The freezing phenomena in supercooled liquid droplets are important for many engineering applications. For instance, a theoretical model of this phenomenon can offer insights for tailoring surface coatings and for achieving icephobicity to reduce ice adhesion and accretion. In this work, a mathematical model and hybrid numerical–analytical solutions are developed for the freezing of a supercooled droplet immersed in a cold air stream, subjected to the three main transport phenomena at the interface between the droplet and the surroundings: convective heat transfer, convective mass transfer and thermal radiation. Error-controlled hybrid solutions are obtained through the extension of the generalized integral transform technique to the transient partial differential formulation of this moving boundary heat transfer problem. The nonlinear boundary condition for the interface temperature is directly accounted for by the choice of a nonlinear eigenfunction expansion base. Also, the nonlinear equation of motion for the freezing front is solved together with the ordinary differential system for the integral transformed temperatures. After comparisons of the solution with previously reported numerical and experimental results, the influence of the related physical parameters on the droplet temperatures and freezing time is critically analysed.

过冷液滴中的冻结现象对于许多工程应用都很重要。例如，这种现象的理论模型可以为定制表面涂层和实现疏冰性以减少冰的粘附和积聚提供见解。在这项工作中，开发了一个数学模型和混合数值分析解决方案，用于冻结浸入冷空气流中的过冷液滴，在液滴与周围环境之间的界面处受到三种主要传输现象：对流热传递，对流传质和热辐射。通过将广义积分变换技术扩展到该移动边界传热问题的瞬态偏微分公式，得到了误差控制的混合解。界面温度的非线性边界条件直接通过选择非线性特征函数展开基来说明。此外，冻结锋的非线性运动方程与积分变换温度的常微分系统一起求解。在将解决方案与先前报道的数值和实验结果进行比较后，对相关物理参数对液滴温度和冻结时间的影响进行了批判性分析。