Stability analysis of free convection in a liquid-saturated sparsely-packed porous medium with local-thermal-non-equilibrium (LTNE) effect is presented. For the vertical boundaries free–free, adiabatic and rigid–rigid, adiabatic are considered while for horizontal boundaries it is the stress-free, isothermal and rigid–rigid, isothermal boundary combinations we consider. From the linear theory, it is apparent that there is advanced onset of convection in a shallow enclosure followed by that in square and tall enclosures. Asymptotic analysis of the thermal Rayleigh number for small and large values of the inter-phase heat transfer coefficient is reported. Results of Darcy–Benard convection (DBC) and Rayleigh–Benard convection can be obtained as limiting cases of the study. LTNE effect is prominent in the case of Brinkman–Benard convection compared to that in DBC. Using a multi-scale method and by performing a non-linear stability analysis the Ginzburg–Landau equation is derived from the five-mode Lorenz modal. Heat transport is estimated at the lower plate of the channel. The effect of the Brinkman number, the porous parameter and the inter-phase heat transfer coefficient is to favour delayed onset of convection and thereby enhanced heat transport while the porosity-modified ratio of thermal conductivities shows the opposite effect.

中文翻译：

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具有局部热非平衡效应的液体饱和多孔外壳中的不稳定自然对流

介绍了具有局部热非平衡 (LTNE) 效应的液体饱和稀疏填充多孔介质中自由对流的稳定性分析。对于自由-自由、绝热和刚性-刚性边界的垂直边界，考虑绝热，而对于水平边界，我们考虑无应力、等温和刚性-刚性、等温边界组合。从线性理论来看，很明显，浅外壳中的对流开始提前，其次是方形和高外壳中的对流。报告了对小和大相间传热系数值的热瑞利数的渐近分析。Darcy-Benard 对流 (DBC) 和 Rayleigh-Benard 对流的结果可以作为研究的极限情况获得。与 DBC 相比，Brinkman-Benard 对流的 LTNE 效应更为突出。使用多尺度方法并通过执行非线性稳定性分析，Ginzburg-Landau 方程从五模洛伦兹模态导出。在通道的下板估计热传输。Brinkman 数、多孔参数和相间传热系数的影响有利于延迟对流开始，从而增强传热，而孔隙率修正的热导率则显示出相反的效果。