Modelica.Thermal.HeatTransfer.Components

Lumped thermal components

Information

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
HeatCapacitor	Lumped thermal element storing heat
ThermalConductor	Lumped thermal element transporting heat without storing it
ThermalResistor	Lumped thermal element transporting heat without storing it
Convection	Lumped thermal element for heat convection (Q_flow = Gc*dT)
ConvectiveResistor	Lumped thermal element for heat convection (dT = Rc*Q_flow)
BodyRadiation	Lumped thermal element for radiation heat transfer
ThermalCollector	Collects m heat flows
ThermalCollectorMatrix	Collects Ns x Np heat flows
GeneralHeatFlowToTemperatureAdaptor	Signal adaptor for a HeatTransfer port with temperature and derivative of temperature as outputs and heat flow as input (especially useful for FMUs)
GeneralTemperatureToHeatFlowAdaptor	Signal adaptor for a HeatTransfer port with heat flow as output and temperature and derivative of temperature as input (especially useful for FMUs)

Modelica.Thermal.HeatTransfer.Components.HeatCapacitor

Lumped thermal element storing heat

Information

This is a generic model for the heat capacity of a material. No specific geometry is assumed beyond a total volume with uniform temperature for the entire volume. Furthermore, it is assumed that the heat capacity is constant (independent of temperature).

The temperature T [Kelvin] of this component is a state. A default of T = 25 degree Celsius (= Modelica.Units.Conversions.from_degC(25)) is used as start value for initialization. This usually means that at start of integration the temperature of this component is 25 degrees Celsius. You may, of course, define a different temperature as start value for initialization. Alternatively, it is possible to set parameter steadyStateStart to true. In this case the additional equation 'der(T) = 0' is used during initialization, i.e., the temperature T is computed in such a way that the component starts in steady state. This is useful in cases, where one would like to start simulation in a suitable operating point without being forced to integrate for a long time to arrive at this point.

Note, that parameter steadyStateStart is not available in the parameter menu of the simulation window, because its value is utilized during translation to generate quite different equations depending on its setting. Therefore, the value of this parameter can only be changed before translating the model.

This component may be used for complicated geometries where the heat capacity C is determined my measurements. If the component consists mainly of one type of material, the mass m of the component may be measured or calculated and multiplied with the specific heat capacity cp of the component material to compute C:

C = cp*m.
Typical values for cp at 20 degC in J/(kg.K):
   aluminium   896
   concrete    840
   copper      383
   iron        452
   silver      235
   steel       420 ... 500 (V2A)
   wood       2500

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.ThermalConductor

Lumped thermal element transporting heat without storing it

Information

This is a model for transport of heat without storing it; see also: ThermalResistor. It may be used for complicated geometries where the thermal conductance G (= inverse of thermal resistance) is determined by measurements and is assumed to be constant over the range of operations. If the component consists mainly of one type of material and a regular geometry, it may be calculated, e.g., with one of the following equations:

• Conductance for a box geometry under the assumption that heat flows along the box length:

  G = k*A/L
  k: Thermal conductivity (material constant)
  A: Area of box
  L: Length of box
      

• Conductance for a cylindrical geometry under the assumption that heat flows from the inside to the outside radius of the cylinder:

  G = 2*pi*k*L/log(r_out/r_in)
  pi   : Modelica.Constants.pi
  k    : Thermal conductivity (material constant)
  L    : Length of cylinder
  log  : Modelica.Math.log;
  r_out: Outer radius of cylinder
  r_in : Inner radius of cylinder
      

Typical values for k at 20 degC in W/(m.K):
  aluminium   220
  concrete      1
  copper      384
  iron         74
  silver      407
  steel        45 .. 15 (V2A)
  wood         0.1 ... 0.2

Extends from Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy).

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.ThermalResistor

Lumped thermal element transporting heat without storing it

Information

This is a model for transport of heat without storing it, same as the ThermalConductor but using the thermal resistance instead of the thermal conductance as a parameter. This is advantageous for series connections of ThermalResistors, especially if it shall be allowed that a ThermalResistance is defined to be zero (i.e. no temperature difference).

Extends from Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy).

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.Convection

Lumped thermal element for heat convection (Q_flow = Gc*dT)

Information

This is a model of linear heat convection, e.g., the heat transfer between a plate and the surrounding air; see also: ConvectiveResistor. It may be used for complicated solid geometries and fluid flow over the solid by determining the convective thermal conductance Gc by measurements. The basic constitutive equation for convection is

Q_flow = Gc*(solid.T - fluid.T);
Q_flow: Heat flow rate from connector 'solid' (e.g., a plate)
   to connector 'fluid' (e.g., the surrounding air)

Gc = G.signal[1] is an input signal to the component, since Gc is nearly never constant in practice. For example, Gc may be a function of the speed of a cooling fan. For simple situations, Gc may be calculated according to

Gc = A*h
A: Convection area (e.g., perimeter*length of a box)
h: Heat transfer coefficient

where the heat transfer coefficient h is calculated from properties of the fluid flowing over the solid. Examples:

Machines cooled by air (empirical, very rough approximation according to [Fischer2017, p. 452]:

h = 7.8*v^0.78 [W/(m2.K)] (forced convection)
  = 12         [W/(m2.K)] (free convection)
where
  v: Air velocity in [m/s]

