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Main >> Applications >> Sample problems >> Underfloor heating temperature

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/m^{2}-K;

Radiation coefficient β = 0.4;

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;

**Task:**

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/m^{3}], which can be calculated as:
*Q = q/S*_{c}, where *S*_{c} = π**d*^{2}/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/m^{2}. 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.