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:

where is the radiation conductance and $\mathrm{σ}$ is the Stefan-Boltzmann constant.  can be determined by the measurements; this value is assumed to be constant over the range of operations.

In simple cases,  may be analytically computed. The analytical equations use $\mathrm{ϵ}$, 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 $\mathrm{ϵ}$:

 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

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

where

$\mathbf{ϵ}$: Emission value of object (0..1)

A: Surface area of object where radiation

heat transfer takes place

Two parallel plates:

where

$\mathbf{ϵ1}$: Emission value of plate1 (0..1)

$\mathbf{ϵ2}$: 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):

where

L : Length of the two cylinders

$\mathbf{ϵ1}$: Emission value of inner cylinder (0..1)

$\mathbf{ϵ2}$: Emission value of outer cylinder (0..1)

Connections

 Name Description ${\mathrm{port}}_{a}.$ Input port a ${\mathrm{port}}_{b}.$ Input port b

Variables

 Symbol Units Description ${T}_{x}$ - Temperature at port $x$ where

Parameters

 Symbol Default Units Description Modelica ID $G{}_{r}$ - ${m}^{2}$ Net radiation conductance between two surfaces Gr

Initial Conditions

 Symbol Units Description Modelica ID ${Q}_{\mathrm{flow0}}$ W Heat flow rate from to ${\mathrm{port}}_{b}$ Q_flow ${\mathrm{ΔT}}_{\mathit{0}}$ $K$ Initial temperature difference dT