MR-CFD experts are ready for Radiation analysis, consulting, training, and CFD simulation.

## Radiation

In general, heat transfer occurs in three categories, including **Conduction** heat transfer, **Convection** heat transfer, and **Radiation** heat transfer. The radiation energy model is generally divided into two categories of radiation between different surfaces (including P1, S2S, DTRM, DO and MC methods) and **Solar-Ray Tracing**. In the Solar Calculator section, the Latitude and Longitude, Time Zones, Hours and Days of radiation in the geographic Region are defined. In the Sun Direction Factor section, the direction of the solar radiation can be determined. Direct Solar Irradiation is also considered (W.m-2). In addition, by enabling the Use Direction Computed from The Solar Calculator option, the solar radiation direction to the model is defined based on the input data to the Solar Calculator.

In general, fluid heat transfer occurs in three categories, including:

- Conduction
- Convection
- Radiation

Radiation heat transfer is heat transfer through electromagnetic waves. Since these waves are transmitted at the speed of light, so the energy transfer rate in this state is also equal to the speed of light. In general, all objects at a given temperature, radiate heat from their surface, known as radiation heat transfer, which rotational and vibrational motions of the molecules and atoms can be said to be the main cause of the radiation. Radiation heat transfer is one of the volumetric phenomena; however, for **opaque** objects such as metals, radiation occurs superficially.

Radiation energy exited from the surface of an environment is obtained by the Stephen Boltzmann relation in which T is the temperature of the surface and the environment, Ԑ is equivalent to the Emissivity coefficient (for black bodies equals 1), and the coefficient σ is 5.67 * 108:

Various radiation heat transfer models are available in Fluent software, including:

- DO
- DRTM
- P1
- S2S
- Rosseland
- MC
- solar ray tracing

### Discrete Ordinates model (DO)

The discrete ordinates model (DO) is used for cases where the radiative heat transfer equations are solved for a discrete number of solid finite angles. Its advantages are that it is the most comprehensive radiation model, the solution accuracy is enhanced by better discretization, a stable method that results in a thermal energy balance for coarse discretization, and use for light scattering, semi-transparent environments, glossy sheets such as mirrors, and wavelength-dependent transmission using the gray environment while resolving it with a wide variety of angles is heavy for CPU, as a limitation of this model.

### Discrete Transfer Radiation Model (DTRM)

The discrete transfer radiation model (DTRM) is used for cases where the radiation emitted from a surface element in continuous and specified intervals of solid angles can be considered as a single ray. Its advantages are that the model is relatively simple, capable of increasing accuracy with the increasing number of rays, and can be applied to a wide range of optical thicknesses, while limitations is that not all pages are scattered, the effects of radiation scattering are not taken into account, and the solution is very heavy for the CPU.

### P1

The P1 model is used for cases where the independence of direction is integrated into the radiative heat transfer equations and thus results in a diffusion equation for random radiations. Its benefits include that the radiation heat transfer equation can be easily solved with low CPU, including the effects of light scattering, such as the effects of particles or droplets of water or soot, and work well in applications such as combustion that have high optical thicknesses; while the limitations are that all plates are scattered, they may have low accuracy in some cases, especially in low-thickness geometries, and it is prone to predicting fluxes from local heat sources or sinks.

### Surface to Surface radiation model (S2S)

The Surface to Surface Radiation Model (S2S) is used for cases where there is no material environment or interference with radiation modeling in the radiation-related situation. Examples of this radiation modeling include solar collector systems, spacecraft back-heating systems, radiant space heaters, and automotive underground cooling systems. This model is also based on the view factor and is suitable for non-interference modes. Its limitations are that the required storage space increases rapidly when the number of pages is increased, assuming that the radiation is gray, all the pages are diffuse, and symmetric or intermittent boundary conditions are not used.

### Solar Ray Tracing

The solar ray-tracing model is called the ray tracing algorithm for thermal energy transfer from the sun, which is compatible with other radiation models and is used only for 3D models. Features of this model also include the solar directional vectors, the solar intensity (in terms of direct radiation and scattered emission), the solar calculator to calculate the direction and intensity of direct radiation using maximum theoretical or equilibrium conditions.

In general, in order to select the best model of radiation heat transfer, the following is done:

- From a computational cost point of view:

P1 is reasonably accurate but low effort.

- From the point of view of solution accuracy:

DO and DTRM are more accurate.

- Optical Thickness point of view:

DTRM and DO Suitable for Thin Optical Thickness (𝛂L≪1) and P1 Suitable for Thick Optical Thickness.

- In terms of dispersion or diffusion:

P1 and DO suitable for diffusion.

- In terms of particle effects:

P1 and DO are suitable for the radiation exchange between gas and fine particles.

- From the viewpoint of local heat sources:

DO and DRTM are good enough with high radiation.

### Theta divisions (NӨ) and Phi divisions (Nφ)

divisions (NӨ) and phi divisions (Nφ): The number of control angles used to break up every eighth of the angular space. In two-dimensional models, there are only four one-eighth zones due to the symmetry lines in two directions, thus a total of 4 * NӨNφ for the vector (with angles of Ө and φ) must be solved; As in 3D models, there are eight eighth-region, so a total of 8 * NӨNφ for the vector (with angles Ө and φ) must be solved. These angles are by default equal to two, but for more complex problems involving specific radiation exchange, more angles are suggested for these angles, which can usually be chosen from three to five. In general, increasing the number of these angles and better discretization will lead to a better resolution of the effects of small geometrical features or strong spatial variables on temperature, but will subsequently increase computational costs.

### Theta pixel and Phi pixel

Theta pixel and Phi pixel: Pixels have bumps on each surface. For gray matter radiation, 1 * 1 pixelation is sufficient; Increasing the number of pixel insertion also results in increased computational cost but has less computational effort than angular segmentation.

### non-gray model

Generally, surfaces whose radiation is independent of the path are called diffuse surfaces, and surfaces whose radiation is independent of wavelength are called gray surfaces. Therefore, in order to simulate non-gray radiation models, it is necessary to define spectra of specific wavelengths (with start and end wavelengths in micrometers). Here, too, increasing the number of optical spectra increases the computational cost.

### Emissivity (Boundary condition)

The proportion of energy emitted by a surface to the energy emitted by a black body (the body most fully absorbing and emitting, or in other words, no object at a given temperature and wavelength can be greater than the black body emits energy) at the same temperature, called the emissivity, which always has a value between zero and one. This diffusion coefficient is used for inlet and outlet boundaries. The rough surfaces also have scattered and random radiative reflections and smooth surfaces such as mirrors have reflective boundary conditions. The semi-transparent boundary condition is used to model objects such as glass boards in the air, and the opaque model is used to model matte walls that behave like gray objects. Then we can determine the diffuse fraction, which is the fraction of the reflective radiation flux in the form of propagation so that when it is equal to 1, all radiation is propagated, and when it is equal to zero, that is poor reflection radiation.

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