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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Boundary layer flow of a nanof luid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno's model
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Boundary layer flow of a nanof luid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno's model

机译：使用Buongiorno模型，通过对流边界条件，纳米流体流过可渗透指数收缩表面的边界层流

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Purpose - The purpose of this paper is to numerically solve the problem of steady boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective surface condition. The Buongiorno's mathematical nanofluid model has been used. Design/methodology/approach - Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters, stretching/shrinking parameter λ, suction parameter s, Prandtl number Pr, Lewis number Le, Biot number, the Brownian motion parameter Nb and the thermophoresis parameter Nt, using the bvp4c function from Matlab. The effects of these parameters on the reduced skin friction coefficient, heat transfer from the surface of the sheet, Sherwood number, dimensionless velocity, and temperature and nanoparticles volume fraction distributions are presented in tables and graphs, and are in details discussed. Findings - Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking case (λ ＜ 0). A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible. In addition, it is shown that for a regular fluid (Nb = Nt = 0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications - The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation, negligible radiative heat transfer and a new boundary condition is imposed on nanoparticles and base fluid locally in thermal equilibrium. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Originality/value - The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a nanofluid. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids. The results show that in the presence of suction the dual solutions may exist for the flow of a nanofluid over an exponentially shrinking as well as stretching surface.
机译：目的-本文的目的是从数值上解决纳米流体在对流表面条件下通过可渗透指数收缩表面的稳定边界层流动的问题。已经使用了Buongiorno的数学纳米流体模型。设计/方法/方法-使用适当的相似性转换，基本的偏微分方程被转换为常微分方程。使用bvp4c函数，已针对控制参数的不同值，拉伸/收缩参数λ，吸力参数s，普朗特数Pr，路易斯数Le，比奥数，布朗运动参数Nb和热泳参数Nt数值求解了这些方程式来自Matlab。这些参数对降低的皮肤摩擦系数，从片材表面传热，Sherwood数，无量纲速度，温度和纳米颗粒体积分数分布的影响在表格和图表中给出，并进行了详细讨论。研究结果-获得了减少皮肤摩擦，热传递以及速度和温度曲线的数值结果。结果表明，在收缩情况下（λ＜0）存在对偶解。进行了稳定性分析，以显示上部分支解决方案是稳定的并在物理上可实现，而下部分支解决方案则不稳定，因此在物理上不可行。此外，表明对于常规流体（Nb = Nt = 0），当前数值结果与公开文献中报道的数值之间存在很好的一致性。研究局限/意义-该问题是针对不可压缩的纳米流体而制定的，该纳米流体没有化学反应，稀混合物，可忽略的粘性耗散，可忽略的辐射热传递，并且在热平衡条件下对纳米粒子和基础流体局部施加了新的边界条件。分析表明边界层与板分离。超过转折点，不可能基于边界层近似值获得解。为了获得进一步的解，必须解决全部基本的偏微分方程。原创性/价值-对于通过纳米流体中的收缩片的边界层流动和传热，目前的结果是新颖的。因此，这项研究对于研究相对较新的纳米流体领域的研究人员来说是重要的，以便熟悉此类纳米流体的流动行为和特性。结果表明，在存在吸力的情况下，对于纳米流体在指数收缩和拉伸表面上的流动，可能存在双重溶液。

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