Modelica.Fluid.Pipes.BaseClasses.HeatTransfer

Heat transfer for flow models

Information


Heat transfer correlations for pipe models

Package Content

NameDescription
Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer PartialFlowHeatTransfer base class for any pipe heat transfer correlation
Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer IdealFlowHeatTransfer IdealHeatTransfer: Ideal heat transfer without thermal resistance
Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.ConstantFlowHeatTransfer ConstantFlowHeatTransfer ConstantHeatTransfer: Constant heat transfer coefficient
Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialPipeFlowHeatTransfer PartialPipeFlowHeatTransfer Base class for pipe heat transfer correlation in terms of Nusselt number heat transfer in a circular pipe for laminar and turbulent one-phase flow
Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.LocalPipeFlowHeatTransfer LocalPipeFlowHeatTransfer LocalPipeFlowHeatTransfer: Laminar and turbulent forced convection in pipes, local coefficients


Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer

base class for any pipe heat transfer correlation

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialFlowHeatTransfer

Information


Base class for heat transfer models of flow devices.

The geometry is specified in the interface with the surfaceAreas[n], the roughnesses[n] and the lengths[n] along the flow path. Moreover the fluid flow is characterized for different types of devices by the characteristic dimensions[n+1] and the average velocities vs[n+1] of fluid flow. See Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber for examplary definitions.

Extends from Modelica.Fluid.Interfaces.PartialHeatTransfer (Common interface for heat transfer models).

Parameters

TypeNameDefaultDescription
Ambient
CoefficientOfHeatTransferk0Heat transfer coefficient to ambient [W/(m2.K)]
TemperatureT_ambientsystem.T_ambientAmbient temperature [K]
Internal Interface
replaceable package MediumPartialMediumMedium in the component
Integern1Number of heat transfer segments
Booleanuse_kfalse= true to use k value for thermal isolation
Geometry
RealnParallel number of identical parallel flow devices

Connectors

TypeNameDescription
HeatPorts_aheatPorts[n]Heat port to component boundary

Modelica definition

partial model PartialFlowHeatTransfer 
  "base class for any pipe heat transfer correlation"
  extends Modelica.Fluid.Interfaces.PartialHeatTransfer;

  // Additional inputs provided to flow heat transfer model
  input SI.Velocity[n] vs "Mean velocities of fluid flow in segments";

  // Geometry parameters and inputs for flow heat transfer
  parameter Real nParallel "number of identical parallel flow devices";
  input SI.Length[n] lengths "Lengths along flow path";
  input SI.Length[n] dimensions 
    "Characteristic dimensions for fluid flow (diameter for pipe flow)";
  input SI.Height[n] roughnesses "Average heights of surface asperities";

end PartialFlowHeatTransfer;

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer

IdealHeatTransfer: Ideal heat transfer without thermal resistance

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.IdealFlowHeatTransfer

Information


Ideal heat transfer without thermal resistance.

Extends from PartialFlowHeatTransfer (base class for any pipe heat transfer correlation).

Parameters

TypeNameDefaultDescription
Ambient
CoefficientOfHeatTransferk0Heat transfer coefficient to ambient [W/(m2.K)]
TemperatureT_ambientsystem.T_ambientAmbient temperature [K]
Internal Interface
replaceable package MediumPartialMediumMedium in the component
Integern1Number of heat transfer segments
Booleanuse_kfalse= true to use k value for thermal isolation
Geometry
RealnParallel number of identical parallel flow devices

Connectors

TypeNameDescription
HeatPorts_aheatPorts[n]Heat port to component boundary

Modelica definition

model IdealFlowHeatTransfer 
  "IdealHeatTransfer: Ideal heat transfer without thermal resistance"
  extends PartialFlowHeatTransfer;
equation 
  Ts = heatPorts.T;
end IdealFlowHeatTransfer;

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.ConstantFlowHeatTransfer Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.ConstantFlowHeatTransfer

ConstantHeatTransfer: Constant heat transfer coefficient

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.ConstantFlowHeatTransfer

Information


Simple heat transfer correlation with constant heat transfer coefficient, used as default component in 

Extends from PartialFlowHeatTransfer (base class for any pipe heat transfer correlation).

Parameters

TypeNameDefaultDescription
CoefficientOfHeatTransferalpha0 heat transfer coefficient [W/(m2.K)]
Ambient
CoefficientOfHeatTransferk0Heat transfer coefficient to ambient [W/(m2.K)]
TemperatureT_ambientsystem.T_ambientAmbient temperature [K]
Internal Interface
replaceable package MediumPartialMediumMedium in the component
Integern1Number of heat transfer segments
Booleanuse_kfalse= true to use k value for thermal isolation
Geometry
RealnParallel number of identical parallel flow devices

Connectors

TypeNameDescription
HeatPorts_aheatPorts[n]Heat port to component boundary

Modelica definition

model ConstantFlowHeatTransfer 
  "ConstantHeatTransfer: Constant heat transfer coefficient"
  extends PartialFlowHeatTransfer;
  parameter SI.CoefficientOfHeatTransfer alpha0 "heat transfer coefficient";
equation 
  Q_flows = {alpha0*surfaceAreas[i]*(heatPorts[i].T - Ts[i])*nParallel for i in 1:n};
end ConstantFlowHeatTransfer;

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialPipeFlowHeatTransfer Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialPipeFlowHeatTransfer

Base class for pipe heat transfer correlation in terms of Nusselt number heat transfer in a circular pipe for laminar and turbulent one-phase flow

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.PartialPipeFlowHeatTransfer

Information


Base class for heat transfer models that are expressed in terms of the Nusselt number and which can be used in distributed pipe models.

