多孔介质中水热对流流动的有限元模型：水力阻力与热扩散率的影响
A Finite Element Model for Hydro-thermal Convective Flow in a Porous Medium: Effects of Hydraulic Resistivity and Thermal Diffusivity
AI总结：
本文提出一种基于达西定律与能量方程耦合的有限元模型，用于模拟多孔介质水热对流，并通过数值实验验证最优收敛性，揭示水力阻力线性变化和热扩散率二次变化可提高传热速率。
摘要：
本文实现了一个有限元模型，用于分析多孔介质中的水热对流流动。该数学模型包含描述不可压缩流体行为的达西定律，并与对流-扩散型能量方程耦合，以刻画多孔介质中的温度分布。当前研究为水热对流流动模型提出了一种高效、稳定且精确的有限元离散格式。由于数值方法的解耦性质和线性特性，所提出的离散 Galerkin 有限元格式的适定性得到保证。计算实验针对一个制造解验证了最优收敛阶。针对水力阻力和热扩散率的变化，获得了若干数值结果。在本研究中，底壁保持恒定的较高热温度，侧向竖直壁面绝热，顶壁保持恒定的冷温度。加热底壁处的传热速率以局部 Nusselt 数给出。水力阻力的线性变化和热扩散率的二次变化均显示传热速率有所提高。
英文摘要：
In this article, a finite element model is implemented to analyze hydro-thermal convective flow in a porous medium. The mathematical model encompasses Darcy's law for incompressible fluid behavior, which is coupled with a convection-diffusion-type energy equation to characterize the temperature in the porous medium. The current investigation presents an efficient, stable, and accurate finite element discretization for the hydro-thermal convective flow model. The well-posedness of the proposed discrete Galerkin finite element formulation is guaranteed due to the decoupling property and the linearity of the numerical method. Computational experiments confirm the optimal convergence rates for a manufactured solution. Several numerical results are obtained for the variations of the hydraulic resistivity and thermal diffusivity. In the present study, the bottom wall is maintained at a constant higher hot temperature while side vertical walls are thermally insulated and the top wall is maintained at a constant cold temperature. Heat transfer rates at the heated bottom wall are presented in terms of local Nusselt number. A linear variation in hydraulic resistivity and a quadratic variation in thermal diffusivity show an increase in the heat transfer rate.
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