specific confirmation. Installation, pressure testing and commissioning must be carried out by a qualified person.