In this study, the effects of partitioning a square cavity with both vertical and horizontal porous walls on conjugate natural convection heat transfer are investigated numerically using a non-linear Darcy-Brinkman-Forchheimer model. The primary objective is to establish benchmark solutions and a dataset for validating Computational Fluid Dynamics (CFD) simulations. The governing equations, including mass, Navier-Stokes, and energy, are discretized using a staggered grid system based on the control volume method. To handle porous media, a FORTRAN code is developed based on the non-linear Darcy-Brinkman-Forchheimer model and initially validated against three challenging benchmark cases. These cases involve mixed and natural convection heat transfer in a square porous cavity, with and without a magnetic field. Through comparative analysis with existing data, the accuracy and robustness of the numerical model in capturing complex flow and heat transport phenomena in porous media are confirmed. Subsequently, the validated numerical model is applied to examine conjugate natural convection heat transfer in a square cavity partitioned with both vertical and horizontal porous matrices. In the final stage of the investigation, the influence of a magnetic field on the heat transfer rate within the partitioned enclosure is also explored. The results reveal significant impacts of the Darcy number and porous region orientation on the thermal and hydrodynamic characteristics of the system. Moreover, substantial variations in heat transfer rate and flow intensity within the computational domain are observed with decreasing the Darcy number and increasing Hartman numbers.

中文翻译：

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使用非线性 Darcy-Brinkman-Forchheimer 模型对多孔分隔腔中的流场和温度场进行数值分析


在本研究中，使用非线性 Darcy-Brinkman-Forchheimer 模型对用垂直和水平多孔壁划分方形空腔对共轭自然对流换热的影响进行了数值研究。主要目标是建立基准解决方案和数据集来验证计算流体动力学 (CFD) 模拟。控制方程，包括质量、纳维-斯托克斯和能量，使用基于控制体积法的交错网格系统进行离散化。为了处理多孔介质，基于非线性 Darcy-Brinkman-Forchheimer 模型开发了 FORTRAN 代码，并针对三个具有挑战性的基准案例进行了初步验证。这些案例涉及方形多孔腔中的混合和自然对流换热，有或没有磁场。通过与现有数据的对比分析，证实了数值模型在捕捉多孔介质中复杂流动和传热现象方面的准确性和鲁棒性。随后，应用经过验证的数值模型来检查由垂直和水平多孔基质分隔的方形腔中的共轭自然对流换热。在研究的最后阶段，还探讨了磁场对分区外壳内传热速率的影响。结果揭示了达西数和多孔区域方向对系统的热和流体动力学特性的显着影响。此外，随着达西数的减少和哈特曼数的增加，观察到计算域内传热速率和流动强度的显着变化。