Extends from PartialFlowHeatTransfer (base class for any pipe heat transfer correlation).

Parameters

TypeNameDefaultDescription
CoefficientOfHeatTransferalpha0100guess value for heat transfer coefficients [W/(m2.K)]
Ambient
CoefficientOfHeatTransferk0Heat transfer coefficient to ambient [W/(m2.K)]
TemperatureT_ambientsystem.T_ambientAmbient temperature [K]
Internal Interface
replaceable package MediumPartialMediumMedium in the component
Integern1Number of heat transfer segments
Booleanuse_kfalse= true to use k value for thermal isolation
Geometry
RealnParallel number of identical parallel flow devices

Connectors

TypeNameDescription
HeatPorts_aheatPorts[n]Heat port to component boundary

Modelica definition

partial model PartialPipeFlowHeatTransfer 
  "Base class for pipe heat transfer correlation in terms of Nusselt number heat transfer in a circular pipe for laminar and turbulent one-phase flow"
  extends PartialFlowHeatTransfer;
  parameter SI.CoefficientOfHeatTransfer alpha0=100 
    "guess value for heat transfer coefficients";
  SI.CoefficientOfHeatTransfer[n] alphas(each start=alpha0) 
    "CoefficientOfHeatTransfer";
  Real[n] Res "Reynolds numbers";
  Real[n] Prs "Prandtl numbers";
  Real[n] Nus "Nusselt numbers";
  Medium.Density[n] ds "Densities";
  Medium.DynamicViscosity[n] mus "Dynamic viscosities";
  Medium.ThermalConductivity[n] lambdas "Thermal conductivity";
  SI.Length[n] diameters = dimensions "Hydraulic diameters for pipe flow";
equation 
  ds=Medium.density(states);
  mus=Medium.dynamicViscosity(states);
  lambdas=Medium.thermalConductivity(states);
  Prs = Medium.prandtlNumber(states);
  Res = CharacteristicNumbers.ReynoldsNumber(vs/nParallel, ds, mus, diameters);
  Nus = CharacteristicNumbers.NusseltNumber(alphas, diameters, lambdas);
  Q_flows={alphas[i]*surfaceAreas[i]*(heatPorts[i].T - Ts[i])*nParallel for i in 1:n};
end PartialPipeFlowHeatTransfer;

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.LocalPipeFlowHeatTransfer Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.LocalPipeFlowHeatTransfer

LocalPipeFlowHeatTransfer: Laminar and turbulent forced convection in pipes, local coefficients

Modelica.Fluid.Pipes.BaseClasses.HeatTransfer.LocalPipeFlowHeatTransfer

Information


Heat transfer model for laminar and turbulent flow in pipes. Range of validity:

The correlation takes into account the spatial position along the pipe flow, which changes discontinuously at flow reversal. However, the heat transfer coefficient itself is continuous around zero flow rate, but not its derivative.

References

Verein Deutscher Ingenieure (1997):
VDI Wärmeatlas. Springer Verlag, Ed. 8, 1997.

Extends from PartialPipeFlowHeatTransfer (Base class for pipe heat transfer correlation in terms of Nusselt number heat transfer in a circular pipe for laminar and turbulent one-phase flow).

Parameters

TypeNameDefaultDescription
CoefficientOfHeatTransferalpha0100guess value for heat transfer coefficients [W/(m2.K)]
Ambient
CoefficientOfHeatTransferk0Heat transfer coefficient to ambient [W/(m2.K)]
TemperatureT_ambientsystem.T_ambientAmbient temperature [K]
Internal Interface
replaceable package MediumPartialMediumMedium in the component
Integern1Number of heat transfer segments
Booleanuse_kfalse= true to use k value for thermal isolation
Geometry
RealnParallel number of identical parallel flow devices

Connectors

TypeNameDescription
HeatPorts_aheatPorts[n]Heat port to component boundary

Modelica definition

model LocalPipeFlowHeatTransfer 
  "LocalPipeFlowHeatTransfer: Laminar and turbulent forced convection in pipes, local coefficients"
  extends PartialPipeFlowHeatTransfer;
protected 
  Real[n] Nus_turb "Nusselt number for turbulent flow";
  Real[n] Nus_lam "Nusselt number for laminar flow";
  Real Nu_1;
  Real[n] Nus_2;
  Real[n] Xis;
equation 
  Nu_1=3.66;
  for i in 1:n loop
   Nus_turb[i]=smooth(0,(Xis[i]/8)*abs(Res[i])*Prs[i]/(1+12.7*(Xis[i]/8)^0.5*(Prs[i]^(2/3)-1))*(1+1/3*(diameters[i]/lengths[i]/(if vs[i]>=0 then (i-0.5) else (n-i+0.5)))^(2/3)));
   Xis[i]=(1.8*Modelica.Math.log10(max(1e-10,Res[i]))-1.5)^(-2);
   Nus_lam[i]=(Nu_1^3+0.7^3+(Nus_2[i]-0.7)^3)^(1/3);
   Nus_2[i]=smooth(0,1.077*(abs(Res[i])*Prs[i]*diameters[i]/lengths[i]/(if vs[i]>=0 then (i-0.5) else (n-i+0.5)))^(1/3));
   Nus[i]=spliceFunction(Nus_turb[i], Nus_lam[i], Res[i]-6150, 3850);
  end for;
end LocalPipeFlowHeatTransfer;

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