Lumped thermal element for radiation heat transfer

## Library

Modelica/Thermal/HeatTransfer/Components

## Description

This is a model describing the thermal radiation, i.e., electromagneticradiation 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-Boltzmannconstant (= Modelica.Constants.sigma). Gr may be determined bymeasurements and is assumed to be constant over the range of operations.

For simple cases, Gr may be analytically computed. The analyticalequations use epsilon, the emission value of a body which is in therange 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 takesplace 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

NameLabelDescriptionData TypeValid Values

mo_Gr

Gr

Net radiation conductance between two surfaces (see docu)

Scalar

NameLabelDescriptionData TypeValid Values

mo__nmodifiers

Number of Modifiers

Specifies the number of modifiers

Number

mo__modifiers

Modifiers

Structure

mo__modifiers/varname

Variable name

Cell of strings

'Q_flow'
'dT'

mo__modifiers/attribute

Attribute

Cell of strings

'start'
'fixed'

mo__modifiers/value

Value

## Ports

NameTypeDescriptionIO TypeNumber

port_a

implicit

input

1

port_b

implicit

output

1