Radiation Behaviour for Convective & Conjugate Heat Transfer

Radiation is defined as the transfer of energy using electromagnetic waves. When these waves interact with any type of matter, they become heat. All bodies with a temperature greater than absolute zero emit radiation, and in contrast to conduction or convection, this radiation behavior phenomenon requires no medium.

In SimScale, radiation is modeled using a Diffuse View Factors Model. This approximation implies several assumptions that can be applied to most of the engineering problems:

• Diffuse radiation is hemispheric and uniform. For every surface, its emission is independent of direction.
• View Factors only consider the radiative heat exchange between surfaces. Thus, the medium (air) is supposed to have no interference. This is true when there are no particles suspended in the fluid which makes it less transparent (like dust or fog). The View Factor of two surfaces measures the proportion of the total radiation that is exchanged between them. It only depends on the geometrical parameters.

The different surfaces of the model will exchange heat between them, and they will also provide or subtract heat from the adjacent fluid. Coupling of both convection and radiation will be achieved once the simulation converges.

In SimScale, radiation is available for Convective Heat Transfer, Conjugate Heat Transfer, and Conjugate Heat Transfer v2.0 analysis types and can be activated by toggling on Radiation in the global settings. As a result, you should be able to set radiative behavior, emissivity, additional radiative source, and the far-field temperature while assigning the boundary conditions.

Radiation Behavior

Radiative behaviour specifies the relationship between the net radiative heat per unit surface area, \(Q_r\ [W/m^2]\) and the temperature of every surface, \(T_s\ [K]\). In SimScale, you can set two radiative surface behaviours, transparent and opaque:

Transparent Surface

A Transparent surface establishes no relation between \(Q_r\) and \(T_s\). This means that the surface temperature remains unaffected by the net radiative heat that the surface emits or receives. This implies that \(T_s\) is determined by other heat transport means (conduction or convection) or by a boundary condition. This option is mainly applied to surfaces that are not solid, like inlets or outlets (for example, an open window).

Additional Radiative Source

For convective and conjugate heat transfer analysis, apart from the radiative heat interchange that the surfaces will perform, we can set an additional radiative source. This represents any additional (mainly external) source of radiation that goes through the surface and it will not heat it up. The best example is the solar radiation getting into the domain through an open window.

Far Field Temperature

Available to only conjugate heat transfer v2.0 analysis, far field temperature represents the temperature of the black body in the far field needed for inclusion of radiation effects at the open boundaries. Hence, instead of mentioning the power of the radiative source you can just mention its temperature.

Opaque Surface

An Opaque behavior couples \(Q_r\) and \(T_s\) using the Stefan-Boltzmann law for diffuse and hemispheric radiation. Supposing two different surfaces \(S\) and \(S’\), the \(Q_r\) that \(S\) provides to \(S’\) is:

$$ Q_r(S→S’) = F. \epsilon . \sigma .(T_S – T_{S’})^4$$

Where \(F\) is the view factor between \(S\) and \(S’\), \(\sigma\) is the Stefan-Boltzmann constant (5.6696e-8 \(W /m²K\)), and \(\epsilon\) is the emissivity of the surface \(S\).

Emissivity

The emissivity depends on the material of the surface, and it measures its capability to emit radiation, otherwise known as its radiation behavior. The default value in the Workbench is 0.9, which is a good approximation for walls made of brick or concrete.

Numerics for Radiation

For radiative heat transfer problems, further settings can be changed within the numerics, as shown in the picture below. Most importantly, the radiation resolution can be changed. This affects the discretization of the directions for which the radiative problem is solved. The settings are coarse, moderate and fine. Increasing the radiation resolution will lead to a higher number of directions and hence improved angular discretization of the radiative problem (usually a more accurate result).

Additional Notes for Radiation Behavior

• Radiation becomes more important when the simulation has high temperatures.
• To save time and avoid mistakes, transparent radiative behavior is assigned by default to all inlets and outlets.
• Simulations that include radiation often need more iterations to converge because of this additional heat transference. It is advisable to switch off the “Compressible” toggle in global settings.
• Emissivity is considered constant for every material. In reality, it depends on the wavelength of the radiation that is being emitted. In CFD simulations, the total emissivity is specified, which is the integrated emissivity over all wavelengths.
• Solar radiation is usually directional. However, it can be considered diffuse on cloudy days.
• Also, symmetric boundary conditions are not supported by the current radiation solver.

To read more about supported types of radiation and radiation behavior check out this documentation page. 

Validation Cases for Radiation Behavior

• Case 1: Cylinder
• Case 2: Closed ring

Last updated: August 11th, 2022