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# Underfloor heating

Example of a heat transfer simulation for an underfloor heating system.

Problem type:
Plane-parallel problem of steady-state heat transfer.

Geometry:

All dimensions are in millimeters.

Given:
Air temperature above the floor = 18°C;
Air temperature below the floor = 20°C;
Convection coefficient α = 5 W/m2-K;
Cable heat power q = 100 W/m.

Thermal conductivity of materials:
Cement 1.4 W/m-K;
Insulation 0.05 W/m-K;
Cable (copper) 401 W/m-K;
Floor slab 1.69 W/m-K;

Problem:
Calculate the distribution of temperature for underfloor heating and evaluate the efficiency of heating.

Solution:
The model represents only a small part of the floor with a size of 1m x 1m.
QuickField takes input of heat power as volume power density in [W/m3], which can be calculated as:
Q = q/Sc, where Sc = π*d2/4 - cable cross-sectional area, d - cable diameter (5 mm).

Portion of the heat flux that goes downward is considered as a waste. The efficiency of the underfloor heating can be estimated as a ratio of heat flux directed upward to the total produced heat power.

Results:
The cable is laid in such a way that the total heat power is 100 W/m2. The upward-directed heat flux is 83% of the total power produced by the cable. Then 17% of the heat flux goes downward.
The average floor surface temperature is 29°C.