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Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method

谱松弛法研究时变Darcy-Forchheimer 流体的Navier 滑动条件

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Abstract

In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.

摘要

在金属和聚合物薄片的工业应用中, 流动情况非常不稳定, 并且薄片温度由设定的表面温度和 热通量共同决定。此外, 合理选择冷却液对实验结果也十分重要。本研究中, 结合了各种效应(如布 朗效应、热泳效应、Navier 滑动条件和对流边界条件), 对流过不稳定拉伸片表面的Darcy-Forchheimer 流体进行了数值分析。为了求解控制方程, 使用了适当的相似变换, 导出了非线性常微分方程, 并使 用谱松弛法对得到的耦合动量和能量方程进行了数值求解。通过系统的数值求解, 分析了现有模型中 的重要物理参数。发现不稳定参数的存在对速度、温度和浓度场以及相关的热量和质量传输速率具有 显着影响。同时, 增大惯性系数和孔隙率可加快边界处的速度。

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Authors and Affiliations

  1. Department of Mathematics, KNU-Center for Nonlinear Dynamics, Kyungpook National University, Daegu, 41566, Korea

    Younghae Do

  2. Department of Mathematics, K.L.E. Society’s J.T. College, Gadag, 582102, Karnataka, India

    G. K. Ramesh

  3. Department of Mathematics, Malnad College of Engineering, Hassan, 573202, Karnataka, India

    G. S. Roopa

  4. Department of Mathematics, School of Engineering, Presidency University, Bengaluru, 560064, Karnataka, India

    M. Sankar

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  1. Younghae Do
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  2. G. K. Ramesh
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  3. G. S. Roopa
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  4. M. Sankar
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Correspondence to G. K. Ramesh.

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Foundation item

Project(NRF-2016R1A2B4011009) supported by National Research Foundation of Korea; Project(KSTePS/VGST-KFIST(L1)/2017) supported by Vision Group of Science and Technology, Government of Karnataka, India

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Do, Y., Ramesh, G.K., Roopa, G.S. et al. Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method. J. Cent. South Univ. 26, 2000–2010 (2019). https://doi.org/10.1007/s11771-019-4147-y

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  • DOI: https://doi.org/10.1007/s11771-019-4147-y

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