# Radiative Heat Transfer

Heat transfer by radiation

## Library

Thermal Elements

## Description

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.

### Variables

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

## Parameters

**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.

## Ports

The block has the following ports:

`A`

Thermal conserving port associated with body A.

`B`

Thermal conserving port associated with body B.

## References

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

## Extended Capabilities

**Introduced in R2007b**