## 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) Glass Glass 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc Specific heat capacity [J/(kg.K)]
Densityd Mass density [kg/m3]
RealRx/kThermal resistance of a unit area of material [m2.K/W]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
Properties for phase change material
TemperatureTSol293.15Solidus temperature, used only for PCM. [K]
TemperatureTLiq293.15Liquidus temperature, used only for PCM [K]
SpecificInternalEnergyLHea0Latent heat of phase change [J/kg]
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk0.89Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc790Specific heat capacity [J/(kg.K)]
Densityd1920Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk1.4Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc840Specific heat capacity [J/(kg.K)]
Densityd2240Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk0.03Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc1200Specific heat capacity [J/(kg.K)]
Densityd40Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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.Glass

Glass

### Parameters

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk1.0Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc700Specific heat capacity [J/(kg.K)]
Densityd2500Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber of states as a real number

### Modelica definition

record Glass = Buildings.HeatTransfer.Data.Solids.Generic ( k=1.0, d=2500, c=700) "Glass";

## Buildings.HeatTransfer.Data.Solids.GypsumBoard

Gypsum board (k=0.58)

### Parameters

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk0.16Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc1090Specific heat capacity [J/(kg.K)]
Densityd800Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk0.12Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc1210Specific heat capacity [J/(kg.K)]
Densityd540Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete
BooleansteadyState(c < Modelica.Constants.eps ...Flag, if true, then material is computed using steady-state heat conduction
IntegernStamax(1, integer(ceil(nStaReal...Actual number of state variables in material
RealpiRef331.4Ratio x/sqrt(alpha) for reference material of 0.2 m concrete
RealpiMatif steadyState then piRef el...Ratio x/sqrt(alpha)
RealnStaRealnStaRef*piMat/piRefNumber 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

TypeNameDefaultDescription
Lengthx Material thickness [m]
ThermalConductivityk50.2Thermal conductivity [W/(m.K)]
SpecificHeatCapacityc450Specific heat capacity [J/(kg.K)]
Densityd7850Mass density [kg/m3]
IntegernStaRef3Number of state variables in a reference material of 0.2 m concrete