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ISO 11855-2:2015. Pipe in the floor - QuickField simulation example

This is a simulation example from ISO 11855-2:2015 Building environment design — Design, dimensioning, installation and control of embedded radiant heating and cooling systems. Part 2: Determination of the design heating and cooling capacity.

Engineering question

How to calculate temperature distribution in the floor and heat flux at top and bottom surfaces?

Answer
Model one repeating floor section, set the inner pipe surface to the water temperature, solve steady-state heat transfer, and integrate heat flux at the top and bottom floor surfaces.

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Typical applications
radiant floor cooling pipes, embedded floor pipe systems, hydronic floor cooling systems

ISO 11855-2:2015. Pipe in the floor

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Simulation problem

Problem Type
Plane-parallel problem of Heat Transfer.

Geometry
ISO 11855-2:2015. Pipe in the floor Floor temperature distribution and heat flux through the top and bottom surfaces for the embedded-pipe floor system specified by ISO 11855-2:2015. Floor covering Concrete Insulation Screed PE-X pipe Water, +18°C Air, +26°C, α = 7 W/m²K Air, +26°C, α = 11 W/m²K Symmetry: zero thermal flux Symmetry: zero thermal flux 15 60 30 30 20 10 180 mm D 20 mm 150 mm

Given
Air temperature +26°C, heat exchange coefficient at the top surface αtop = 7 W/m²K, heat exchange coefficient at the bottom surface αbottom = 11 W/m²K,
Water temperature = 18 °C, turbulent flow.
Pipe wall thickness = 2.3 mm
Thermal conductivity λ of materials:
- floor covering, 0.23 W/(m·K)
- screed, 1.2 W/(m·K)
- thermal insulation, 0.04 W/(m·K)
- concrete, 2.1 W/(m·K)
- pipe PE-X, 0.35 W/(m·K)

Task
Calculate temperature distribution in the floor and heat flux at top and bottom surfaces.

Solution
Thermal resistance between water and inner pipe surface is assumed to be zero, so the fixed temperature boundary condition is used.

Results
Average heat loss density at the top surface is 4.13 W /0.15 m² = 27.5 W/m² (ISO 11855-2:2015 gives 27.4 W/m²)
Average heat loss density at the bottom surface is 1.05 W /0.15 m² = 7.0 W/m² (ISO 11855-2:2015 gives 7.0 W/m²)
Difference between the calculated and reference values is less than 3%. This simulation accuracy complies with the requirements of ISO 11855-2:2015.
ISO 11855:2015 D1 heat flux and temperature distribution in the floor

* Reference: ISO 11855-2:2015 Building environment design — Design, dimensioning, installation and control of embedded radiant heating and cooling systems — Part 2: Determination of the design heating and cooling capacity.

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