Description

The Heat Radiation component models the thermal radiation emitted between two bodies as a result of their temperatures.

This component has 4 options to express the type of radiation which is defined by the parameter Radiation type.

Refer to the below matrix which shows the implemented options.

 Radiation type Radiation geometry Use Correction input Constant - false or true External input - false or true General - false or true Use References Surrounded object false or true Two parallel plates false or true Two long concentric cylinders false or true Concentric spheres false or true

The following table is the image of radiation geometry when Radiation type is Use References.

 Radiation type Radiation geometry Use References Surrounded object Two parallel plates Two long concentric cylinders Concentric spheres

Additionally, if you set Use reference of emissivity for Material 1 / 2 as true, the built-in emissivity data can be used as references.

Refer to the below matrix about the built-in emissivity data.

 Material Emissivity value Brass Polished 0.03 Brass Oxidized 600oC 0.6 Copper electroplated 0.03 Copper Polished 0.04 Steel Oxidized 0.79 Steel Polished 0.07 Steel Galvanized New 0.23 Steel Galvanized Old 0.88 Stainless Steel, Polished 0.075 Stainless Steel, weathered 0.85 Aluminum Foil 0.04 Aluminium Heavily Oxidized 0.25 Iron, dark gray surface 0.31 Iron, plate rusted red 0.61 Cast Iron 0.65 Cast Iron, newly turned 0.44 Wrought Iron 0.94 Lead Oxidized 0.43 Carbon, not oxidized 0.81 Plastics 0.91 Rubber Nat Hard 0.91 Porcelain, glazed 0.92 Glass smooth 0.93 Paper 0.93

Equations

Fundamental equation is :

The extended equation which is implemented in this library is :

when Use Correction input = true, $\mathrm{cor}$ is specified by the input signal. If Use Correction input = false, $\mathrm{cor}$ is the constant value "1".

Net radiation conductance between two surfaces $\mathrm{Gr__act}$ is defined based on the selected option. The equation for each option is shown below.

 Radiation type : Constant With this type, the net radiation conductance is specified by the value of parameter $\mathrm{Gr}$. $\mathrm{Gr__act}=\mathrm{Gr}$
 Radiation type : External input If you use this type, the net radiation conductance is specified by the signal input ${\mathrm{Gr}}_{\mathit{in}}$. $\mathrm{Gr__act}=\mathrm{Gr__in}$
 Radiation type : General If you use this type, the generalized equation is valid for the net radiation conductance. The following equation is based on the radiation network for two surfaces which exchange heat each other and no other route of heat. $\mathrm{Gr__act}=\frac{1}{\left(\frac{1-\mathrm{ε__act1}}{\mathrm{A__1}\cdot \mathrm{ε__act1}}+\frac{1}{\mathrm{A__1}\cdot \mathrm{F__12}}+\frac{1-\mathrm{ε__act2}}{\mathrm{A__2}\cdot \mathrm{ε__act2}}\right)}$

If you use this type, references can be used for the net radiation conductance, and there are 4 options.

 • "Surrounded object" : Radiation Geometry = Surrounded object

$\mathrm{Gr__act}=\mathrm{A__1}\cdot \mathrm{ε__act1}$

 • "Two parallel plates" : Radiation Geometry = Two parallel plates

$\mathrm{Gr__act}=\frac{\mathrm{A__1}}{\frac{1}{\mathrm{ε__act1}}+\frac{1}{\mathrm{ε__act2}}-1}$

 • "Two long concentric cylinders" : Radiation Geometry = Two long concentric cylinders

$\mathrm{Gr__act}=\frac{2\cdot \mathrm{π}\cdot \mathrm{r__1}\cdot \mathrm{L__1}}{\frac{1}{\mathrm{ε__act1}}+\left(\frac{1}{\mathrm{ε__act2}}-1\right)\cdot \frac{\mathrm{r__1}}{\mathrm{r__2}}}$

 • "Concentric spheres" : Radiation Geometry = Concentric spheres

$\mathrm{Gr__act1}=\frac{4\cdot \mathrm{π}\cdot {\mathrm{r__1}}^{2}}{\frac{1}{\mathrm{ε__act1}}+\frac{1-\mathrm{ε__act2}}{\mathrm{ε__act2}}\cdot {\left(\frac{\mathrm{r__1}}{\mathrm{r__2}}\right)}^{2}}$

Variables

 Symbol Units Description Modelica ID $\mathrm{Q__flow}$ $W$ Heat flow rate from port a to port b Q_flow $K$ Temperature of port a $K$ Temperature of port b $\mathrm{Gr__act}$ ${m}^{2}$ Net radiation conductance between two surfaces Gr_act $\stackrel{}{\mathrm{σ}}$ $\frac{w}{{m}^{2}\cdot {K}^{4}}$ Stefan-Boltzmann constant 5.670373e-8 sigma $\mathrm{ε__act1}$  Emissivity of object 1 on port a eps_act1 $\mathrm{ε__act2}$  Emissivity of object 2 on port b eps_act2

Connections

 Name Units Condition Description Modelica ID $\mathrm{port_a}$ - - Thermal port, a port_a $\mathrm{port_b}$ - - Thermal port, b port_b $\mathrm{Gr__in}$ ${m}^{2}$ if Radiation type is External input. Input signal of the heat transfer coefficient Gr_in $\mathrm{cor}$ - if Use correction input is true. Input signal of the correction factor for ${Q}_{\mathrm{flow}}$ cor

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{General}$  Select Type of Radiation  General : Use the generalized equation  Constant : Radiation conductance is constant  External input: Radiation conductance given by input  Use References : Use references for Radiation conductance TypeOfRadiation  Geometry type of Radiation. RadiationGeometry $\mathrm{false}$  If true, Emissivity for Material 1 are defined by reference data use_reference_emissivity1 $\mathrm{false}$  If true, Emissivity for Material 2 are defined by reference data use_reference_emissivity2  Emissivity for Material 1 if Use references of emissivity  for Material 1 is true. TypeOfMaterial1  Emissivity for Material 2 if Use references of emissivity  for Material 2 is true. TypeOfMaterial2 $\mathrm{ε__1}$ $1$ Emissivity of object 1 on port a eps1 $\mathrm{ε__2}$ $1$ emissivity of object 2 on port b eps2 $\mathrm{A__1}$ $1$ ${m}^{2}$ Surface area of object 1 A1 $\mathrm{A__2}$ $1$ ${m}^{2}$ Surface area of object 2 A2 $\mathrm{r__1}$ $0.1$ $m$ Radius of object 1, Inner r1 $\mathrm{r__2}$ $0.2$ $m$ Radius of object 2, Outer r2 $\mathrm{L__1}$ $0.1$ $m$ Length of object 1 L1 $\mathrm{F__12}$ $1$  View factor for Radiation F12 $\mathrm{Gr}$ $1$ ${m}^{2}$ Net radiation conductance between two surfaces Gr $\mathrm{false}$  If true, input of correction for Gr_act is valid use_correction