Abstract Linear and weakly nonlinear stability analyses of Rayleigh-Benard convection with internal heat generation/absorption in water-based nanoliquids is studied analytically in the paper using the generalized Buongiorno two-phase model. The Boussinesq approximation and small-scale convective motion are assumed to be valid. By considering a minimal-mode Fourier representation, we arrived at an analytically intractable fifth-order, autonomous, generalized Lorenz model. Results on linear stability (direct and pitchfork bifurcations) and subcritical instability (inverse bifurcation) are obtained using the generalized Buongiorno two-phase model. The generalized Lorenz model with quadratic nonlinearities is then reduced to an analytically tractable Ginzburg-Landau equation with cubic nonlinearity. The analytical solution of this equation is used to quantify heat transport in terms of the Nusselt number. The contribution of nanoparticles/nanotubes in advancement of onset of convection and hence in the enhancement of heat transport by water is explained. The results of the enclosure problem are extracted from those of the Rayleigh-Benard convection problem. Tall, square and shallow enclosures are considered in the study by varying aspect ratio. The study reveals that among the three enclosures, tall enclosure transports maximum heat. The influence of heat generation/absorption is shown to augment/inhibit onset of convection and enhance/diminish heat transport. A mechanism of improving heat-removal in water-based cooling systems through the use of nanoparticles/nanotubes is proposed. Several limiting cases of the study are presented.

中文翻译：

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内部发热/吸收对纳米颗粒或碳纳米管分散良好的水中瑞利-贝纳对流的影响

摘要 本文利用广义Buongiorno 两相模型对水基纳米液体中具有内部发热/吸收的Rayleigh-Benard 对流的线性和弱非线性稳定性分析进行了分析研究。假设 Boussinesq 近似和小尺度对流运动是有效的。通过考虑最小模式傅里叶表示，我们得出了一个难以解析的五阶、自治、广义洛伦兹模型。使用广义 Buongiorno 两相模型获得线性稳定性（直接和干草叉分叉）和亚临界不稳定性（逆分叉）的结果。然后将具有二次非线性的广义 Lorenz 模型简化为具有三次非线性的解析上易处理的 Ginzburg-Landau 方程。该方程的解析解用于根据 Nusselt 数量化热传递。解释了纳米颗粒/纳米管在促进对流开始并因此增强水传热方面的贡献。封闭问题的结果是从 Rayleigh-Benard 对流问题的结果中提取的。在研究中通过不同的纵横比考虑了高、方形和浅外壳。研究表明，在三个围栏中，高大的围栏传输的热量最大。热量产生/吸收的影响被证明会增加/抑制对流的发生并增强/减少热传输。提出了一种通过使用纳米颗粒/纳米管改善水基冷却系统散热的机制。介绍了该研究的几个限制性案例。