The paper presents results of the modelling of heat transfer at film boiling of a liquid in a porous medium on a vertical heated wall bordering with the porous medium. Such processes are observed at cooling of high-temperature surfaces of heat pipes, microstructural radiators etc. Heating conditions at the wall were the constant wall temperature or heat flux. The outer boundary of the vapor film was in contact with moving or stationary liquid inside the porous medium. An analytical solution was obtained for the problem of fluid flow and heat transfer using the porous medium model in the Darcy–Brinkman and Darcy–Brinkman–Forchheimer approximation. It was shown that heat transfer at film boiling in a porous medium was less intensive than in the absence of a porous medium (free fluid flow) and further decreased with the decreasing permeability of the porous medium. Significant differences were observed in frames of both models: 20% for small Darcy numbers at Da < 2 for the Darcy–Brinkman model, and 80% for the Darcy–Brinkman–Forchheimer model. In the Darcy–Brinkman model, depending on the interaction conditions at the vapor–liquid interface (no mechanical interaction or stationary fluid), a sharp decrease in heat transfer was observed for the Darcy numbers lower than five. The analytical predictions of heat transfer coefficients qualitatively agreed with the data of Cheng and Verma (Int J Heat Mass Transf 24:1151–1160, 1981) though demonstrated lower values of heat transfer coefficients for the conditions of the constant wall temperature and constant wall heat flux.

中文翻译：

---

多孔介质中薄膜沸腾的 Darcy-Brinkman-Forchheimer 模型

本文介绍了多孔介质中液体在与多孔介质接壤的垂直加热壁上薄膜沸腾时的传热建模结果。在冷却热管、微结构散热器等的高温表面时观察到这种过程。壁处的加热条件是恒定的壁温或热通量。蒸气膜的外边界与多孔介质内部的移动或静止液体接触。使用 Darcy-Brinkman 和 Darcy-Brinkman-Forchheimer 近似中的多孔介质模型获得了流体流动和传热问题的解析解。结果表明，多孔介质中薄膜沸腾时的传热强度低于没有多孔介质（自由流体流动）时的传热，并且随着多孔介质渗透率的降低而进一步降低。在两种模型的框架中都观察到了显着差异：对于 Darcy-Brinkman 模型，Da < 2 的小达西数为 20%，对于 Darcy-Brinkman-Forchheimer 模型为 80%。在达西-布林克曼模型中，根据汽液界面的相互作用条件（无机械相互作用或静止流体），观察到达西数低于 5 时传热急剧下降。传热系数的分析预测定性地与 Cheng 和 Verma 的数据一致（Int J Heat Mass Transf 24:1151–1160，