WOLFRAM SYSTEM MODELER

Lumped thermal element for radiation heat transfer

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# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

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