# Review of Convective Heat Transfer Modelling in CFD Simulations of Fire-Driven Flows
## 5 Applications
### Flame Spread  
The target test case includes the Single Burning Item (SBI) experiments with Medium Density Fiberboard (MDF) reported by [PERSON] et al. [74,75]. The experiments include two flammable walls (i.e., long and short) positioned perpendicular to each other to form a corner (see Figure 5). The widths of the long and short walls are 1 m and 0.5 m, respectively, while their height is 1.5 m. A 30 kW triangular propane (C\({}_{3}\)H\({}_{8}\)) burner is used as fire source having a side dimension of 0.25 m, located at the corner at a distance of 0.04 m from the walls. There is a ramp-up time of 30 s until the peak HRR of the burner is reached. The presented numerical results are reproduced from [12]. The computational domain has a rectangular shape with dimensions of 1 m \(\times\) 2 m \(\times\) 1 m (length \(\times\) height \(\times\) width). A local grid refinement was considered using mesh sizes ranging between 1 cm to 4 cm, focusing on having the smaller grid resolution in locations where burning would occur (see Figure 5). The dynamic Smagorinsky model was used to model turbulence together with a dynamic procedure for the Prandtl number. Chemistry was considered to be infinitely fast and the Eddy Dissipation Model (EDM) (i.e., \(C_{EDM}=2\)) was used for modelling the turbulence-chemistry interactions. The finite volume discrete ordinates model (fvDOM) was used for radiation, neglecting absorption and modelling the emission term through the constant radiative fraction approach. The global radiative fraction, \(\chi_{r}\), in the simulations  
Figure 4: Average convective heat fluxes at the methanol pool surface as a function of grid size with the approach based on (**a**) the effective thermal diffusivity, (**b**) forced convection, (**c**) natural convection and (**d**) the stagnant film theory. Experimental data from [59,60] and simulation results from [PERSON] et al. [67]. varied between \(\chi_{r,\, burner}=0.25\) and \(\chi_{r,\, wall}=0.35\) depending on the mass flow rates of burner and the burning walls. In total, 72 solid angles were used for angular discretization in the solution of the radiative transfer equation (i.e., with radiation solved every 20 th time step). For the thermal decomposition of the solid walls a simplified 1D pyrolysis model was employed which solved conservation equations for mass and energy using a fully implicit scheme. Pyrolysis was modelled using a single-step Arrhenius reaction considering three species: virgin material, char and pyrolysate. More details regarding the modelling as well as the optimised material used for the MDF walls are provided in [12]. The characteristic lengths, \(L_{c}\), for the natural convection modelling approach presented below is chosen as \(L_{c,\, natural}=1.5\) m (i.e., height of walls--see Section 3.1.3). The evolution of the total (i.e., burner plus walls) heat release rate and the convective heat fluxes at sensor S1 (i.e., located on the long wall and positioned 21 cm from the bottom and 5 cm from the corner) as a function of time, with different approaches for modelling convective heat transfer, is presented in Figure 6. Given the uncertainties related to gas phase (i.e., turbulence, combustion, radiation and heat transfer) and solid phase (i.e., pyrolysis) modelling, the predictions using the effective thermal diffusivity are fairly good when compared to the experiments. More specifically, the predicted initial flame growth period, the maximum value of the HRR as well as the burning of the walls during the decay phase are all fairly well predicted. The predictions of the stagnant film theory approach were fair in the initial flame growth period but under-estimated the maximum value of the HRR and over-estimated the burning intensity of the flammable walls in the decay phase. These discrepancies can be potentially linked to the calculation of the convection coefficient which does not consider the local flow properties.