标题： 多孔介质中Darcy-Brinkman流动的分析，考虑粘性耗散和非均匀热边界条件 显示英文标题

标题： Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition

摘要： 本研究探讨了在薄的饱和多孔域内的稳态达西-布林克曼流动，重点研究粘性耗散和温度非均匀边界条件的影响。 采用关于域厚度的渐近技术，我们严格推导出描述流体流动的简化耦合模型。 数学分析基于推导出精确的先验估计并证明了缩放函数的紧性结果。 所得的极限模型包含了粘性耗散和热边界条件的贡献，因此在涉及多孔介质的工程应用中可能具有实用性。 显示英文摘要

摘要： This study investigates the steady-state Darcy-Brinkman flow within a thin, saturated porous domain, focusing on the effects of viscous dissipation and non-homogeneous boundary condition for the temperature. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the simplified coupled model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions. The resulting limit model incorporates contributions of viscous dissipation and thermal boundary conditions and thus could prove useful in the engineering applications involving porous media.