浮力驱动流中纳米颗粒输运的Newton-Raphson和Streamlines-Upwind Petrov-Galerkin联合迭代
Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nano-particles transport in buoyancy driven flow
摘要：
本研究涉及的有限元离散化的纳米流体对流输运在一个封闭的可变属性。我们研究的Buongiorno模型，它耦合的纳维-斯托克斯方程的基础流体，对流扩散方程的热传递，和对流占主导地位的纳米粒子分数浓度受热泳和布朗运动力。我们开发了一个迭代的数值方案，结合牛顿的方法（致力于解决的动量和能量方程）的传输方程，管理的纳米粒子浓度在外壳中。我们表明，流逆风彼得罗夫-伽辽金正则化方法需要妥善解决不适定的Buongiorno传输模型作为一个变分问题下的平均值约束。非平凡的数值计算报告显示，我们提出的数值方法的有效性，在其能力，提供合理的良好协议与文献中的实验结果。数值实验表明，在浓度输运方程中只考虑热泳和布朗运动力，模型不能再现由于基液中悬浮纳米颗粒的存在而引起的传热损伤.然而，它揭示了这两个术语在热壁和冷壁附近所起的重要作用。
英文摘要：
The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the Navier-Stokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines Newton's method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that Stream Upwind Petrov-Galerkin regularization approach is required to solve properly the ill-posed Buongiorno transport model being tackled as a variational problem under mean value constraint. Non-trivial numerical computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature. The numerical experiments demonstrate that by accounting for only the thermophoresis and Brownian motion forces in the concentration transport equation, the model is not able to reproduce the heat transfer impairment due to the presence of suspended nanoparticles in the base fluid. It reveals, however, the significant role that these two terms play in the vicinity of the hot and cold walls.
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