.Buildings.HeatTransfer.Data.Solids

Information

Package with records for solid materials. The material is characterized by its thermal conductivity, mass density and specific heat capacity.

These material records automatically compute the spatial grid that is used to compute transient heat conduction. In building materials, the thermal diffusivity of adjacent layer materials can differ by an order of magnitude. If the spatial grid generation were not to account for the material properties, then the time rate of change of the different temperature nodes would be significantly different from each other. Therefore, records in the packages Buildings.HeatTransfer.Data.Solids and Buildings.HeatTransfer.Data.SolidsPCM generate the spatial grid so that under the assumption of equal heat transfer, each node temperature has a similar time rate of change.

The computation is as follows:

From dimensionless analysis, one can obtain a characteristic time, called the Fourier number, as

Fo = α t ⁄ L²

where α denotes the thermal diffusivity, t denotes time and L denotes the characteristic length. We like to generate the spatial grid so that the ratio t ⁄ Fo is equal to an arbitrary constant Π, which we define as

Π = ( t ⁄ Fo )^1/2

and hence

Π = L ⁄ √ α.

Now, let x denote the thickness of the material layer. Then, we compute the time constant of the material layer as

Π_x = x ⁄ √ α,

and we compute the estimated number of elements N' ∈ ℝ for the material layer as

N' = N_ref Π_x ⁄ Π_ref

where Π_ref ∈ ℕ is a user-specified number of elements for a reference material, which is equal to the parameter nStaRef, and defined as a concrete construction with thickness L_ref = 0.20 meter and thermal diffusivity α_ref = 3.64E-7 m²/s. Hence, Π_ref = L_ref/ √ α_ref = 331.4 √s.

Next, we define the number of elements for the material layer as

N_x = ⌈ N' ⌉

where the notation ⌈ ⋅ ⌉ is defined, for s ∈ ℝ, as

⌈ s ⌉ = min{ k ∈ ℤ | k ≥ s }.

Finally, we divide the material layer in compartments of length Δ = x ⁄ N_x.

Contents

Name	Description
Generic	Thermal properties of solids with heat storage
Brick	Brick (k=0.89)
Concrete	Concrete (k=1.4)
InsulationBoard	Insulation board (k=0.03)
Glass	Glass
GypsumBoard	Gypsum board (k=0.58)
Plywood	Plywood (k=0.12)
Steel	Steel (k=50.2)

Revisions

• October 31, 2016, by Michael Wetter:
  Added thermal properties of glass.
• September 9, 2010, by Michael Wetter:
  First implementation.