Description: "Package with solid material, characterized by thermal conductance, density and specific heat capacity"

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## Buildings.HeatTransfer.Data.Solids

Package with solid material, characterized by thermal conductance, density and specific heat capacity

### 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

Πx = x ⁄ √ α,

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

N' = Nref Πx ⁄ Πref

where Πref ∈ 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 Lref = 0.20 meter and thermal diffusivity αref = 3.64E-7 m2/s. Hence, Πref = Lref/ √ αref = 331.4 √s.

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

Nx = ⌈ 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 ⁄ Nx.

Extends from Modelica.Icons.MaterialPropertiesPackage (Icon for package containing property classes).

### Package Content

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)
GypsumBoard | Gypsum board (k=0.58)
Plywood | Plywood (k=0.12)
Steel | Steel (k=50.2)

## Buildings.HeatTransfer.Data.Solids.Generic

Thermal properties of solids with heat storage

### Information

Generic record for solid materials. The material is characterized by its thermal conductivity, mass density and specific heat capacity.

Extends from Buildings.HeatTransfer.Data.BaseClasses.Material (Thermal properties of materials w/o storage).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k |  | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c |  | Specific heat capacity [J/(kg.K)]
Density | d |  | Mass density [kg/m3]
Real | R | x/k | Thermal resistance of a unit area of material [m2.K/W]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Properties for phase change material
Temperature | TSol | 293.15 | Solidus temperature, used only for PCM. [K]
Temperature | TLiq | 293.15 | Liquidus temperature, used only for PCM [K]
SpecificInternalEnergy | LHea | 0 | Latent heat of phase change [J/kg]
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record Generic "Thermal properties of solids with heat storage" extends Buildings.HeatTransfer.Data.BaseClasses.Material(final R=x/k, final TSol=293.15, final TLiq=293.15, final LHea=0, final phasechange=false); end Generic;

## Buildings.HeatTransfer.Data.Solids.Brick

Brick (k=0.89)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 0.89 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 790 | Specific heat capacity [J/(kg.K)]
Density | d | 1920 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record Brick = Buildings.HeatTransfer.Data.Solids.Generic ( k=0.89, d=1920, c=790) "Brick (k=0.89)";

## Buildings.HeatTransfer.Data.Solids.Concrete

Concrete (k=1.4)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 1.4 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 840 | Specific heat capacity [J/(kg.K)]
Density | d | 2240 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record Concrete = Buildings.HeatTransfer.Data.Solids.Generic ( k=1.4, d=2240, c=840) "Concrete (k=1.4)";

## Buildings.HeatTransfer.Data.Solids.InsulationBoard

Insulation board (k=0.03)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 0.03 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 1200 | Specific heat capacity [J/(kg.K)]
Density | d | 40 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record InsulationBoard = Buildings.HeatTransfer.Data.Solids.Generic ( k=0.03, d=40, c=1200) "Insulation board (k=0.03)";

## Buildings.HeatTransfer.Data.Solids.GypsumBoard

Gypsum board (k=0.58)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 0.16 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 1090 | Specific heat capacity [J/(kg.K)]
Density | d | 800 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record GypsumBoard = Buildings.HeatTransfer.Data.Solids.Generic ( k=0.16, d=800, c=1090) "Gypsum board (k=0.58)";

## Buildings.HeatTransfer.Data.Solids.Plywood

Plywood (k=0.12)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 0.12 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 1210 | Specific heat capacity [J/(kg.K)]
Density | d | 540 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | (c == 0 or d == 0) | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record Plywood = Buildings.HeatTransfer.Data.Solids.Generic ( k=0.12, d=540, c=1210) "Plywood (k=0.12)";

## Buildings.HeatTransfer.Data.Solids.Steel

Steel (k=50.2)

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Material thickness [m]
ThermalConductivity | k | 50.2 | Thermal conductivity [W/(m.K)]
SpecificHeatCapacity | c | 450 | Specific heat capacity [J/(kg.K)]
Density | d | 7850 | Mass density [kg/m3]
Integer | nStaRef | 3 | Number of state variables in a reference material of 0.2 m concrete
Boolean | steadyState | true | Flag, if true, then material is computed using steady-state heat conduction
Advanced
Integer | nSta | max(1, integer(ceil(nStaReal... | Actual number of state variables in material
Real | piRef | 331.4 | Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
Real | piMat | if steadyState then piRef el... | Ratio x/sqrt(alpha)
Real | nStaReal | nStaRef*piMat/piRef | Number of states as a real number

### Modelica definition

record Steel = Buildings.HeatTransfer.Data.Solids.Generic ( k=50.2, d=7850, c=450, steadyState=true) "Steel (k=50.2)";