Construction Heat Conduction

Overview

Every surface with an assigned building component is simulated as a construction instance: transient, one-dimensional heat conduction through the multi-layer component assembly. Two models share the work:

• The construction state model discretizes the layer assembly into finite-volume elements and computes the element temperatures, surface temperatures and internal conduction fluxes from the balanced energy densities.
• The construction balance model applies the boundary fluxes at both surfaces (side A and side B) and sets up the energy balance of each element.

Balance equation

For each element $i$ with width $\Delta x_i$, the volume-related energy density $u_i = \rho_i c_i\, T_i$ is balanced:

$$\frac{du_i}{dt} \;=\; \frac{1}{\Delta x_i}\left( q_{i-\frac{1}{2}} - q_{i+\frac{1}{2}} \right)$$

The conduction fluxes between adjacent elements are formed from the element temperatures using weighted thermal conductivities of the materials involved. Material properties (bulk density $\rho$, specific heat capacity $c$, thermal conductivity $\lambda$) come from the material database. The initial value of all elements is the initial temperature.

Discretization (grid generation)

The fineness of the computation grid is controlled by three solver parameters (NANDRAD SolverParameter, default values in parentheses):

Parameter	Default	Effect
DiscMinDx	2 mm	Minimum element width at the layer edge
DiscStretchFactor	4	Grid stretch factor
DiscMaxElementsPerLayer	20	Maximum number of elements per material layer

Depending on the stretch factor:

• Stretch factor 0 — no refinement: each inner material layer becomes exactly one element, and the two edge layers are each split into two elements (coarse grid, e.g. for quick preliminary studies).
• Stretch factor 1 — equidistant grid with element widths of about DiscMinDx per layer.
• Otherwise (default) — grid refined on both sides per layer (tanh stretching): fine elements at the layer edges, coarser ones in the middle of the layer. At least 3 elements are generated per layer; the number of elements is increased until the edge element reaches at most 1.1 times DiscMinDx, up to a maximum of DiscMaxElementsPerLayer (in which case the stretch factor is automatically increased and a warning is logged).

Very thin layers (< 1 mm) generate a warning — they hardly affect the result, but degrade numerical performance.

Boundary conditions (side A / side B)

At both surfaces, the balance model applies the exchange mechanisms defined in the boundary conditions:

• Surface heat transfer (convective): $q = \alpha\,(T_{\mathrm{ambient}} - T_{\mathrm{surface}})$ with the heat transfer coefficient $\alpha$; depending on the location, the ambient is the adjacent zone, the outdoor air or a fixed temperature (ground/scheme).
• Shortwave radiation: absorbed share of the incident solar radiation (absorption coefficient of the boundary condition); outside from the radiation model including shading factors, inside from the solar distribution of the window gains.
• Longwave radiation: emission and absorbed counter-radiation; for longwave radiation exchange between interior surfaces, pre-computed view factors are used (automatic view-factor calculation at simulation start).

If the boundary condition is missing on one side, the surface behaves adiabatically there. Available result quantities include FluxHeatConductionA/B [W], the area-specific variants [W/m²], FluxShortWaveRadiationA/B, FluxLongWaveRadiationA/B as well as the surface temperatures SurfaceTemperatureA/B.

Active layer (surface heating)

If an active layer is defined in the building component (assign surface heating), the construction takes up the load ActiveLayerThermalLoad of the assigned heating model. The load is distributed as a volumetric source uniformly over all elements of the active layer:

$$\dot{q}_{\mathrm{source}} = \frac{\dot{Q}_{\mathrm{active}}}{V_{\mathrm{layer}}}$$

In addition, the state model provides the mean temperature of the active layer, which is used, for example, by the ideal pipe register as a return-temperature reference.