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 ⁄ L^{2}
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 m^{2}/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}.
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) |