Modelica.Thermal.HeatTransfer.Components

Information

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

Modelica.Thermal.HeatTransfer.Components.HeatCapacitor

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 (= SIunits.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

Name	Description
C	Heat capacity of element (= cp*m) [J/K]

Connectors

Name	Description
port

Modelica.Thermal.HeatTransfer.Components.ThermalConductor

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

Parameters

Name	Description
G	Constant thermal conductance of material [W/K]

Connectors

Name	Description
port_a
port_b

Modelica.Thermal.HeatTransfer.Components.ThermalResistor

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).

Parameters

Name	Description
R	Constant thermal resistance of material [K/W]

Connectors

Name	Description
port_a
port_b

Modelica.Thermal.HeatTransfer.Components.Convection

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 R. Fischer: Elektrische Maschinen, 10th edition, Hanser-Verlag 1999, p. 378):

    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 J.P.Holman: Heat Transfer, 8th edition, McGraw-Hill, 1997, p.270):

   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/mue (Reynolds number)
      Pr : = cp*mue/k    (Prandtl number)
      v  : Absolute velocity of fluid
      x  : distance from leading edge of flat plate
      rho: density of fluid (material constant
      mue: 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

Name	Description
Gc	Signal representing the convective thermal conductance in [W/K] [W/K]
solid
fluid

Modelica.Thermal.HeatTransfer.Components.ConvectiveResistor

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

Name	Description
Rc	Signal representing the convective thermal resistance in [K/W] [K/W]
solid
fluid

Modelica.Thermal.HeatTransfer.Components.BodyRadiation

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)

Parameters

Name	Description
Gr	Net radiation conductance between two surfaces (see docu) [m2]

Connectors

Name	Description
port_a
port_b

Modelica.Thermal.HeatTransfer.Components.ThermalCollector

Information

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

Parameters

Name	Description
m	Number of collected heat flows

Connectors

Name	Description
port_a[m]
port_b