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Body Radiation

Lumped thermal element for radiation heat transfer

Description

The Body Radiation component models the thermal radiation emitted between two bodies as a result of their temperatures. The following constitutive equation is used:

Qflow =GrσTA4TB4

where G ris the radiation conductance and σ is the Stefan-Boltzmann constant. G r can be determined by the measurements; this value is assumed to be constant over the range of operations.

In simple cases, G r may be analytically computed. The analytical equations use ϵ, the emission value of a body, which is 1 if the body absorbs all radiation (black body), or 0 if the body reflects and does not absorb radiation.

Typical values for ϵ:

Medium

Value

aluminum, 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 G r

Small convex object in large enclosure (e.g., a hot machine in a room):

G r= ϵ A

    where

       ϵ: Emission value of object (0..1)

       A: Surface area of object where radiation

          heat transfer takes place

Two parallel plates:

G r=A1ϵ1+1ϵ21

    where

       ϵ1: Emission value of plate1 (0..1)

       ϵ2: Emission value of plate2 (0..1)

       A : Area of plate1 (= area of plate2)

Two long concentric cylinders (where radiation takes place from the inner to the outer cylinder):

G r=2πr1L1ϵ1+1ϵ21r1r2

    where

       r1: Radius of inner cylinder

       r2: Radius of outer cylinder

       L : Length of the two cylinders

       ϵ1: Emission value of inner cylinder (0..1)

       ϵ2: Emission value of outer cylinder (0..1)

Connections

Name

Description

porta.

Input port a

portb.

Input port b

Variables

Symbol

Units

Description

Tx

-

Temperature at port x where x A,B

Parameters

Symbol

Default

Units

Description

Modelica ID

Gr

-

m2

Net radiation conductance between two surfaces  

Gr

Initial Conditions

Symbol

Units

Description

Modelica ID

Qflow0

W

Heat flow rate from porta to portb

Q_flow

ΔT0

K

Initial temperature difference

dT

See Also

Heat Transfer Components

Thermal Overview

The components described in this topic are from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.

 

 

 

 

 


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