论文标题
多孔培养基和流体层之间的有效传热：均质化和模拟
Effective Heat Transfer Between a Porous Medium and a Fluid Layer: Homogenization and Simulation
论文作者
论文摘要
我们正在研究在数学均质化的背景下，在涉及多孔培养基和周围流体层的复杂系统中的有效传热。我们区分了两个根本不同的情况：案例（a），其中假定多孔介质的固体部分由断开的包含物和病例（b）组成，其中假定固体基质已连接。对于这两种情况，我们都考虑了一个带有对流的热方程，其中小规模参数Epsilon表征了多孔介质的异质性，并通过两尺度收敛来进行限制过程，用于epsilon-Problems的解决方案。在（a）的情况下，我们达成了一个单个温度的问题，该问题表现出记忆项，如果（b）在两相混合模型下。我们通过有没有对流的几项模拟研究比较和讨论这两个限制模型。
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a), where the solid part of the porous media is assumed to consist of disconnected inclusions and Case (b), where the solid matrix is assumed to be connected. For both scenarios, we consider a heat equation with convection where a small scale parameter epsilon characterizes the heterogeneity of the porous medium and conduct a limit process via two-scale convergence for the solutions of the epsilon-problems. In Case (a), we arrive at a one-temperature problem exhibiting a memory term and, in Case (b), at a two-phase mixture model. We compare and discuss these two limit models with several simulation studies both with and without convection.
