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Flow and natural convection heat transfer characteristics of non-Newtonian nanofluid flow bounded by two infinite vertical flat plates in presence of magnetic field and thermal radiation using Galerkin method

Galerkin 法研究磁场和热辐射作用下的非牛顿纳米流体在垂直平板间的流动和自然对流换热特性

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Abstract

The main goal of this paper is to investigate natural convective heat transfer and flow characteristics of non-Newtonian nanofluid streaming between two infinite vertical flat plates in the presence of magnetic field and thermal radiation. Initially, a similarity transformation is used to convert momentum and energy conservation equations in partial differential forms into non-linear ordinary differential equations (ODE) applying meaningful boundary conditions. In order to obtain the non-linear ODEs analytically, Galerkin method (GM) is employed. Subsequently, the ODEs are also solved by a reliable numerical solution. In order to test the accuracy, precision and reliability of the analytical method, results of the analytical analysis are compared with the numerical results. With respect to the comparisons, fairly good compatibilities with insignificant errors are observed. Eventually, the impacts of effective parameters including magnetic and radiation parameters and nanofluid volume fraction on the velocity, skin friction coefficient and Nusselt number distributions are comprehensively described. Based on the results, it is revealed that with increasing the role of magnetic force, velocity profile, skin friction coefficient and thermal performance descend. Radiation parameter has insignificant influence on velocity profile while it obviously has augmentative and decreasing effects on skin friction and Nusselt number, respectively.

摘要

研究了在磁场和热辐射作用下, 非牛顿纳米流体在两个无限大的垂直平板间流动的自然对流换 热和流动特性。首先, 采用相似变换法, 将偏微分形式的动量和能量守恒方程转化为特殊边界条件下 的非线性常微分方程组。应用Galerkin 方法(GM), 获得非线性常微分方程组的解析解, 并给出了非线 性常微分方程组的数值解。对比分析解析解和数值解, 验证了模型的准确性、精度和可靠性。最后, 综合考虑了磁场、辐射参数和纳米流体体积分数等参数对速度、摩擦阻力系数和 Nusselt 数分布的影 响。结果表明, 随着磁力作用的增大, 速度场、摩擦阻力系数和热性能下降。辐射参数虽然对增强的 速度场影响不大, 但降低了摩擦阻力系和 Nusselt 数的影响。

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Authors and Affiliations

  1. School of Engineering, University of Tehran, Tehran, 1417466191, Iran

    Peyman Maghsoudi

  2. School of Engineering, Iran University of Science and Technology, Tehran, 1684613114, Iran

    Gholamreza Shahriari, Hamed Rasam & Sadegh Sadeghi

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  1. Peyman Maghsoudi
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  2. Gholamreza Shahriari
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  4. Sadegh Sadeghi
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Correspondence to Gholamreza Shahriari.

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Maghsoudi, P., Shahriari, G., Rasam, H. et al. Flow and natural convection heat transfer characteristics of non-Newtonian nanofluid flow bounded by two infinite vertical flat plates in presence of magnetic field and thermal radiation using Galerkin method. J. Cent. South Univ. 26, 1294–1305 (2019). https://doi.org/10.1007/s11771-019-4088-5

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