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Heat transfer by radiation

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:

$Q=k·A·\left({T}_{A}^{4}-{T}_{B}^{4}\right)$

where

 Q Heat flow k Radiation coefficient A Emitting body surface area TA, TB 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 ε1, ε2 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 r1 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.

Dialog Box and Parameters

Parameters Tab

Area

Radiating body area of heat transfer. The default value is 0.0001 m^2.

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.

Variables Tab

Use the Variables tab 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.

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.