This paper presents physics-inspired mathematical model to predict the time varying burn rate of unsteady pool fires. The model benefits from the observations on the thermal behaviour and select data from systematically and carefully designed experiments on small and large pool fires of n-heptane and small pool fires of diesel, kerosene and ethanol fuels. All modelling features are based on dimensionless quantities. Amongst the three controlling heat transfer mechanisms, convection is dealt with simply. However, conduction and radiant heat transfer models have needed new considerations. A combination of steady and unsteady conduction along the pan wall affected by the thermal properties of the wall material and liquid phase conduction are modelled and validated against specific experiments. Radiant heat transfer modelling differs from the conventional approach to account for fuel depth-dependent enhancement in burn flux in small pans to values comparable to large pool fires. The radiation view factor invokes mass flux based Reynolds number to account for fuel depth-related effects. Several constants are modelled in terms of dimensionless parameters constructed from a large number of physical variables of the pan and the fuel and used in the model such that they allow the best fits between the simulation and a part of the experimental data. All the sub-models combined into a surface heat flux balance provide the temporal variation of the mass depletion as also the relative magnitudes of the fluxes in a MATLAB code. Comparisons of the predictions on the dependence of the burn behaviour on fuel depth, free board, pan diameter and wall material with the experimental data of the present authors and from literature on n-heptane are set out. Comparisons between the predictions and experimental data on diesel, kerosene and ethanol are also set out to show the ability of the model to track the mass loss history based on fundamental properties of the fuel and the pan. The outstanding-to-good quality of predictions in most cases is attributed to the necessary physics taken into account in the model.

本文提出了受物理启发的数学模型来预测不稳定池火的时变燃烧率。该模型受益于对热行为的观察，并从系统和精心设计的正庚烷小型和大型池火以及柴油、煤油和乙醇燃料的小型池火实验中选择数据。所有建模特征均基于无量纲量。在三种控制传热机制中，对流处理比较简单。然而，传导和辐射传热模型需要新的考虑。对受壁材料的热特性和液相传导影响的沿锅壁的稳态和非稳态传导的组合进行了建模，并针对特定实验进行了验证。辐射传热建模与传统方法不同，该方法将小锅中燃烧通量的燃料深度依赖性增强解释为与大型池火相当的值。辐射视角因子调用基于质量通量的雷诺数来解释与燃料深度相关的影响。几个常数根据由锅和燃料的大量物理变量构成的无量纲参数建模，并在模型中使用，以便它们允许模拟和部分实验数据之间的最佳拟合。结合到表面热通量平衡中的所有子模型提供了质量损耗的时间变化以及 MATLAB 代码中通量的相对大小。对燃烧行为对燃料深度、自由板、盘直径和壁材料与本作者的实验数据和来自关于正庚烷的文献列出。还对柴油、煤油和乙醇的预测和实验数据进行了比较，以显示该模型基于燃料和锅的基本特性跟踪质量损失历史的能力。在大多数情况下，预测的优秀到良好的质量归因于模型中考虑的必要物理特性。