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首页> 外文期刊>International Journal of Heat and Mass Transfer >Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate
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Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate

机译：移动垂直板上纳米流体混合对流的双重解

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摘要

This paper deals with the development of a mixed convection flow of nanofluids over a moving vertical plate. The external flow and the stretching velocities are assumed to be constant. It is assumed that the plate moves in the same or opposite direction to the free stream. Using the local similarity method, it has been shown that the dual solutions of velocity and temperature fields exist for certain values of suction/ injection, mixed convection, nanoparticle volume fraction and velocity ratio parameters. The non-linear ordinary differential equations along with the boundary conditions form a two point boundary value problem and are solved using Shooting method, by converting into an initial value problem. The initial value problem for a final set of first order system of ordinary differential equations is solved by fourth-order Runge-Kutta method. Three different types of nanoparticles, namely Copper (Cu), Aluminum Oxide (Al_2O_3), and Titanium Oxide (TiO_2) are considered by using water-based fluid with Prandtl number Pr = 6.2. The effect of the solid volume fraction parameter φ of nanofluids on the heat transfer characteristics is also investigated. The results indicate that dual solutions exist when the plate and the free stream moves in the same as well as in the opposite direction. The effects of various parameters on the velocity and temperature profiles are also presented here.
机译：本文研究了在垂直移动板上纳米流体混合对流的发展。假定外部流动和拉伸速度是恒定的。假定板沿与自由流相同或相反的方向运动。使用局部相似性方法，已经表明，对于一定的吸入/注入，混合对流，纳米颗粒体积分数和速度比参数，存在速度和温度场的双重解。非线性常微分方程与边界条件一起形成两点边界值问题，并通过转换为初始值问题使用Shooting方法进行求解。通过四阶Runge-Kutta方法解决了常微分方程的一阶系统的最终集合的初值问题。通过使用普朗特数Pr = 6.2的水基流体，考虑了三种不同类型的纳米粒子，即铜（Cu），氧化铝（Al_2O_3）和氧化钛（TiO_2）。还研究了纳米流体的固相体积分数参数φ对传热特性的影响。结果表明，当板和自由流在相同方向和相反方向上移动时，存在双重解。此处还介绍了各种参数对速度和温度曲线的影响。

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