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.

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)

Buildings.HeatTransfer.Data.Solids.Generic

Information

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

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

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

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

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

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

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)";