Laminar flow with constant velocity of a fluid along a flat plate where the heat flow rate from the plate to the fluid (= solid.Q_flow) is kept constant (according to [Holman2010, p.265]):

h  = Nu*k/x;
Nu = 0.453*Re^(1/2)*Pr^(1/3);
where
   h  : Heat transfer coefficient
   Nu : = h*x/k       (Nusselt number)
   Re : = v*x*rho/mu  (Reynolds number)
   Pr : = cp*mu/k     (Prandtl number)
   v  : Absolute velocity of fluid
   x  : distance from leading edge of flat plate
   rho: density of fluid (material constant
   mu : dynamic viscosity of fluid (material constant)
   cp : specific heat capacity of fluid (material constant)
   k  : thermal conductivity of fluid (material constant)
and the equation for h holds, provided
   Re < 5e5 and 0.6 < Pr < 50

Connectors

Modelica.Thermal.HeatTransfer.Components.ConvectiveResistor

Lumped thermal element for heat convection (dT = Rc*Q_flow)

Information

This is a model of linear heat convection, e.g., the heat transfer between a plate and the surrounding air; same as the Convection component but using the convective resistance instead of the convective conductance as an input. This is advantageous for series connections of ConvectiveResistors, especially if it shall be allowed that a convective resistance is defined to be zero (i.e. no temperature difference).

Connectors

Modelica.Thermal.HeatTransfer.Components.BodyRadiation

Lumped thermal element for radiation heat transfer

Information

This is a model describing the thermal radiation, i.e., electromagnetic radiation emitted between two bodies as a result of their temperatures. The following constitutive equation is used:

Q_flow = Gr*sigma*(port_a.T^4 - port_b.T^4);

where Gr is the radiation conductance and sigma is the Stefan-Boltzmann constant (= Modelica.Constants.sigma). Gr may be determined by measurements and is assumed to be constant over the range of operations.

For simple cases, Gr may be analytically computed. The analytical equations use epsilon, the emission value of a body which is in the range 0..1. Epsilon=1, if the body absorbs all radiation (= black body). Epsilon=0, if the body reflects all radiation and does not absorb any.

Typical values for epsilon:
aluminium, polished    0.04
copper, polished       0.04
gold, polished         0.02
paper                  0.09
rubber                 0.95
silver, polished       0.02
wood                   0.85..0.9

Analytical Equations for Gr

Small convex object in large enclosure (e.g., a hot machine in a room):

Gr = e*A
where
   e: Emission value of object (0..1)
   A: Surface area of object where radiation
      heat transfer takes place

Two parallel plates:

Gr = A/(1/e1 + 1/e2 - 1)
where
   e1: Emission value of plate1 (0..1)
   e2: Emission value of plate2 (0..1)
   A : Area of plate1 (= area of plate2)

Two long cylinders in each other, where radiation takes place from the inner to the outer cylinder):

Gr = 2*pi*r1*L/(1/e1 + (1/e2 - 1)*(r1/r2))
where
   pi: = Modelica.Constants.pi
   r1: Radius of inner cylinder
   r2: Radius of outer cylinder
   L : Length of the two cylinders
   e1: Emission value of inner cylinder (0..1)
   e2: Emission value of outer cylinder (0..1)

Extends from Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy).

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.ThermalCollector

Collects m heat flows

Information

This is a model to collect the heat flows from m heatports to one single heatport.

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.ThermalCollectorMatrix

Collects Ns x Np heat flows

Information

This is a model to collect the heat flows from Ns x Np heatports to one single heatport.

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.GeneralHeatFlowToTemperatureAdaptor

Signal adaptor for a HeatTransfer port with temperature and derivative of temperature as outputs and heat flow as input (especially useful for FMUs)

Information

Adaptor between a heatport connector and a signal representation of the flange. This component is used to provide a pure signal interface around a HeatTransfer model and export this model in form of an input/output block, especially as FMU (Functional Mock-up Unit). Examples of the usage of this adaptor are provided in HeatTransfer.Examples.GenerationOfFMUs. This adaptor has heatflow as input and temperature and derivative of temperature as output signals.

Extends from Modelica.Blocks.Interfaces.Adaptors.FlowToPotentialAdaptor (Signal adaptor for a connector with flow, 1st derivative of flow, and 2nd derivative of flow as inputs and potential, 1st derivative of potential, and 2nd derivative of potential as outputs (especially useful for FMUs)).

Parameters

Connectors

Modelica.Thermal.HeatTransfer.Components.GeneralTemperatureToHeatFlowAdaptor

Signal adaptor for a HeatTransfer port with heat flow as output and temperature and derivative of temperature as input (especially useful for FMUs)

Information

Adaptor between a heatport connector and a signal representation of the flange. This component is used to provide a pure signal interface around a HeatTransfer model and export this model in form of an input/output block, especially as FMU (Functional Mock-up Unit). Examples of the usage of this adaptor are provided in HeatTransfer.Examples.GenerationOfFMUs. This adaptor has temperature and derivative of temperature as input signals and heatflow as output signal.

Note, the input signals must be consistent to each other (derT=der(T)).

Extends from Modelica.Blocks.Interfaces.Adaptors.PotentialToFlowAdaptor (Signal adaptor for a connector with potential, 1st derivative of potential, and 2nd derivative of potential as inputs and flow, 1st derivative of flow, and 2nd derivative of flow as outputs (especially useful for FMUs)).

Parameters

Connectors