# Computational Fluid Dynamics of Compartent Fires: A Review of Methods and Applications
## 3 CFD Simulation in Compartment Fires
### Physical Models
#### 3.3.4 Heat Transfer: Radiation Transport  
The thermal interaction between fuel, product gases, smoke, ambient air, and the compartment solid boundaries (or any kind of media), is known as heat transfer. Besides the thermal energy movement and the temperature distribution in the compartment, heat transfer is crucial in pyrolysis [7]. One of the heat transfer modes which can affect the combustion and fluid dynamics in the compartment fire is thermal radiation [7; 93; 94]. Although other heat transfer modes, including conduction and convection, have their own level of importance in CFD simulation of compartment fire, radiation is the governing mechanism of heat transfer in fires [38]. Therefore, only numerical modeling of radiative heat transfer is discussed in this study. A sensitivity analysis for heat transfer in compartment fire by [PERSON] et al. [95] indicated that conductivity and emissivity are important factors for thermally thick walls, while for thermally thin walls, emissivity is key. Thermally thick and thermally thin are two definitions in heat transfer science which describe how temperature is distributed across the material thickness when exposed to a heat source: thermally thick shows the significant temperature gradient, while thermally thin has a relatively uniform temperature. [PERSON] et al. [96] illustrated that in the compartments with thermally thin walls, heat loss through walls is the determining factor in fire dynamics inside the compartment, whereas it is the induced pressure (such as the one caused by outside wind) in thermally thick walls. [PERSON] et al. [97] conducted a CFD study investigating the effect of radiation on flamelet calculation in a compartment fire. They found that including radiation in the model can improve the accuracy of soot concentration and temperature prediction. However, the prediction of CO\({}_{2}\), H\({}_{2}\)O, and CO is not very sensitive to radiation model presence. Heat transfer in the form of electromagnetic radiation through a media (fuel, product gases, smoke, soot particles, walls, etc.) is described as the Radiative Transfer Equation (RTE) and it includes the following:  
* Emission--radiation emitted by the media itself;
* Absorption--radiation absorbed by media and reducing the intensity of radiation passing through it;
* Scattering--radiation deflected by particles in the media, changing its direction without being absorbed. In other words, the RTE predicts the effect of how much radiative heat reaches a surface or moves through a fluid based on the material properties and surrounding conditions. Regarding the importance of radiative heat transfer, it should be noted that radiation has a considerable influence on kinetics and flame structure, as it can affect the temperature distribution [97]. [PERSON] and [PERSON] [98] illustrated that radiative heat loss may result in the temperature decreasing by 100 K in laminar flames. According to [PERSON] and [PERSON] [99], quoted by [PERSON] et al. [100], the mathematical definition of the radiation transport equation is defined as Equation (5):  
\[\frac{dI}{dS}=-(k_{\alpha}+k_{sca})I+k_{\alpha}E_{g}+\frac{k_{sca}}{4\pi}\int_ {4\pi}P\big{(}\Omega,\Omega^{\prime}\big{)}I\big{(}\Omega^{\prime}\big{)}d \Omega^{\prime} \tag{5}\]  
where \(\frac{dI}{dS}\) represents the rate of change in radiative intensity I along the path S. It shows how the radiation intensity changes as it moves through the media. \(k_{\alpha}\) is the absorption coefficient, \(k_{sca}\) is the soot scattering coefficient, and \((k_{\alpha}+k_{sca})I\) is the radiation intensity loss due to absorption and scattering in the media. \(k_{\alpha}E_{g}\) is the emission term, where \(E_{g}\) represents the blackbody emissive power at the local temperature of the media (\(E_{g}=\sigma T_{S}^{4},\sigma=5.67\times 10^{-8}\Big{(}\frac{W}{m^{2}K^{4}} \Big{)}\)). The last term describes the scattering term, representing how radiation is redistributed.