Heat transfer by radiation

Thermal Elements

The Radiative Heat Transfer block represents a heat transfer by radiation between two bodies. The transfer is governed by the Stefan-Boltzmann law and is described with the following equation:

$$Q=k\xb7A\xb7({T}_{A}^{4}-{T}_{B}^{4})$$

where

Q | Heat flow |

k | Radiation coefficient |

A | Emitting body surface area |

T_{A}, T_{B} | Temperatures of the bodies |

The radiation coefficient is determined by geometrical shapes, dimensions, and surface emissivity. For example, the radiation constant for the heat transfer between two parallel plates is computed as

$$k=\frac{\sigma}{\frac{1}{{\epsilon}_{1}}+\frac{1}{{\epsilon}_{2}}-1}$$

where

σ | Stefan-Boltzmann constant |

ε_{1}, ε_{2} | Surface emissivity for the emitting and receiving plate, respectively |

Similarly, the radiation coefficient for concentric cylinders is determined with the formula

$$k=\frac{\sigma}{\frac{1}{{\epsilon}_{1}}+\frac{1-{\epsilon}_{2}}{{\epsilon}_{2}}\frac{{r}_{1}}{{r}_{2}}}$$

where *r*_{1} and *r* _{2}
are the emitting and receiving cylinder radii, respectively. Reference
[1] contains formulas
for a wide variety of shapes.

Connections A and B are thermal conserving ports associated with the emitting and receiving bodies, respectively. The block positive direction is from port A to port B. This means that the heat flow is positive if it flows from A to B.

**Area**Radiating body area of heat transfer. The default value is

`0.0001`

m^2.**Radiation coefficient**Radiation coefficient of the two bodies, based on their geometrical shapes, dimensions, and surface emissivity. See [1] for more information. The default value is

`4e-8`

W/m^2/K^4.

Use the **Variables** tab in the block dialog
box (or the **Variables** section in the block Property
Inspector) to set the priority and initial target values for the block
variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

The block has the following ports:

`A`

Thermal conserving port associated with body A.

`B`

Thermal conserving port associated with body B.

[1] Siegel, R. and J.R. Howell. *Thermal Radiation
Heat Transfer*. New York: Taylor and Francis, 2002.

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